flexural wave propagation in beams with periodically attached vibration absorbers band gap behavior and band formation mechanisms abstract this paper is concerned with flexural wave propagation and vibration transmission in beams with periodically attached vibration absorbers such periodic systems feature unique wave filtering characteristics that can find applications in the control of wave propagation in flexural beam structures the study is performed by using an exact analytical approach based on a combination of the spectral element method and periodic structure theory both infinite and finite periodic structures are considered an explicit expression is provided for the calculation of propagation constants and thus the complex band structures and it is further developed to examine the effects of various system parameters on the band gap behavior including the position width and wave attenuation performance of all the band gaps the band formation mechanisms of such periodic systems are explained via both derivations and physical models yielding explicit equations to enable the prediction of all the band edge frequencies in an exact manner without the need to calculate propagation constants based on these equations explicit formulas are further derived to determine the conditions for the transition and near coupling between local resonance and bragg scattering each being a unique band gap opening mechanism

generalized parametric solutions in stokes flow abstract design optimization and uncertainty quantification among other applications of industrial interest require fast or multiple queries of some parametric model the proper generalized decomposition pgd provides a separable solution a computational vademecum explicitly dependent on the parameters efficiently computed with a greedy algorithm combined with an alternated directions scheme and compactly stored this strategy has been successfully employed in many problems in computational mechanics the application to problems with saddle point structure raises some difficulties requiring further attention this article proposes a pgd formulation of the stokes problem various possibilities of the separated forms of the pgd solutions are discussed and analyzed selecting the more viable option the efficacy of the proposed methodology is demonstrated in numerical examples for both stokes and brinkman models

an inverse method to determine the dispersion curves of periodic structures based on wave superposition abstract phononic crystals and acoustic metamaterials have unique properties such as the existence of band gaps which give them huge potential in many applications such as vibration isolation acoustic cloaking acoustic lensing and more many methods have been proposed to determine the band structure of these materials but almost all require a model of the structure in this paper an inverse method to calculate the band structure of one dimensional periodic structures based on bloch wave boundary conditions and wave superposition is introduced the proposed method only requires the frequency responses measured at a small number of points within the structure this allows the band structures to be determined experimentally using simple equipment like a shaker and accelerometers the band structure of a simple bi material beam was calculated in this study as a demonstration of the method and the results were found to be in agreement with calculations made using the transfer matrix method the proposed method was then extended to predict the response of a finite periodic bi material beam with arbitrary boundary conditions using only the band structure and components of the eigenvectors some resonance peaks were observed within the band gaps and these were found to be caused by the reflection of the waves at the boundaries the effects of the number of unit cells on the transmissibility of a beam were investigated it was found that the transmissibilities within the band gaps can be estimated to be directly proportional to the number of unit cells lastly an attempt was made to extend the method to two and three dimensional periodic structures and the wave superposition method was found to be able to measure a portion of the dispersion surface of two dimensional structures with a fair degree of accuracy especially at lower bands errors and scatter are present at high frequencies caused by more waves significantly affecting the responses of the system this issue can be alleviated by taking measurements further away from the boundaries or increasing the number of waves considered however the key limitation of the method for two and three dimensional periodic structure is that it can only measure a portion of the dispersion surface or volume

vibration transmission through periodic structures using a mobility power flow approach the transmission of vibrational power time averaged through multiple coupled periodic structures is examined the analysis is performed in the frequency domain and the coupling between the sub elements of the periodic structure is expressed in terms of structural mobility functions for the junction points and between the junction points of the sub elements equal length spans between stiffeners or supports of the periodic structure are considered through the use of the mobility power flow approach the influence of sub element and junction parameters including damping at the joints can be investigated the results from the analysis can be in the form of either structural intensity or alternatively structural power content for each of the sub elements the examples discussed are for a thin perfectly periodic beam with a finite number of spans with different types of stiffeners and or supports between the spans the excitation of the structure is by a point load located midway along the first span

randomly flashing diffusion asymptotic properties the theory of abstract markov operators and semigroups is applied for studying asymptotics of a randomly flashing diffusion process the probability distribution of the process is determined by a set of two partial differential equations and sufficient conditions for the existence of a stationary solution of the equations are formulated and convergence of solutions to the stationary solution is proved

on modifications of newton s second law and linear continuum elastodynamics in this paper we suggest a new perspective where newton s second law of motion is replaced by a more general law which is a better approximation for describing the motion of seemingly rigid macroscopic bodies we confirm a finding of willis that the density of a body at a given frequency of oscillation can be anisotropic the relation between the force and the acceleration is non local but causal in time conversely for every response function satisfying these properties and having the appropriate high frequency limit there is a model which realizes that response function in many circumstances the differences between newton s second law and the new law are small but there are circumstances such as in specially designed composite materials where the difference is enormous for bodies which are not seemingly rigid the continuum equations of elastodynamics govern behaviour and also need to be modified the modified versions of these equations presented here are a generalization of the equations proposed by willis to describe elastodynamics in composite materials it is argued that these new sets of equations may apply to all physical materials not just composites the willis equations govern the behaviour of the average displacement field whereas one set of new equations governs the behaviour of the averageweighted displacement field where the weighted displacement field may attach zero weight to hidden areas in the material where the displacement may be unobservable or not defined from knowledge of the average weighted displacement field one obtains an approximate formula for the ensemble averaged energy density two other sets of new equations govern the behaviour when the microstructure has microinertia i e where there are internal spinning masses below the chosen scale of continuum modelling in the first set the average displacement field is assumed to be observable while in the second set an average weighted displacement field is assumed to be observable

dynamics of kolmogorov systems of competitive type under the telegraph noise abstract this paper studies the dynamics of kolmogorov systems of competitive type under the telegraph noise the telegraph noise switches at random two kolmogorov competition type deterministic models the aim of this work is to describe the omega limit set of the system and investigates properties of stationary density

wave propagation in three coupled periodic structures free wave propagation patterns for general three coupled periodic structures are investigated by means of the transfer matrix approach it is shown that an exhaustive description of the propagation domains requires spaces that are stratified in homogeneous regions whose dimension is given by the number of invariants of the transfer matrix characteristic equation and whose boundaries are represented by codimension one manifolds three types of three coupled periodic mechanical models characterized by constitutive elastic and or inertial coupling between mono and bi coupled dynamics namely pipes thin walled beams and truss beams are considered from the design standpoint an adequate representation of the propagation domains pattern is obtained through a nonlinear mapping from the space of the invariants to the physical parameters plane the analyzed models give rise to equations of motion where the three coupled nature stems from the coupling between transversal bi coupled and longitudinal mono coupled dynamics for the pipes and truss beams whilst coupling occurs between transversal and torsional mono coupled dynamics when it comes to the thin walled beams a mechanical interpretation associated with the bounding frequencies of the propagation regions is given and the evolution of the propagation properties when coupling parameters tend to vanish is discussed

finite element solution of the helmholtz equation with high wave number part i the h version of the fem abstract the paper addresses the properties of finite element solutions for the helmholtz equation the h version of the finite element method with piecewise linear approximation is applied to a one dimensional model problem new results are shown on stability and error estimation of the discrete model in all propositions assumptions are made on the magnitude of hk only where k is the wavelength and h is the stepwidth of the fe mesh previous analytical results had been shown with the assumption that k 2 h is small for medium and high wavenumber these results do not cover the meshsizes that are applied in practical applications the main estimate reveals that the error in h 1 norm of discrete solutions for the helmholtz equation is polluted when k 2 h is not small the error is then not quasioptimal i e the relation of the fe error to the error of best approximation generally depends on the wavenumber k it is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution in the result of this analysis thorough and rigorous understanding of error behavior throughout the range of convergence is gained numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior the h p version of the fem is studied in part ii

