transfer function modeling of multi link flexible structures the paper considers the problem of deriving the accurate infinite dimension laplace transfer function matrix of a system consisting of links that are individually governed by a one dimensional wave equation the first step is deriving some single input transfer functions for a single uniform link the building blocks of those transfer functions are time delays representing the wave motion and low order rational expressions representing the boundary phenomena the transfer function approach enables simple yet accurate simulation schemes exact frequency response for the entire frequency range finite time analytical solutions and a good starting point for dedicated control laws the transfer function provides also an alternative way of obtaining many of the well known properties of flexible structures three methods of modeling multi link systems are presented two of them provide systematic and easy to use approaches for deriving models for systems of any order

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

wave finite elements in guided elastodynamics with internal fluid abstract this paper presents a general formulation which addresses the issue of wave propagation in guided elastodynamic structures filled with acoustic fluid the formulation is based on a finite element description of periodic systems it leads to a general spectral problem whose eigenvalues and eigenvectors are related to the free propagating wave properties the formulation incorporates many simplified elastodynamic models of an analytical nature here the formulation is stated for a fluid structure guided medium the free and forced frequency response of such elasto acoustic system is fully formulated in the wave space reduction of the wave basis is discussed numerical simulations and comparisons with classic simplified theories clearly shows the pertinence of the proposed formulation moreover it is clearly shown that unlike most of the existing theories the proposed formulation is not low frequency limited

viewpoint invariant recovery of visual surfaces from sparse data an algorithm for the reconstruction of visual surfaces from sparse data is proposed an important aspect of this algorithm is that the surface estimated from the sparse data is approximately invariant with respect to rigid transformation of the surface in 3d space the algorithm is based on casting the problem as an ill posed inverse problem that must be stabilized using a priori information related to the image and constraint formation to form a surface estimate that is approximately invariant with respect to viewpoint the stabilizing information is based on invariant surface characteristics with appropriate approximations this results in a convex functional to minimize which is then solved using finite element analysis the relationship of this algorithm to several previously proposed reconstruction algorithms is discussed and several examples that demonstrate its effectiveness in reconstructing viewpoint invariant surface estimates are given

dynamic analysis of space frames the method of reverberation ray matrix and the orthogonality of normal modes the formulation of reverberation ray matrix analysis has been proposed to study wave propagation in planar frames it is applied here to modal analysis of complex three dimensional framed structures optionally with lumped masses and or elastic supports furthermore by means of betti s reciprocity theorem orthogonal conditions are established for different natural modes and hence transient response analysis based on mode superposition is developed both the reverberation ray matrix analysis for free vibration and the mode superposition method for transient response are illustrated by numerical examples

visible surface reconstruction via local minimax approximation abstract visible surface reconstruction is an important early stage in the processing and analysis of 3 d imagery as it provides a compact and manipulable representation of the 3 d structure of perceived objects in a scene in this paper we describe an algorithm for reconstructing visible surfaces from scattered surface depth orientation data using approximation methods the basic unit of the proposed algorithm is a minimax approximation routine which operates over regions of local surface support the minimax approach is attractive for several reasons and the computational cost is not high using fast algorithms a window based scheme is used to achieve a smooth surface reconstruction while maintaining discontinuities arising from object occlusions or sudden changes in surface orientation the discontinuities are detected as part of the algorithm results of the technique as applied to several test objects are provided

coupled tension torsion vibration of repetitive beam like structures equivalent continuum stiffness properties derived from the eigenanalysis of a single cell of a planar beam like repetitive structure have previously been employed within well known dynamic theories such as euler bernoulli and timoshenko for flexural vibration suitably modified to predict natural frequencies of vibration here the approach is applied to two structure types that exhibit tension torsion coupling the first is modelled on a nasa deployable structure with a cross section of equilateral triangular form but with asymmetric triangulation on the faces the second is a related more symmetric structure but with pre twist the simplest tension torsion dynamic theory due to di prima is employed and this is extended to more general end conditions this combined periodic structure substitute continuum approach provides excellent agreement with predictions from the finite element method especially for the lower modes of vibration typically agreement is within 1 for the lowest 8 10 natural frequencies for the longer 30 cell structures considered here the majority of these being torsional modes and within 1 for the lowest 4 5 modes for the shorter ten cell structures this level of accuracy is attainable so long as a single wavelength spans 2 3 cells of the repetitive structure

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

transient response analysis of systems with different damping models a response of systems with different damping models to transient excitations is studied using the finite element method for this purpose an efficient method using fast fourier transform has been developed this method is based on the trigonometrical representation of the input signals and matrix of the transfer functions as an example systems with viscous and viscoelastic structural and external damping are examined two forms of viscous damping are available in the present implementation raleigh damping and element damping the viscoelastic material behaviour is represented by the complex modulus model the present implementation gives the possibility to preserve exactly the frequency dependence of the storage and loss moduli of viscoelastic materials logarithmic decrements are determined using the steady state vibrations of systems to characterize their damping properties test problems and numerical examples are given to demonstrate the validity and application of the approach suggested in this paper

augmented hooke s law in frequency domain a three dimensional material damping formulation abstract an isothermal fully three dimensional material damping modelling technique to some extent alternative to classic viscoelasticity is proposed the method is formulated in the frequency domain as an augmented hooke s law ahl with a constitutive matrix in which material damping is introduced by adding frequency dependent complex valued terms to the classical material modulus matrix of hooke s generalized law the derivations are based on linear irreversible thermodynamics and the concept of hidden coordinates as introduced by biot 1955 phys rev 97 1463 1469 the one dimensional concept of multiple augmenting thermodynamic fields by lesieutre 1992 int j solids structures 29 1567 1579 is generalized to a suitable three dimensional continuum form through the introduction of a special type of hidden coordinate vectors with linear first order time domain relaxation equations consistent with the hidden coordinates a free energy density function assuming isothermal conditions is introduced as the time domain basis of the augmented hooke s law through a time domain model of the coupled evolution of the mechanical displacements and the thermodynamical variables issues of causality are avoided completely in the final frequency domain formulation the general time domain model used is shown to be equivalent to a three dimensional multiple anelastic displacement field model an isotropic augmented hooke s law with both dilatational and shearing damping has been implemented and tested using a 20 node volume element in the finite element code aska acoustics a close agreement between finite element calculations and the corresponding analytically exact results for the studied rod and beam cases is obtained

fractional calculus a different approach to the analysis of viscoelastically damped structures fractional calculus is used to construct stress strain relationships for viscoelastic materials these relationships are used in the finite element analysis of viscoelastically damped structures and closed form solutions to the equations of motion are found the attractive feature of this approach is that very few empirical parameters are required to model the viscoelastic material and calculate the response of the structure for general loading conditions

dynamics of skin stringer panels using modified wave methods the response of a damped periodic simply supported skin stringer structure is studied by two variants of the decaying wave method the proposed method is based on a combination of a wave propagation method with transfer matrices one variant of the decaying wave method is based on an exact solution transfer matrix the other is based on a finite element formulation it is shown that both variants give response curves that compare very well with previous results for the undamped structure which illustrates both the accuracy and the numerical stability of the decaying wave method variants numerical results including deflections at various points at various frequencies as well as mode shapes are presented and comparisons are offered the numerical results demonstrate the accuracy and reliability of both variants of the decaying wave method and this is because advantages of three methods are combined in each variant admittedly difficult to model but much of the fuselage s dynamic behavior can be captured by a much simpler struc ture a flat periodic single row simply supported skin stringer structure of finite length this one row structure seen in fig 1 is designed to emulate somewhat a long circumferen tial strip of the fuselage structure between two supporting circumferential beams whose effects are somewhat simulated by a simple support boundary condition the assumptions of a flat and periodic structure while designed to make the calculation easier are not completely unreasonable thus the simpler structure should contain much of the same dynamic behavior as sections of fuselage skin would the single row simply supported skin stringer structure has been analyzed by many different researchers using several different methods lin1 found the dynamic behavior of this structure analytically using the bending and torsional charac teristics of the stringers his analysis gives some important results such as the existence and location of frequency filter bands in the infinite structure but it does not provide a simple way to get complete response curves for the finite or infinite structure further were the boundary conditions at the top or bottom of the structure to change this type of analysis be comes extremely difficult thus it became necessary to look at this problem using a numerical method the first choice of numerical method for many engineers is the finite element method and finite element codes are com monplace throughout industry with regard to skin stringer structures mei2 obtained the finite element matrices for a thin walled open cross sectional stringer and he takes into account coupled bending and torsional vibrations that com monly occur in this type of beam bogner et al 3 derived a panel element using hermite cubic polynomials for displace ment patterns which ensure continuity of displacement and slope at the element edges the combination of these element types has led to finite element analysis of skin stringer struc