certified reduced basis method for electromagnetic scattering and radar cross section estimation we study nontrivial applications of the reduced basis method rbm for electromagnetic applications with an emphasis on scattering and the estimation of radar cross section rcs the method and several extensions are explained with two examples with different characteristics parameters that are allowed to vary within the model include frequency incident angle and measurement angle as well as the geometry of the scatterers with appropriate applications of the empirical interpolation method eim transformation of the domain configuration of perfectly matched layer exponential convergence of the reduced basis solution over the entire parameter domain is achieved moreover we demonstrate that this approach allows for the effective capture of the critical behavior in this case through shapes that minimize scattering this further highlights the robustness and quality of the greedy approximation and the reduced basis method approach

analysis of in plane wave propagation in periodic structures with sierpinski carpet unit cells abstract in this study the dispersion relationships and characteristics of directional periodic structure waveguides with sierpinski carpet unit cells were investigated finite element method was used to analyze the sierpinski carpet periodic structures with square pb cylinders inserted in the rubber background the dispersion curves of unit cells with different stages were investigated first then group velocities of periodic structures at given frequencies were calculated and used to analyze the directional waveguide characteristics in the sierpinski carpet periodic structures the dynamic responses of finite periodic structures were investigated to observe the directional features and the results were used to support the fact that sierpinski carpet unit cells with different stages can control the propagation behavior of elastic waves in specific ways the dispersion curves grew compressed as the stage increased multiple band characteristics were observed in the case of the second stage fractal configuration the directional propagation characteristics in sierpinski carpet periodic structures can be utilized to further extend the range of vibration reduction zones the results of this study have significant potential in terms of the application of sierpinski carpet periodic structures for vibration isolation

jump control of probability densities with applications to autonomous vehicle motion we investigate the problem of controlling the probability density of the state of a process that is observed by the controller via a fixed but unknown scalar non negative function of the state the goal is to control the process so that its probability density at a point in the state space becomes proportional to the value of the function observed at that point our solution inspired by bacterial chemotaxis involves a randomized controller that switches among different deterministic modes we show that under appropriate existence conditions this controller guarantees convergence of the probability density to the desired function the results can be applied to the problem of in loco optimization of a measurable signal using a team of autonomous vehicles that measure the signal but do not have access to position measurements alternative applications in the area of mobile robotics include deployment and environmental monitoring

a wavelet based model of one dimensional periodic structure for wave propagation analysis in this paper a wavelet based method is developed for wave propagation analysis of a generic multi coupled one dimensional periodic structure ps the formulation is based on the periodicity condition and uses the dynamic stiffness matrix of the periodic cell obtained from finite element fe or other numerical methods here unlike its conventional definition the dynamic stiffness matrix is obtained in the wavelet domain through a daubechies wavelet transform the proposed numerical scheme enables both time and frequency domain analysis of pss under arbitrary loading conditions this is in contrast to the existing fourier transform based analysis that is restricted to frequencydomain study here the dispersion characteristics of pss especially the band gap features are studied in addition the method is implemented to simulate time domain wave response under impulse loading conditions the two examples considered are periodically simply supported beam and periodic frame structures in all cases the responses obtained using the present periodic formulation are compared with the response simulated using the fe model without the periodicity assumption and they show an exact match this validates the accuracy of the periodic assumption to obtain the timeand frequency domain wave responses up to a high frequency range apart from this the proposed method drastically reduces the computational cost and can be implemented for homogenization of pss

free vibration of an orthogonally stiffened flat plate abstract a flat plate reinforced by a regular orthogonal array of uniform beams is analyzed by using techniques developed for studying wave propagation in two dimensional periodic structures a plane wave type of motion is considered which may be characterized by different propagation phase constants in the x and y directions the hierarchical finite element method is used to set up the governing equations of free wave motion and these are then solved as an eigenvalue problem for the frequencies at which particular waves will propagate plots of phase constant surfaces vs frequency are presented for a number of different plate beam configurations excellent agreement is found between some of these and the results of earlier investigators when the plate is supported by flexible beams in both directions wave propagation is found to commerce at zero frequency at higher frequencies alternating and overlapping attenuation and propagation bands occur the nature and explanations of these are discussed wave speed surfaces vs frequency are also presented and these give insight into the critical coincidence frequencies of the plate under acoustic excitation

invariant representation of propagation properties for bi coupled periodic structures general bi coupled periodic systems are dealt with by means of transfer matrices of single units the solutions of the associated characteristic equation are discussed in terms of invariant quantities by exploiting the well known reversibility of its coefficients an exhaustive description of the free wave propagation patterns is given on the invariant plane where propagation domains with qualitatively different character are identified the asymptotic behavior of the roots of the characteristic equation when the invariants tend to infinity is analyzed the contour plot of the real part of the propagation constants responsible for the amount of attenuation of the characteristic waves is illustrated on the invariants plane next several models of bi coupled periodic structures made up of beams resting on elastic supports are considered a non linear mapping from the invariants plane to the physical parameters plane provides a concise representation of the pattern of the propagation domains a mechanical interpretation associated with the boundaries of these regions is given finally the proper selection of the physical parameters governing the propagation modes is discussed

a double expansion method for the frequency response of finite length beams with periodic parameters abstract a double expansion method for the frequency response of finite length beams with periodic distribution parameters is proposed the vibration response of the beam with spatial periodic parameters under harmonic excitations is studied the frequency response of the periodic beam is the function of parametric period and then can be expressed by the series with the product of periodic and non periodic functions the procedure of the double expansion method includes the following two main steps first the frequency response function and periodic parameters are expanded by using identical periodic functions based on the extension of the floquet bloch theorem and the period parametric differential equation for the frequency response is converted into a series of linear differential equations with constant coefficients second the solutions to the linear differential equations are expanded by using modal functions which satisfy the boundary conditions and the linear differential equations are converted into algebraic equations according to the galerkin method the expansion coefficients are obtained by solving the algebraic equations and then the frequency response function is finally determined the proposed double expansion method can uncouple the effects of the periodic expansion and modal expansion so that the expansion terms are determined respectively the modal number considered in the second expansion can be reduced remarkably in comparison with the direct expansion method the proposed double expansion method can be extended and applied to the other structures with periodic distribution parameters for dynamics analysis numerical results on the frequency response of the finite length periodic beam with various parametric wave numbers and wave amplitude ratios are given to illustrate the effective application of the proposed method and the new frequency response characteristics including the parameter excited modal resonance doubling peak frequency response and remarkable reduction of the maximum frequency response for certain parametric wave number and wave amplitude the results have the potential application to structural vibration control

a priori model reduction through proper generalized decomposition for solving time dependent partial differential equations over the past years model reduction techniques have become a necessary path for the reduction of computational requirements in the numerical simulation of complex models a family of a priori model reduction techniques called proper generalized decomposition pgd methods are receiving a growing interest these methods rely on the a priori construction of separated variables representations of the solution of models defined in tensor product spaces they can be interpreted as generalizations of proper orthogonal decomposition pod for the a priori construction of such separated representations in this paper we introduce and study different definitions of pgd for the solution of time dependent partial differential equations we review classical definitions of pgd based on galerkin or minimal residual formulations and we propose and discuss several improvements for these classical definitions we give an interpretation of optimal decompositions as the solution of pseudo eigenproblems we also introduce a new definition of pgd called minimax pgd which can be interpreted as a petrov galerkin model reduction technique where test and trial reduced basis functions are related by an adjoint problem this new definition improves convergence properties of separated representations with respect to a chosen metric it coincides with a classical pod for degenerate time dependent partial differential equations for the numerical construction of each pgd we propose algorithms inspired from the solution of eigenproblems several numerical examples illustrate and compare the different definitions of pgd on transient advection diffusion reaction equations