free vibration analysis of planar curved beams by wave propagation in this paper a systematic approach for the free vibration analysis of a planar circular curved beam system is presented the system considered includes multiple point discontinuities such as elastic supports attached masses and curvature changes neglecting transverse shear and rotary inertia harmonic wave solutions are found for both extensional and inextensional curved beam models dispersion equations are obtained and cut off frequencies are determined wave reflection and transmission matrices are formulated accounting for general support conditions these matrices are combined with the aid of field transfer matrices to provide a concise and efficient method for the free vibration problem of multi span planar circular curved beams with general boundary conditions and supports the solutions are exact since the effects of attenuating wave components are included in the formulation several examples are presented and compared with other methods

a symmetric weak form of biot s equations based on redundant variables representing the fluid using a helmholtz decomposition of the fluid displacement vector field a novel symmetric weak formulation of biot s equations for linear acoustic wave propagation in layered poroelastic media is presented the primary variables used are the frame displacement the acoustic pore pressure the scalar potential and the vector potential obtained from a helmholtz decomposition of the fluid displacement also a symmetric weak form based on the frame displacement the pore pressure and the fluid displacement is obtained as an intermediate result hp finite element simulations of a double leaf partition based on this new weak formulation is verified against simulation results from the classical frame displacement fluid displacement formulation and a frame displacement pore pressure formulation all three formulations simulated displays the same rate of convergence with respect to finite element bases polynomial degree the novel formulation also extends a previously published frame displacement pore pressure scalar fluid displacement potential formulation with an implicit irrotational fluid displacement assumption to a full representation of biot s equations copyright 2010 john wiley sons ltd

calculating the dynamic strain tensor field using modal analysis and numerical differentiation abstract based on vibration response measured at a limited number of points and continuous hilbert space basis functions combined with spatial differentiation a new method for strain tensor field assessment in the frequency domain is proposed essentially results from hybrid modal analysis hma are transformed from the displacement space to the strain space by use of finite difference schemes this approach will produce a continuous strain second order tensor except on a number of surfaces where material discontinuities are present hybrid strain analysis hsa interpreted as dynamic strain analysis based on hma may be done in several ways the method proposed here is the first realization of hsa and it has been verified by an experimental test case the predicted results correspond well with measured strain responses the method is applicable to a vibrating structure regardless of the material properties of the body hence any possible damping e g material damping damping in joints between structural parts etc need not be known a priori moreover the zero frequency elastic properties and mass distribution of the structure need not be the true ones any meaningful arbitrary values of the elastic properties and mass distribution can be assumed in order to obtain the hilbert space basis functions material inhomogeneities present i e in a piecewise continuous structure will cause the method when applied with unknown material properties to be somewhat inaccurate in the vicinity around the discontinuity the derived model is valid for a specific excitation not necessarily known

transfer matrix analysis of the elastostatics of one dimensional repetitive structures transfer matrices are used widely for the dynamic analysis of engineering structures increasingly so for static analysis and are particularly useful in the treatment of repetitive structures for which in general the behaviour of a complete structure can be determined through the analysis of a single repeating cell together with boundary conditions if the structure is not of infinite extent for elastostatic analyses non unity eigenvalues of the transfer matrix of a repeating cell are the rates of decay of selfequilibrated loading as anticipated by saint venant s principle multiple unity eigenvalues pertain to the transmission of load e g tension or bending moment and equivalent homogenized continuum properties such as cross sectional area second moment of area and poisson s ratio can be determined from the associated eigen and principal vectors various disparate results the majority new others drawn from diverse sources are presented these include calculation of principal vectors using the moore penrose inverse bi and symplectic orthogonality and relationship with the reciprocal theorem restrictions on complex unity eigenvalues effect of cell left to right symmetry on both the stiffness and transfer matrices eigenvalue veering in the absence of translational symmetry and limitations on possible jordan canonical forms it is shown that only a repeating unity eigenvalue can lead to a non trivial jordan block form so degenerate decay modes cannot exist the present elastostatic analysis complements langley s langley 1996 proc r soc a 452 1631 1648 transfer matrix analysis of wave motion energetics

incremental model building of polyhedral objects using structured light abstract a vision method using active sensing to construct the complete geometric model of a polyhedral object is presented the model is constructed incrementally from multiple views each view produces a partial object model three different methods are described for integrating all the partial models into a final complete model theorems regarding the sufficient number of views required and how these views can be set up during the reconstruction process are also given from theoretical analysis and experimental results our method is shown to produce an accurate object geometric model not just an approximate model furthermore it does not rely on a precise object to image space transformation moreover the method is fast and robust since the basic geometric entity it derives is a face instead of a point

wave propagation in equivalent continuums representing truss lattice materials abstract stiffness scales linearly with density in stretch dominated lattice meta materials offering the possibility of very light yet very stiff structures current additive manufacturing techniques can assemble structures from lattice materials but the design of such structures will require accurate efficient simulation methods equivalent continuum models have several advantages over discrete truss models of stretch dominated lattices including computational efficiency and ease of model construction however the development an equivalent model suitable for representing the dynamic response of a periodic truss in the small deformation regime is complicated by microinertial effects this paper derives a dynamic equivalent continuum model for periodic truss structures suitable for representing long wavelength wave propagation and verifies it against the full bloch wave theory and detailed finite element simulations the model must incorporate microinertial effects to accurately reproduce long wavelength characteristics of the response such as anisotropic elastic soundspeeds the formulation presented here also improves upon previous work by preserving equilibrium at truss joints for simple lattices and by improving numerical stability by eliminating vertices in the effective yield surface

dynamic response and wave propagation in plane trusses and frames the dynamics of planar frames and trusses is analyzed in terms of the propagation of axial longitudinal and flexural transverse stress waves being structural members the waves are multiscattered at the joints and scattering coefficients representing the reflection and transmission of both types of waves at each joint are derived from the dynamics and compatibility conditions of the joint the complex multireflected waves within the structure are evaluated in the frequency domain by a newly developed reverberation matrix which is formulated from scattering coefficients and propagating phase factors transient waves are then analyzed by fourier synthesis and evaluated by a fast fourier transform algorithm transient responses for the axial and bending strains in all structural members are calculated over a long duration for a model truss with rigid joints comparison to experimental data of the model truss under a step loading shows good agreement for the early as well as considerably long time responses

differential versus integral formulation of fractional hyperviscoelastic constitutive laws for brain tissue modelling for years interest has been constantly growing in biological tissue modelling particularly the mechanical study of the brain has become a major topic in the field of biomechanics a global model of this organ including a realistic mesh and suitable constitutive laws for the different tissues would find applications in various domains such as neurosurgery haptic device design or car manufacturing to evaluate the possible trauma due to an impact several constitutive models have already been designed regarding the strong strain rate dependence of the stress strain curves available in the literature we decided to describe brain tissue as a viscoelastic medium through the use of the fractional derivation operator thanks to this approach we can derive a convolution based model with the mittag leffler function as the regularized kernel

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

time domain finite element analysis of viscoelastic structures with fractional derivatives constitutive relations numerical procedures for the time integration of the spatially discretized finite element equations for viscoelastic structures governed by a constitutive equation involving fractional calculus operators are presented to avoid difficulties concerning fractional order initial conditions a form of the fractlonal calculus model of viscoelasticity involving a convolution integral with a singular memory kernel of mittag lefler type is used the constitutive equation is generalized to three dimensional states for isotropic materials a simplification of the fractional derivative of the memory kernel is used in connection with grunwald s definition of fractional differentiation and a backward euler rule for the time evolution of the convolution term a desirable feature of this process is that no actual evaluation of the memory kernel is needed this together with the newmark method for time integration enables the direct calculation of the time evolution of the nodal degrees of freedom to illustrate the ability of the numerical procedure a few numerical examples are presented in one example the numerically obtained solution is compared with a time series expansion of the analytical solution

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

wave attenuation in nonlinear periodic structures using harmonic balance and multiple scales we study the attenuation caused by weak damping of harmonic waves through a discrete periodic structure with frequency nominally within the propagation zone i e propagation occurs in the absence of the damping the period of the structure consists of a linear stiffness and a weak linear nonlinear damping adapting the transfer matrix method and using harmonic balance for the nonlinear terms a four dimensional linear nonlinear map governing the dynamics is obtained we analyze this map by applying the method of multiple scales upto first order the resulting slow evolution equations give the amplitude decay rate in the structure the approximations are validated by comparing with other analytical solutions for the linear case and full numerics for the nonlinear case good agreement is obtained the method of analysis presented here can be extended to more complex structures