existence of stationary distributions for kolmogorov systems of competitive type under telegraph noise abstract this work focuses on population dynamics of two species described by kolmogorov systems of competitive type under telegraph noise that is formulated as a continuous time markov chain with two states our main effort is on establishing the existence of an invariant or a stationary probability measure in addition the convergence in total variation of the instantaneous measure to the stationary measure is demonstrated under suitable conditions moreover the limit set of a model in which each species is dominant in a state of the telegraph noise is examined in detail

finite element prediction of wave motion in structural waveguides a method is presented by which the wavenumbers for a one dimensional waveguide can be predicted from a finite element fe model the method involves postprocessing a conventional but low order fe model the mass and stiffness matrices of which are typically found using a conventional fe package this is in contrast to the most popular previous waveguide fe approach sometimes termed the spectral finite element approach which requires new spectral element matrices to be developed in the approach described here a section of the waveguide is modeled using conventional fe software and the dynamic stiffness matrix formed a periodicity condition is applied the wavenumbers following from the eigensolution of the resulting transfer matrix the method is described estimation of wavenumbers energy and group velocity discussed and numerical examples presented these concern wave propagation in a beam and a simply supported plate strip for which analytical solutions exist and the more complex case of a viscoelastic laminate which involves postprocessing an ansys fe model the method is seen to yield accurate results for the wavenumbers and group velocities of both propagating and evanescent waves

feller processes on nonlocally compact spaces we consider feller processes on a complete separable metric space x satisfying the ergodic condition of the form lim sup n 1 n n i 1 p i x o 0 for some x x where o is an arbitrary open neighborhood of some point z e x and p is a transition function it is shown that e chains which satisfy the above condition admit an invariant probability measure some results on the stability of such processes are also presented

finite element analysis of the vibrations of waveguides and periodic structures many structural components can be regarded as waveguides they are uniform in one direction so that the cross section of the waveguide has the same physical and geometric properties at all points along the axis of the waveguide in this paper a method is presented to calculate the forced response of such a structure using a combination of wave and finite element fe approaches the method involves post processing a conventional but low order fe model in which the mass and stiffness matrices are typically found using a conventional fe package a section of the waveguide is meshed and the eigenvalues and eigenvectors of the resulting transfer matrix found the eigenvectors form a set of basis functions for the analysis of the structure as a whole allowing the global dynamic stiffness matrix to be built easily and then the forced response to be calculated very efficiently the main advantage of the approach over the alternative waveguide fe approach often termed the spectral fe method is that conventional fe packages can be used to form the stiffness and mass matrices so that structures with complex geometries or material distributions can be analysed with relative ease to demonstrate the efficacy of the method examples of the forced response for a finite beam and plate strip are presented

the latin multiscale computational method and the proper generalized decomposition this paper deals with the synergy between the latin multiscale method and what is called the proper generalized decomposition pgd which is the key of its performances

dispersive elastodynamics of 1d banded materials and structures analysis abstract the elastodynamics of 1d periodic materials and finite structures comprising these materials are studied with particular emphasis on correlating their frequency dependent characteristics and on elucidating their pass band and stop band behaviors dispersion relations are derived for periodic materials and are employed in a novel manner for computing both pass band and stop band complex mode shapes through simulations of harmonically induced wave motion within a finite number of unit cells conformity of the frequency band structure between infinite and finite periodic systems is shown in particular only one or two unit cells of a periodic material could be sufficient for frequency bandedness to carry over from the infinite periodic case and only three to four unit cells are necessary for the decay in normalized transmission within a stop band to practically saturate with an increase in the number of cells dominant speeds in the scattered wave field within the same finite set of unit cells are observed to match those of phase and group velocities of the infinite periodic material within the most active pass band dynamic response due to impulse excitation also is shown to capture the infinite periodic material dynamical characteristics finally steady state vibration analyses are conducted on a finite fully periodic structure revealing a conformity in the natural frequency spread to the frequency band layout of the infinite periodic material the steady state forced response is observed to exhibit mode localization patterns that resemble those of the infinite periodic medium and it is shown that the maximum localized response under stop band conditions could be significantly less than in an equivalent homogenous structure and the converse is true for pass band conditions

proper generalized decomposition of time multiscale models summary models encountered in computational mechanics could involve many time scales when these time scales cannot be separated one must solve the evolution model in the entire time interval by using the finest time step that the model implies in some cases the solution procedure becomes cumbersome because of the extremely large number of time steps needed for integrating the evolution model in the whole time interval in this paper we considered an alternative approach that lies in separating the time axis one dimensional in nature in a multidimensional time space then for circumventing the resulting curse of dimensionality the proper generalized decomposition was applied allowing a fast solution with significant computing time savings with respect to a standard incremental integration copyright 2011 john wiley sons ltd

parametric solutions involving geometry a step towards efficient shape optimization abstract optimization of manufacturing processes or structures involves the optimal choice of many parameters process parameters material parameters or geometrical parameters usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model then an appropriate cost function is evaluated and its optimality checked while the optimum is not reached the process parameters should be updated by using an appropriate optimization procedure and then the model must be solved again for the updated process parameters thus a direct numerical solution is needed for each choice of the process parameters with the subsequent impact on the computing time in this work we focus on shape optimization that involves the appropriate choice of some parameters defining the problem geometry the main objective of this work is to describe an original approach for computing an off line parametric solution that is a solution able to include information for different parameter values and also allowing to compute readily the sensitivities the curse of dimensionality is circumvented by invoking the proper generalized decomposition pgd introduced in former works which is applied here to compute geometrically parametrized solutions

finite element solution of the helmholtz equation with high wave number part ii the h p version of the fem in this paper which is part ii in a series of two the investigation of the galerkin finite element solution to the helmholtz equation is continued while part i contained results on the h version with piecewise linear approximation the present part deals with approximation spaces of order p ge 1 as in part i the results are presented on a one dimensional model problem with dirichlet robin boundary conditions in particular there are proven stability estimates both with respect to data of higher regularity and data that is bounded in lower norms the estimates are shown both for the continuous and the discrete spaces under consideration further there is proven a result on the phase difference between the exact and the galerkin finite element solutions for arbitrary p that had been previously conjectured from numerical experiments these results and further preparatory statements are then employed to show error estimates for the galerkin finite element method fem it becomes evident that the error estimate for higher approximation can with certain assumptions on the data be written in the same form as the piecewise linear case namely as the sum of the error of best approximation plus a pollution term that is of the order of the phase difference the paper is concluded with a numerical evaluation