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

power flow between two continuous one dimensional subsystems a wave solution abstract the power flow between two point coupled wave bearing subsystems is determined by using a wave approach the subsystems are one dimensional in that each supports just one wave mode and are described by a reflection coefficient from which in certain circumstances the modal overlap and modal density can be defined as continuous functions of frequency the coupling element is described by a reflection coefficient and attention is focused on the case of conservative coupling time harmonic point forces or rain on the roof excitations may act on the subsystems uncertainty exists in the properties of the subsystems which are assumed to be drawn from ensembles of similar subsystems the exact power flow and the ensemble statistics are seen to depend on the magnitudes of the subsystem and coupling reflection coefficients for some particular cases the maximum and minimum power flows are examined together with the ensemble mean and geometric mean the cumulative probability distribution and the probability density function for a given power incident upon the coupling the ensemble mean power flow through the coupling is always less than that expected from a normal sea wave approach due to power re radiation the differences are largest when the damping is light and the coupling strong for a given level of excitation power re radiation effects are also apparent for the ensemble mean power flow from an infinite subsystem to a finite subsystem in the opposite case the ensemble mean power flow from a finite to an infinite subsystem is greater than that between two infinite subsystems due to power re injection the differences are largest for light damping and for weak coupling finally the case where there is uncertainty in one subsystem only is considered

non local dispersive model for wave propagation in heterogeneous media one dimensional case non local dispersive model for wave propagation in heterogeneous media is derived from the higher order mathematical homogenization theory with multiple spatial and temporal scales in addition to the usual space time co ordinates a fast spatial scale and a slow temporal scale are introduced to account for rapid spatial fluctuations of material properties as well as to capture the long term behaviour of the homogenized solution by combining various order homogenized equations of motion the slow time dependence is eliminated giving rise to the fourth order differential equation also known as a bad boussinesq problem regularization procedures are then introduced to construct the so called good boussinesq problem where the need for c1 continuity is eliminated numerical examples are presented to validate the present formulation copyright 2002 john wiley sons ltd

statistical distribution of frequency response in disordered periodic structures a structure designed to be spatially periodic cannot be exactly periodic the departure from exact periodicity is known as disorder and it causes localization of normal modes and additional attenuation of wave motions in the structure not related to damping the present investigation is directed at a possible adverse effect of disorder namely higher structural response near the point at which a dynamic excitation is applied than would occur in a perfectly periodic structure thereby reducing structure safety and reliability a systematic procedure is developed herein for the analysis of such an effect for a generic disordered periodic structure in particular the probability distribution of structural response is obtained by analysis and by monte carlo simulation which is needed both for fundamental understanding of the effect and for predicting the reliability of a system it is shown also that given probability distributions of the disordered parameters of a structure the mean and standard deviation of structural response can be obtained exactly for a damped randomly disordered periodic structure if the number of disordered cell units is not large and approximately if the number is large application of the procedure is illustrated by an example and the results are compared with monte carlo simulations

an adaptation of the gear scheme for fractional derivatives abstract the gear scheme is a three level step algorithm backward in time and second order accurate for the approximation of classical time derivatives in this contribution the formal power of this scheme is proposed to approximate fractional derivative operators in the context of finite difference methods some numerical examples are presented and analysed in order to show the effectiveness of the present gear scheme at the power g scheme when compared to the classical grunwald letnikov approximation in particular for a fractional damped oscillator problem the combined g newmark scheme is shown to be second order accurate