resonant frequency primitive waveforms and star waves in lattices for square and triangular lattices we have found a new line localized primitive waveform lpw existing at a resonant frequency in two dimensional 2d case the lpw represents a line of oscillating particles while the lattice outside this line remains at rest we show that a a single lpw does not conduct energy however a band consisting of two or more neighboring lpws is a conductor with the phase shift dependent energy flux velocity b any canonical sinusoidal wave consists of lpws in turn the lpw can be represented by a superposition of the sinusoidal waves these two types of waves are connected by the discrete fourier transform c there are two three lpw orientations for the square triangular lattice and this is why the sinusoidal wave group velocity orientation is piecewise constant at this frequency it coincides with the nearest lpw orientation d lpw can also exist at a lower frequency being localized at the lattice halfplane boundary further for 3d lattices plane localized waveforms are found to exist in a frequency region finally for the point harmonic excitation of 2d lattices we show that starlike waves develop with the rays in the lpw directions

perfectly matched transmission problem with absorbing layers application to anisotropic acoustics in convex polygonal domains this paper presents an original approach to design perfectly matched layers pml for anisotropic scalar wave equations this approach is based first on the introduction of a modified wave equation and second on the formulation of general perfectly matched transmission conditions for this equation the stability of the transmission problem is discussed by way of the adaptation of a high frequency stability necessary condition and we apply our approach to construct pml suited for any convex domain with straight boundaries a new variational formulation of the problem including a lagrange multiplier at the interface between the physical and the absorbing domains is then set and numerical results are presented in 2d and 3d these results show the efficiency of our approach when using constant damping coefficients combined with high order elements

wave propagation in continuous periodic structures research contributions from southampton 1964 1995 abstract after brief reference to some early studies by other investigators this paper focuses mainly on methods developed at the university of southampton since 1964 to analyze and predict the free and forced wave motion in continuous periodic engineering structures beginning with receptance methods which have been applied to periodic beams and rib skin structures it continues with a method of direct solution of the wave equation this uses floquet s principle and has been applied to beams and quasi one dimensional periodic plates and cylindrical shells sample curves of the propagation and attenuation constants pertaining to these structures are presented a limited discussion of the transfer matrix then follows after which the method of space harmonics is introduced as the method best suited to the prediction of sound radiated from a vibrating periodic structure reviewed next are some theorems and variational principles relating to periodic structures which have been developed at southampton and which form a basis for finding natural frequencies of finite structures or for computing free and forced wave notion by energy methods this has led to the finite element method in its standard and hierarchical forms being used to study wave motion in genuine two dimensional and three dimensional structures examples of this work are shown the method of phased array receptance functions is then introduced as possibly the easiest way of setting up exact equations for the propagation constants of uniform quasi one dimensional periodic structures a summary is finally presented of the limited and early work performed at southampton on simple disordered periodic structures

a galerkin least squares finite element method for the two dimensional helmholtz equation in this paper a galerkin least squares gls finite element method in which residuals in least squares form are added to the standard galerkin variational equation is developed to solve the helmholtz equation in two dimensions an important feature of gls methods is the introduction of a local mesh parameter that may be designed to provide accurate solutions with relatively coarse meshes previous work has accomplished this for the one dimensional helmholtz equation using dispersion analysis in this paper the selection of the gls mesh parameter for two dimensions is considered and leads to elements that exhibit improved phase accuracy for any given direction of wave propagation an optimal gls mesh parameter is determined using two dimensional fourier analysis in general problems the direction of wave propagation will not be known a priori in this case an optimal gls parameter is found which reduces phase error for all possible wave vector orientations over elements the optimal gls parameters are derived for both consistent and lumped mass approximations several numerical examples are given and the results compared with those obtained from the galerkin method the extension of gls to higher order quadratic interpolations is also presented

wave propagation in two dimensional periodic lattices plane wave propagation in infinite two dimensional periodic lattices is investigated using floquet bloch principles frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies hexagonal honeycomb kagome lattice triangular honeycomb and the square honeycomb these topologies exhibit dramatic differences in their long wavelength deformation properties long wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices the slenderness ratio of the constituent beams of the lattice or relative density has a significant influence on the band structure the techniques developed in this work can be used to design lattices with a desired band structure the observed spatial filtering effects due to anisotropy at high frequencies short wavelengths of wave propagation are consistent with the lattice symmetries

free vibrations of a mono coupled periodic system abstract vibration problems of periodic systems can be analyzed efficiently by means of the transfer matrix method the frequency equation for the whole system is shown to be obtained in terms of the eigenvalues or their natural logarithms which are often called propagation constants of the transfer matrix for a single periodic subsystem in case of a mono coupled system this frequency equation may be solved graphically by using the propagation constant curve thereby saving a great deal of computational effort two types of mono coupled systems are considered as numerical examples a spring mass oscillating system and a continuous timoshenko beam resting on regularly spaced knife edge supports depending on whether the transfer matrix is derived by an analytical procedure or by the finite element method the numerical solutions become either exact or approximate

asymptotic behavior of distributions of mrna and protein levels in a model of stochastic gene expression abstract the paper is devoted to a stochastic process introduced in the recent paper by lipniacki et al t lipniacki p paszek a marciniak czochra a r brasier m kimmel transcriptional stochasticity in gene expression j theor biol 238 2006 348 367 in modelling gene expression in eukaryotes starting from the full generator of the process we show that its distributions satisfy a fokker planck type system of partial differential equations then we construct a c 0 markov semigroup in l 1 space corresponding to this system the main result of the paper is asymptotic stability of the involved semigroup in the set of densities

tensor decompositions and applications this survey provides an overview of higher order tensor decompositions their applications and available software a tensor is a multidimensional or n way array decompositions of higher order tensors i e n way arrays with n geq 3 have applications in psycho metrics chemometrics signal processing numerical linear algebra computer vision numerical analysis data mining neuroscience graph analysis and elsewhere two particular tensor decompositions can be considered to be higher order extensions of the matrix singular value decomposition candecomp parafac cp decomposes a tensor as a sum of rank one tensors and the tucker decomposition is a higher order form of principal component analysis there are many other tensor decompositions including indscal parafac2 candelinc dedicom and paratuck2 as well as nonnegative variants of all of the above the n way toolbox tensor toolbox and multilinear engine are examples of software packages for working with tensors

free vibrations of finite periodic structures in pass and stop bands of the counterpart infinite waveguides abstract the existence of frequency stop bands in which transmission of the vibro acoustic energy is impossible suggests that the periodic structures may be used for vibro isolation in any technical application however only a finite segment of such a structure can be used this paper is concerned with comparison of the eigenfrequency spectra of finite periodic structures with location of stop bands for their infinite counterparts a hierarchy of four mathematical models is considered in each case special attention is paid to eigenfrequencies and eigenmodes of a single periodicity cell with appropriate boundary conditions the influence of the amount of periodicity cells in a finite compound structure on its eigenfrequency spectrum is analyzed several features common for the considered models are found and discussed in the context of the existing knowledge on the subject

band gap green s functions and localized oscillations we consider some typical continuous and discrete models of structures possessing band gaps and analyse the localized oscillation modes general considerations show that such modes can exist at any

analysis of in plane wave propagation in hexagonal and re entrant lattices plane wave propagation in hexagonal and re entrant lattices is investigated through the application of bloch s theorem two dimensional dispersion relations are estimated and analyzed to illustrate peculiar properties of re entrant configurations and investigate the directional behavior of hexagonal lattices for varying construction angles special attention is devoted to the determination of phase and group wave velocities velocity plots are obtained for varying frequency and direction of wave propagation to analyze the dispersion characteristics of the lattices and further investigate their directional characteristics