3d hierarchical hp fem applied to elasto acoustic modelling of layered porous media this paper presents a 3 d hierarchical p version finite element description of the solid displacement fluid displacement form of biot s equation for elasto acoustic modelling of multiple layered isotropic porous media the convergence related to mesh refinement extensions for different orders of polynomial approximation is briefly discussed for a homogeneous foam the highest computational efficiency for reasonable levels of the error in the low frequency region was obtained for fourth order polynomial finite element interpolations the main focus is on coupling conditions and on the convergence of solutions to biot s equations in cases with multiple layers having different material properties simulations of a two layered porous material with low flow resistivity suggest slow convergence rate of the fluid displacement field close to the interface between the layers

dynamics of complex truss type space structures a laboratory test was conducted to validate experimentally and to help establish the limits of the mbct approach the results show that the mbct method is a vital alternate technique for ground testing large flexible structures a three dimensional mast type truss structure has been successfully simulated

bloch theorem with revised boundary conditions applied to glide screw and rotational symmetric structures abstract wave propagation in complex periodic systems is often addressed with the bloch theorem and consists in applying periodic boundary conditions to a discretized unit cell while this method has been developed for structures periodic by translation in a recent work for quasi one dimensional wave propagation it has been shown that screw translation plus rotation and glide translation plus reflection periodicities can be accounted for as well keeping the cartesian coordinate system but revisiting the periodic boundary conditions the goal of the present paper is to generalize this concept to quasi two dimensional wave propagation two dimensional waves propagating in three dimensional structures dispersion relations for a set of reduced problems are then compared to results from the classical method when available by considering a smaller periodicity the computational cost is decreased and the number of folding curves and non interacting intersecting curves is reduced improving their interpretability while the size of a unit cell is divided by a factor two when glide symmetries are considered this ratio is significantly increased for screw or rotational symmetries moreover the proposed revisited bloch method is applicable to screw symmetric structures that do not possess purely translational symmetries and for which the classical method cannot be used e g chiral nanotubes longitudinally wrinkled helicoids

dynamic stability of a viscoelastic beam with frequency dependent modulus abstract this study presents the dynamic stability of a simply supported viscoelastic beam subjected to an axially harmonic load the complex modulus of viscoelastic material is considered to depend on the frequency of parametric loading applying galerkin s method the governing equation of motion is simplified to the complex form of the mathieu equation with frequency dependent coefficients then the boundary of dynamic stability is determined by coupling the numerical binary search procedure and the complex incremental harmonic balance ihb method which are developed in this study this algorithm is easily simply and conveniently used to perform computer numerical analysis the results indicate that the loss factor presents the damping capacity of viscoelastic material the numerical results reveal that the frequency influences the dynamic stability

mechanics of materials with periodic truss or frame micro structures this paper describes the mechanics of materials with periodic skeletal micro structures in infinite domains the principal technical results consist of certain korn type inequalities that provide upper and lower bounds for the linear elastic strain energy in the material using these inequalities existence and uniqueness results for the equations of linear elastic equilibrium are derived and some asymptotic properties of the solutions are described particular attention is paid to the question of when a lattice structure can accurately be modeled as a pin jointed truss and when a rigid node frame model must be employed a practical technique for how to distinguish between the two types of material is given and the distinct differences in their mechanical behavior are described

plane wave propagation and frequency band gaps in periodic plates and cylindrical shells with and without heavy fluid loading free plane wave propagation in infinitely long periodic elastic structures with and without heavy fluid loading is considered the structures comprise continuous elements of two different types connected in an alternating sequence in the absence of fluid loading an exact solution which describes wave motion in each unboundedly extended element is obtained analytically as a superposition of all propagating and evanescent waves continuity conditions at the interfaces between elements are formulated and standard floquet theory is applied to set up a characteristic determinant an efficient algorithm to compute bloch parameters propagation constants as a function of the excitation frequency is suggested and the location of band gaps is studied as a function of non dimensional parameters of the structure s composition in the case of heavy fluid loading an infinitely large number of propagating or evanescent waves exist in each unboundedly extended elasto acoustic element of a periodic structure wave motion in each element is then presented in the form of a modal decomposition with a finite number of terms retained in these expansions and the accuracy of such an approximation is assessed a generalized algorithm is used to compute bloch parameters for a periodic structure with heavy fluid loading as a function of the excitation frequency and similarly to the previous case the location of band gaps is studied