a new method of analyzing wave propagation in periodic structures applications to periodic timoshenko beams and stiffened plates a response function is found for an infinite uniform one dimensional structure which is subjected to an array of harmonic forces or moments spaced equidistantly and which have a constant phase or ratio between any adjacent pair receptance functions are derived for these phased arrays they are used to set up a general determinantal equation for the propagation constants of the infinite structure when it is made periodic by the addition of an infinite set of regular constraints they are also used to set up equations for the response of the structure to a convected harmonic pressure field the method enables the equations for the propagation constants and for the response to convected loading to be set up with much greater facility than by earlier methods it only requires a knowledge of the response function of the infinite uninterrupted structure under a single point harmonic force or moment the general equation for the propagation constants is used to study a a simply supported periodic timoshenko beam and b a parallel plate with periodic beam type stiffeners some calculated propagation constants are presented and discussed the periodic plate results are relevant to integrally stiffened skins of the type used in aeroplanes

a generalized finite element method for solving the helmholtz equation in two dimensions with minimal pollution when using the galerkin fem for solving the helmholtz equation in two dimensions the error of the corresponding solution differs substantially from the error of the best approximation and this effect increases with higher wave number k in this paper we will design a generalized finite element method gfem for the helmholtz equation such that the pollution effect is minimal

interpolation method for adapting reduced order models and application to aeroelasticity reduced order models are usually thought of as computationally inexpensive mathematical representations that offer the potential for near real time analysis although most reduced order models can operate in near real time their construction can be computationally expensive as it requires accumulating a large number of system responses to input excitations furthermore reduced order models usually lack robustness with respect to parameter changes and therefore must often be rebuilt for each parameter variation together these two issues underline the need for a fast and robust method for adapting precomputed reduced order models to new sets of physical or modeling parameters to this effect this paper presents an interpolation method based on the grassmann manifold and its tangent space at a point that is applicable to structural aerodynamic aeroelastic and many other reduced order models based on projection schemes this method is illustrated here with the adaptation of computational fluid dynamics based aeroelastic reduced order models of complete fighter configurations to new values of the freestream mach number good correlations with results obtained from direct reduced order model reconstruction high fidelity nonlinear and linear simulations are reported thereby highlighting the potential of the proposed reduced order model adaptation method for near real time aeroelastic predictions using precomputed reduced order model databases

multiscale model reduction for fluid infiltration simulation through dual continuum porous media with localized uncertainties abstract here we present some reduced basis rb methods for fluid infiltration problems through certain porous media modeled as dual continuum with localized uncertainties we apply dimension reduction techniques to construct a reduced order model in the rb methods to perform the offline online computation decomposition the model inputs need to be affinely dependent on the uncertainties we develop a proper orthogonal decomposition and greedy pod greedy rb method for stochastic dual continuum models in the pod greedy rb framework for heterogeneous porous media we need to solve the stochastic dual continuum models many times using very fine grid to construct a set of snapshots for building optimal reduced basis this offline computation may be very expensive to improve the offline computational efficiency we further develop a local global rb method which integrates the coupled multiscale and multicontinuum approach using generalized multiscale finite element method gmsfem to the pod greedy rb method to illustrate the efficiency of the proposed methods we present two numerical examples for stochastic dual continuum models our numerical results show that both the pod greedy rb method and the local global rb method greatly improve the computation efficiency with high approximation accuracy

a few new facts about infinite elements we discuss the conjugated bubnov galerkin and petrov galerkin infinite element ie discretizations to helmholtz equation including the use of elements of locally variable order optimal choice of ie shape functions calculation of echo area ea and automatic hp adaptivity the discussion is illustrated with 2d numerical experiments

existence of invariant densities for semiflows with jumps abstract the problem of existence and uniqueness of absolutely continuous invariant measures for a class of piecewise deterministic markov processes is investigated using the theory of substochastic semigroups obtained through the kato voigt perturbation theorem on the l 1 space we provide a new criterion for the existence of a strictly positive and unique invariant density for such processes the long time qualitative behavior of the corresponding semigroups is also considered to illustrate our general results we give a detailed study of a two dimensional model of gene expression with bursting

simplified analytical models for transient uniaxial waves in a layered periodic stack abstract a physical understanding is gained of some results acquired in the analysis of transient propagation of uniaxial elastic waves in weakly coupled periodic stacks using simple analytical models three simplified models are examined a mass spring chain a single mass spring attached to a delayed moving base and high frequencies of an elastic mass reacted upon by a spring closed form expressions and asymptotic behavior are obtained for attenuation of maximum stress characteristic velocities internal stress distribution and transmission or suppression of highfrequency oscillations the results provide insights in the design of impact resistant structural systems using layered periodic stacks

an exact modal analysis approach to vibration analysis of structures with mass spring subsystems and rotational joints abstract a novel exact modal analysis approach is presented for vibration analysis of plane continuous structures which are coupled with discrete mass spring subsystems and include elastic rotational joints modelling local flexibility using the theory of generalised functions to handle the discontinuities of the response variables every continuous member with any number of mass spring subsystems and joints is treated as a two node element for which a 6 6 exact dynamic stiffness matrix is obtained in closed form as a result the global dynamic stiffness matrix is built by a standard finite element assembling procedure with size depending only on the number of nonzero nodal degrees of freedom of member to member nodes upon deriving pertinent orthogonality conditions for the modes the system response under arbitrary loads is obtained by modal impulse and modal frequency response functions under the assumption of proportional damping the solutions are exact and can be used as benchmark for classical finite element solutions the approach is formulated for various mass spring subsystems acting in transverse and axial directions relative to every member

stability of markov semigroups and applications to parabolic systems abstract a new theorem for asymptotic stability of markov semigroups is proved this result is applied to semigroups generated by parabolic systems describing the evolution of densities of two state diffusion processes

recent advances on the use of separated representations separated representations based on finite sum decompositions constitute an appealing strategy for reducing the computer resources and the calculation costs by reducing drastically the number of degrees of freedom that the functional approximations involve the number of degrees of freedom scale linearly with the dimension of the space in which the model is defined instead of the exponential growing characteristic of mesh based discretization strategies in our knowledge the use of separated representations is the only possibility for circumventing the terrific curse of dimensionality related to some highly multidimensional models involving hundreds of dimensions as we proved in some of our former works its application is not restricted to multidimensional models obviously separated representation can also be applied in standard 2d or 3d models allowing for high resolution computations because its early life numerous issues persist many of them attracting the curiosity of many research groups within the computational mechanics community in this paper we are focusing in two issues never until now addressed i the imposition of non homogenous essential boundary conditions and ii the consideration of complex geometries copyright 2009 john wiley sons ltd

a generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations we propose a new robust technique for solving stochastic partial differential equations the solution is approximated by a series of terms each of which being the product of a scalar stochastic function by a deterministic function none of these functions are fixed a priori but determined by solving a problem which can be interpreted as an extended eigenvalue problem this technique generalizes the classical spectral decomposition namely the karhunen loeve expansion ad hoc iterative techniques to build the approximation inspired by the power method for classical eigenproblems then transform the problem into the resolution of a few uncoupled deterministic problems and stochastic equations this method drastically reduces the calculation costs and memory requirements of classical resolution techniques used in the context of galerkin stochastic finite element methods finally this technique is particularly suitable to non linear and evolution problems since it enables the construction of a relevant reduced basis of deterministic functions which can be efficiently reused for subsequent resolutions

the response of two dimensional periodic structures to point harmonic forcing abstract this analysis is concerned with the response of an infinite two dimensional periodic structure to point harmonic loading initially a damped finite system is considered and the system size is then allowed to tend to infinity it is shown that the response in the far field can be expressed in terms of the properties of the phase constant surfaces which arise in the analysis of plane wave motion through the system within a pass band it is found that the physical nature of the response is strongly affected by the presence or otherwise of a caustic in the absence of a caustic the response amplitude has a relatively smooth spatial distribution if a caustic is present then the response amplitude has a complex spatial pattern and a dead region of very low response occurs the theory is applied to a two dimensional mass spring periodic system and a comparison is made with an exact calculation for the response of a large finite system excellent agreement is obtained between the two sets of results the work has application to all types of two dimensional periodic structures including orthogonally stiffened plates and shells and it raises the possibility of designing a periodic structure to act as a spatial filter to isolate sensitive equipment from a localized excitation source

continuous markov semigroups and stability of transport equations a new theorem for asymptotic stability of markov semigroups is proved this result is applied to transport equations connected with diffusion and jumping processes and randomly perturbed dynamical systems

wave dispersion in periodic post buckled structures wave propagation in pinned supported post buckled beams can be described with the korteweg de vries kdv equation finite element simulations however show that the kdv is applicable only to post buckled beams with strong pre compression for weak and moderate pre stress a dispersive front is present and it is the aim of the current paper to analyze sources of dispersion beyond periodicity given three support types guided pinned and free bloch theorem and a transfer matrix method are employed to obtain numerical dispersion relations and characteristic wave modes which are used to analyze the effects of pre stress initial curvature and the influence of support types additionally a new method is proposed to obtain a semi analytical dispersion equation for the acoustic branch powers of frequency and the propagation constant are explicitly expressed and their coefficients are based on stiffness and mass matrix components obtained from finite elements this allows a physical interpretation of the dispersion sources based on which equivalent mass spring models of post buckled beam are proposed it is found that mass and stiffness coupling are significant dispersion sources in the present paper a reduced form of bloch theorem is presented exploiting glide reflection symmetries reducing the size of the unit cell and allowing an easier representation and interpretation of results

high frequency dynamics of an isotropic timoshenko periodic beam by the use of the time domain spectral finite element method in this work results of numerical simulations and experimental measurements related to the high frequency dynamics of an aluminium timoshenko periodic beam are presented it was assumed by the authors that the source of beam structural periodicity comes from periodical alterations to its geometry due to the presence of appropriately arranged drill holes as a consequence of these alterations dynamic characteristics of the beam are changed revealing a set of frequency band gaps the presence of the frequency band gaps can help in the design process of effective sound filters or sound barriers that can selectively attenuate propagating wave signals of certain frequency contents in order to achieve this a combination of three numerical techniques were employed by the authors they comprise the application of the time domain spectral finite element method in the case of analysis of finite and semi infinite computational domains damage modelling in the case of analysis of drill hole influence as well as the bloch reduction in the case of analysis of periodic computational domains as an experimental technique the scanning laser doppler vibrometry was chosen a combined application of all these numerical and experimental techniques appears as new for this purpose and not reported in the literature available

an error estimator for separated representations of highly multidimensional models fine modeling of the structure and mechanics of materials from the nanometric to the micrometric scales uses descriptions ranging from quantum to statistical mechanics most of these models consist of a partial differential equation defined in a highly multidimensional domain e g schrodinger equation fokker planck equations among many others the main challenge related to these models is their associated curse of dimensionality we proposed in some of our former works a new strategy able to circumvent the curse of dimensionality based on the use of separated representations also known as finite sums decomposition this technique proceeds by computing at each iteration a new sum that consists of a product of functions each one defined in one of the model coordinates the issue related to error estimation has never been addressed this paper presents a first attempt on the accuracy evaluation of such a kind of discretization techniques

proper generalized decomposition for parameterized helmholtz problems in heterogeneous and unbounded domains application to harbor agitation abstract solving the helmholtz equation for a large number of input data in an heterogeneous media and unbounded domain still represents a challenge this is due to the particular nature of the helmholtz operator and the sensibility of the solution to small variations of the data here a reduced order model is used to determine the scattered solution everywhere in the domain for any incoming wave direction and frequency moreover this is applied to a real engineering problem water agitation inside real harbors for low to mid high frequencies the proper generalized decomposition pgd model reduction approach is used to obtain a separable representation of the solution at any point and for any incoming wave direction and frequency here its applicability to such a problem is discussed and demonstrated more precisely the contributions of the paper include the pgd implementation into a perfectly matched layer framework to model the unbounded domain and the separability of the operator which is addressed here using an efficient higher order projection scheme then the performance of the pgd in this framework is discussed and improved using the higher order projection and a petrov galerkin approach to construct the separated basis moreover the efficiency of the higher order projection scheme is demonstrated and compared with the higher order singular value decomposition

perfectly matched layers for time harmonic elastodynamics of unbounded domains theory and finite element implementation abstract one approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outwards from the bounded domain a perfectly matched layer pml is an unphysical absorbing layer model for linear wave equations that absorbs almost perfectly outgoing waves of all non tangential angles of incidence and of all non zero frequencies this paper develops the pml concept for time harmonic elastodynamics in cartesian coordinates utilising insights obtained with electromagnetics pmls and presents a novel displacement based symmetric finite element implementation of the pml for time harmonic plane strain or three dimensional motion the pml concept is illustrated through the example of a one dimensional rod on elastic foundation and through the anti plane motion of a two dimensional continuum the concept is explored in detail through analytical and numerical results from a pml model of the semi infinite rod on elastic foundation and through numerical results for the anti plane motion of a semi infinite layer on a rigid base numerical results are presented for the classical soil structure interaction problems of a rigid strip footing on a i half plane ii layer on a half plane and iii layer on a rigid base the analytical and numerical results obtained for these canonical problems demonstrate the high accuracy achievable by pml models even with small bounded domains

formation of local resonance band gaps in finite acoustic metamaterials a closed form transfer function model abstract the objective of this paper is to use transfer functions to comprehend the formation of band gaps in locally resonant acoustic metamaterials identifying a recursive approach for any number of serially arranged locally resonant mass in mass cells a closed form expression for the transfer function is derived analysis of the end to end transfer function helps identify the fundamental mechanism for the band gap formation in a finite metamaterial this mechanism includes a repeated complex conjugate zeros located at the natural frequency of the individual local resonators b the presence of two poles which flank the band gap and c the absence of poles in the band gap analysis of the finite cell dynamics are compared to the bloch wave analysis of infinitely long metamaterials to confirm the theoretical limits of the band gap estimated by the transfer function modeling the analysis also explains how the band gap evolves as the number of cells in the metamaterial chain increases and highlights how the response varies depending on the chosen sensing location along the length of the metamaterial the proposed transfer function approach to compute and evaluate band gaps in locally resonant structures provides a framework for the exploitation of control techniques to modify and tune band gaps in finite metamaterial realizations

on wave based weak trefftz discontinuous galerkin approach for medium frequency heterogeneous helmholtz problem abstract medium frequency heterogeneous helmholtz problem gives rise to severe numerical challenge to finite element method fem an extended variational theory of complex rays vtcr is developed for solving this problem since vtcr is kind of trefftz method analytic solutions of governing equation need to be known a priori but this requirement limits the application of vtcr to some specific forms of governing equations recently a new computational method named weak trefftz discontinuous galerkin method wtdg is proposed to enable hybrid finite element method fem variational theory of complex rays vtcr strategies to be developed easily in acoustics and vibrations this hybrid method combines the advantages of fem and vtcr to solve efficiently low frequency and medium frequency problems this paper proposes a wave based wtdg for heterogeneous helmholtz problem without knowing analytic solution of governing equation wtdg method provides a simple and general resolution strategy for medium frequency heterogeneous helmholtz problem

optimizing the perfectly matched layer the berenger perfectly matched layer or pml 4 3 is used in computational electromagnetism as a sponge layer to terminate finite element approximations of scattering problems an infinite perfectly matched layer creates no reflection for incident waves of any frequency or any incident direction and the waves decay exponentially in magnitude into the layer this property is lost when the layer is truncated since the truncation boundary generates a reflected wave discretization of the differential equations further changes the reflection coefficient of the layer in this talk we shall describe the pml in the simple case of a two dimensional electromagnetic problem the first part of this abstract is expository we shall show how to derive the layer using a change of variable approach 5 9 6 after this derivation we describe some new analysis to show the effects of truncating and discretizing the pml 9 we end by showing how to compute an optimal layer and make some remarks about pml for the full maxwell system

real wave vectors for dynamic analysis of periodic structures a modified version of the traditional wave vector computational scheme for the dynamic analysis of long undamped periodic structures is presented first the consistency of the complex wave vector mathematical formulation is discussed placing particular emphasis on the real or complex nature of the resulting characteristic equation from which the natural frequencies are derived it is shown that the rearrangement in terms of complex waves entering the domain devised to overcome ill conditioning arising in the transfer matrix formulation entails as a side effect an ill posed problem as it leads to a complex characteristic equation in a real unknown next the proposed approach is described it provides for transformation of frequency dependent real transfer matrices for state vectors to real transfer matrices for wave vectors thus avoiding an ill conditioned and ill posed problem finally applications to mono coupled and bi coupled structures are illustrated aiming at comparing the proposed method with the transfer matrix and complex wave vector approaches

exact wave based bloch analysis procedure for investigating wave propagation in two dimensional periodic lattices abstract this paper presents an exact wave based approach for determining bloch waves in two dimensional periodic lattices this is in contrast to existing methods which employ approximate approaches e g finite difference ritz finite element or plane wave expansion methods to compute bloch waves in general two dimensional lattices the analysis combines the recently introduced wave based vibration analysis technique with specialized bloch boundary conditions developed herein timoshenko beams with axial extension are used in modeling the lattice members the bloch boundary conditions incorporate a propagation constant capturing bloch wave propagation in a single direction but applied to all wave directions propagating in the lattice members this results in a unique and properly posed bloch analysis results are generated for the simple problem of a periodic bi material beam and then for the more complex examples of square diamond and hexagonal honeycomb lattices the bi material beam clearly introduces the concepts but also allows the bloch wave mode to be explored using insight from the technique the square diamond and hexagonal honeycomb lattices illustrate application of the developed technique to two dimensional periodic lattices and allow comparison to a finite element approach differences are noted in the predicted dispersion curves and therefore band gaps which are attributed to the exact procedure more faithfully modeling the finite nature of lattice connection points the exact method also differs from approximate methods in that the same number of solution degrees of freedom is needed to resolve low frequency and arbitrarily high frequency dispersion branches these advantageous features may make the method attractive to researchers studying dispersion characteristics band gap behavior and energy propagation in two dimensional periodic lattices

the variational theory of complex rays a predictive tool for medium frequency vibrations abstract today the main numerical modeling techniques for the analysis of medium frequency vibrations are all based on finite element or boundary element approaches in order to represent small wavelength phenomena in complex structures such as car chassis satellites or ships these techniques require a huge number of degrees of freedom at least seven elements per wavelength are required to represent oscillating solutions in addition the solution obtained is highly sensitive to material properties and boundary conditions the use of high frequency approaches such as the statistical energy analysis sea or any of its improvements does not appear to be suitable for medium frequency vibrations the vibrational behavior becomes too smooth and in general the coupling loss factor cannot be calculated in a predictive way in this paper a new and multiscale approach to the calculation of the vibrations of elastic structures in the medium frequency range called the variational theory of complex rays is presented the feasibility and effectiveness of the method are demonstrated for structures made of plate assemblies several 3d examples are analyzed and compared to the results from a classical finite element approach and from a sea code this comparison shows that our method is able to predict the effective quantities at a very low numerical cost

noise and conditional entropy evolution abstract we study the convergence properties of the conditional kullback leibler entropy in stochastic systems we have proved general results showing that asymptotic stability is a necessary and sufficient condition for the monotone convergence of the conditional entropy to its maximal value of zero additionally we have made specific calculations of the rate of convergence of this entropy to zero in a one dimensional situation illustrated by ornstein uhlenbeck and rayleigh processes higher dimensional situations and a two dimensional ornstein uhlenbeck process with a stochastically perturbed harmonic oscillator and colored noise as examples we also apply our general results to the problem of conditional entropy convergence in the presence of dichotomous noise in both the one dimensional and multidimensional cases we show that the convergence of the conditional entropy to zero is monotone and at least exponential in the specific cases of the ornstein uhlenbeck and rayleigh processes as well as the stochastically perturbed harmonic oscillator and colored noise examples we obtain exact formulae for the temporal evolution of the conditional entropy starting from a concrete initial distribution the rather surprising result in this case is that the rate of convergence of the entropy to zero is independent of the noise amplitude

a perfectly matched layer for the helmholtz equation in a semi infinite strip the perfectly matched layer pml has become a widespread technique for preventing reflections from far field boundaries for wave propagation problems in both the time dependent and frequency domains we develop a discretization to solve the helmholtz equation in an infinite two dimensional strip we solve the interior equation using high order finite differences schemes the combined helmholtz pml problem is then analyzed for the parameters that give the best performance we show that the use of local high order methods in the physical domain coupled with a specific second order approximation in the pml yields global high order accuracy in the physical domain we discuss the impact of the parameters on the effectiveness of the pml numerical results are presented to support the analysis

proper generalized decomposition applied to linear acoustic a new tool for broad band calculation the calculation of the acoustic response of systems in frequency bands is becoming increasingly important in simulation based engineering design this is particularly true in medium frequency bands where the response is very sensitive to the frequency some standard techniques for addressing these problems present a frequency dependent formulation and may involve fixed frequency calculations at many different frequencies in this paper we propose a new technique which combines the variational theory of complex rays vtcr with proper generalized decomposition pgd and does not require the resolution of acoustic problems at many frequencies in this approach the vtcr is used to find an approximate solution of a medium frequency acoustic problem using only a few degrees of freedom dofs then pgd is used to find a representation of the approximate solution which is separated between two variables the wave propagation direction and the frequency a relevant numerical example is used to present the strategy and illustrate its applicability for frequency band calculations

dynamic behavior of stochastic gene expression models in the presence of bursting this paper considers the behavior of discrete and continuous mathematical models for gene expression in the presence of transcriptional translational bursting we treat this problem in generality with respect to the distribution of the burst size as well as the frequency of bursting and our results are applicable to both inducible and repressible expression patterns in prokaryotes and eukaryotes we have given numerous examples of the applicability of our results especially in the experimentally observed situation that burst size is geometrically or exponentially distributed

asymptotic decomposition of substochastic operators and semigroups abstract theorems on asymptotic decomposition of substochastic operators and semigroups are given general results are applied to show asymptotic periodicity asymptotic stability and sweeping of substochastic operators and semigroups

the response of infinite periodic beams to point harmonic forces a flexural wave analysis abstract an exact analysis is presented of the vibration response of an infinite beam on periodic supports subjected to a transverse harmonic point force the supports must all be the same and can be simply supported or be generally linear with elastic inertial and dissipative properties the total response is found as the sum of the flexural wave fields generated by the applied force and the infinite number of support reaction forces and moments the concept of phased arrays of forces and moments is used to sum the support generated wave fields this utilizes the propagation constants of free wave motion in the periodic beam equations for either four six or eight of the unknown complex reactions depending on the nature of the supports are set up and solved numerically this finite number is sufficient to permit the calculation of the beam displacement at any point and of all the other reactions some computed values of the beam direct receptance are presented to demonstrate its variation with forcing frequency the effect of the location of the excitation force and the effect of changing the elastic properties of the supports

a quasi optimal petrov galerkin method for helmholtz problem a petrov galerkin finite element formulation is introduced for helmholtz problem in two dimensions using polynomial weighting functions at each node of the mesh a global basis function for the weighting space is obtained adding to the bilinear c 0 lagrangian weighting function linear combinations of polynomial bubbles defined on a macroelement containing this node quasi optimal weighting functions with the same support of the corresponding global test functions are obtained after computing the coefficients of these linear combinations attending to optimality criteria this is done numerically through a simple preprocessing technique naturally applied to non uniform and unstructured meshes in particular for uniform mesh a quasi optimal interior stencil of the same order of the quasi stabilized finite element method stencil derived by babuska et al comput methods appl mech engrg 1995 128 325 359 is obtained numerical results are presented illustrating the great stability and accuracy of this formulation with uniform and non uniform meshes

propagation of decaying waves in periodic and piecewise periodic structures of finite length abstract a new method is described for the analysis of long and complicated structures which are composed of spatially periodic units or sections of spatially periodic units the response of such a structure to external excitations is treated as a superposition of wave motions with account taken of the effects of wave reflection due to change in the construction pattern along the structure and boundary conditions since damping usually exists in a real structure a wave motion always decays as it propagates along the structure however this can cause numerical difficulties if the structure is rather long because a decaying wave appears as a growing wave in the opposite direction and since propagations in both directions must be accounted for in the analysis computational errors associated with the apparent growing waves also grow and the numerical results become meaningless in the proposed new scheme use is made of wave reflection and transmission matrices making it possible for all computations to proceed in the direction of wave propagation so that the results are always stable numerically furthermore the required computing time is greatly reduced in comparison with that of an all encompassing finite element analysis for the entire structure application of the new method is illustrated by examples

a geometric multiscale finite element method for the dynamic analysis of heterogeneous solids abstract this paper presents a geom etric multiscale finite element formulation developed for predicting the response of heterogeneous materials and structures the method is based on multi node elements whose shape functions are computed numerically by means of an auxiliary fine scale discretization of the element itself the elements explicitly resolve the geometry of heterogeneities occurring at sub elemental length scales and ensure compatibility across the element boundaries the local auxiliary mesh is only used at the elemental level to compute the shape functions and does not need to be retained as part of macroscale simulations the formulation of 2d and 3d elements is illustrated through examples where error estimates are conducted and which illustrate the effectiveness of the method for the static and dynamic analyses of solids with local heterogeneities

proper generalized decomposition solution of the parameterized helmholtz problem application to inverse geophysical problems this is the peer reviewed version of the following article signorini m zlotnik s and diez p 2017 proper generalized decomposition solution of the parameterized helmholtz problem application to inverse geophysical problems int j numer meth engng 109 1085 1102 doi 10 1002 nme 5313 which has been published in final form at http onlinelibrary wiley com doi 10 1002 nme 5313 full this article may be used for non commercial purposes in accordance with wiley terms and conditions for self archiving

dispersion and pollution of the fem solution for the helmholtz equation in one two and three dimensions for high wave numbers the helmholtz equation suffers the so called pollution effect this effect is directly related to the dispersion a method to measure the dispersion on any numerical method related to the classical galerkin fem is presented this method does not require to compute the numerical solution of the problem and is extremely fast numerical results on the classical galerkin fem p method is compared to modified methods presented in the literature a study of the influence of the topology triangles is also carried out the efficiency of the different methods is compared the numerical results in two of the mesh and for square elements show that the high order elements control the dispersion well the most effective modified method is the qsfem 1 2 but it is also very complicated in the general setting the residual free bubble 3 4 is effective in one dimension but not in higher dimensions the least square method 1 5 approach lowers the dispersion but relatively little the results for triangular meshes show that the best topology is the criss cross pattern copyright 1999 john wiley sons ltd

vibration reduction in piecewise bi coupled periodic structures the problem of minimizing transmitted vibrations through finitely long periodic structures is addressed bi coupled periodic element properties and arrangement are tailored to localize the response around the excitation source within any assigned frequency range bi dimensional analytical maps of the single unit free wave propagation domains stop pass and complex domains provide the optimal choice of the cell properties and ordering moreover the amount of vibration suppression along the periodic structure is also controlled as it can be described through iso attenuation curves representing the contour plot of the real part of the propagation constants applications to both undamped and damped beams resting on elastic supports are illustrated the response of the periodic structures to harmonic excitations is expressed through the wave vector method taking into account the effects of wave reflection due to changes in the cell properties along the structure and boundary conditions such computational schemes enables one to overcome numerical difficulties arising in the transfer matrix formulation for structures with a large number of periodic units

analysis of high order finite elements for convected wave propagation in this paper we examine the performance of high order finite element methods fem for aeroacoustic propagation based on the convected helmholtz equation a methodology is presented to measure the dispersion and amplitude errors of the p fem including non interpolating shape functions such as bubble shape functions a series of simple test cases are also presented to support the results of the dispersion analysis the main conclusion is that the properties of p fem that make its strength for standard acoustics e g exponential p convergence low dispersion error remain present for flow acoustics as well however the flow has a noticeable effect on the accuracy of the numerical solution even when the change in wavelength due to the mean flow is accounted for and an approximation of the dispersion error is proposed to describe the influence of the mean flow also discussed is the so called aliasing effect which can reduce the accuracy of the solution in the case of downstream propagation this can be avoided by an appropriate choice of mesh resolution

alleviating mesh constraints model reduction parallel time integration and high resolution homogenization industrial processes involving composite materials need for efficient numerical simulations in order to optimize the process parameters even if the thermo mechanical models are nowadays well established efficient simulations need for further developments in this work we are addressing some of these issues in particular the one related to fast solutions combining model reduction and parallel time integration a separated representation will be also proposed in the context of material homogenization allowing to alleviate the usual mesh constraints

the forced vibration of one dimensional multi coupled periodic structures an application to finite element analysis abstract a general theory for the forced vibration of multi coupled one dimensional periodic structures is presented as a sequel to a much earlier general theory for free vibration starting from the dynamic stiffness matrix of a single multi coupled periodic element it derives matrix equations for the magnitudes of the characteristic free waves excited in the whole structure by prescribed harmonic forces and or displacements acting at a single periodic junction the semi infinite periodic system excited at its end is first analysed to provide the basis for analysing doubly infinite and finite periodic systems in each case total responses are found by considering just one periodic element an already known method of reducing the size of the computational problem is reexamined expanded and extended in detail involving reduction of the dynamic stiffness matrix of the periodic element through a wave coordinate transformation use of the theory is illustrated in a combined periodic structure finite element analysis of the forced harmonic in plane motion of a uniform flat plate excellent agreement between the computed low frequency responses and those predicted by simple engineering theories validates the detailed formulations of the paper the primary purpose of the paper is not towards a specific application but to present a systematic and coherent forced vibration theory carefully linked with the existing free wave theory