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

exact solutions for dynamic response of a periodic spring and mass structure this paper derives exact analytical solutions for the dynamic response of a periodic structure for which the unit cell consists of one mass and one spring the solutions cover arbitrary initial conditions and both polynomial and harmonic external forces they involve bessel lommel weber and hypergeometric functions

time domain modeling of damping using anelastic displacement fields and fractional calculus abstract a fractional derivative model of linear viscoelasticity based on the decomposition of the displacement field into an anelastic part and elastic part is developed the evolution equation for the anelastic part is then a differential equation of fractional order in time by using a fractional order evolution equation for the anelastic strain the present model becomes very flexible for describing the weak frequency dependence of damping characteristics to illustrate the modeling capability the model parameters are fit to available frequency domain data for a high damping polymer by studying the relaxation modulus and the relaxation spectrum the material parameters of the present viscoelastic model are given physical meaning the use of this viscoelastic model in structural modeling is discussed and the corresponding finite element equations are outlined including the treatment of boundary conditions the anelastic displacement field is mathematically coupled to the total displacement field through a convolution integral with a kernel of mittag leffler function type finally a time step algorithm for solving the finite element equations are developed and some numerical examples are presented

micro inertia effects in nonlinear heterogeneous media summary the manuscript presents a dispersive nonlinear continuum theory for the case where the shortest wavelength is several times larger than the characteristic size of the microstructure and the observation window is large we develop a general purpose computational framework which is valid for nonlinear problems and requires standard c 0 continuous formalism the fine scale inertia effect is accounted for by formulating a quasidynamic unit cell problem where the fine scale inertia effect is represented by so called inertia induced eigenstrain the solution of the nonlinear quasi dynamic unit cell problem gives rise to the modification of either coarse scale mass matrix in the implicit solvers or internal force in the explicit solvers similarly to the classical homogenization theory scale separation is assumed but higher order homogenization is not pursued to avoid higher order coarse scale gradients higher order continuity and higher order boundary conditions numerical examples for both the one dimensional model problem and three dimensional heterogeneous medium with layered and fibrous composite microstructure are used to validate the computational framework proposed copyright 2012 john wiley sons ltd

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

dynamic response analysis of truss type structural networks a wave propagation approach abstract a typical space structure is composed of piece wise periodic arrays of connected truss units these arrays can intersect each other and form multiple closed loops in this paper a detailed step by step numerical procedure is provided for computing the response of such a structure to external excitations the basic idea is to treat an array of connected truss units as a multi channel waveguide capable of transmitting several types of wave motions each waveguide or each junction where several waveguides intersect can be characterized by a wave scattering matrix which is composed of the transmission and reflection submatrices a reflection submatrix reverses the direction of incoming waves whereas a transmission submatrix permits the incoming waves to enter or to be directed to other waveguides by use of wave scattering matrices in the formulation the numerical computation always follows the directions of propagation of various waves thus numerical stability is assured since the amplitude of wave motion decays as it propagates along a path due to structural damping the numerical procedure described herein represents an extension of the author s previous works by 1 describing for the first time the dynamics of individual truss arrays in terms of scattering matrices 2 adopting a new bookkeeping system to accommodate more complicated configurations of structural networks and 3 developing an efficient procedure to eliminate step by step superfluous unknowns thus simplifying the calculation combination of the three advances makes it possible to treat for the first time such complicated configurations as multiple closed loops since the actual truss type construction is retained when obtaining the wave scattering matrices the procedure is considered more accurate than those based on substitution for truss construction of timoshenko beam elements application of the procedure is illustrated by an example

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

symplectic random vibration analysis of a vehicle moving on an infinitely long periodic track based on the pseudo excitation method pem symplectic mathematical scheme and schur decomposition the random responses of coupled vehicle track systems are analyzed the vehicle is modeled as a spring mass damper system and the track is regarded as an infinitely long substructural chain consisting of three layers i e the rails sleepers and ballast the vehicle and track are coupled via linear springs and the moving vehicle model is adopted the latter assumes that the vehicle moves along a static track for which the rail irregularity is further assumed to be a zero mean valued stationary gaussian random process the problem is then solved efficiently as follows initially pem is used to transform the rail random excitations into deterministic harmonic excitations the symplectic mathematical scheme is then applied to establish a low degree of freedom equation of motion with periodic coefficients in turn these are transformed into a linear equation set whose upper triangular coefficient matrix is established using the schur decomposition scheme finally the frequency dependent terms are separated from the load vector to avoid repeated computations for different frequencies associated with the pseudo excitations the proposed method is subsequently justified by comparison with a monte carlo simulation the fixed vehicle model and the moving vehicle model are compared and the influences of vehicle velocity and class of track on system responses are also discussed

on wave propagation in repetitive structures two forms of transfer matrix abstract two forms of dynamic transfer matrix are derived for a one dimensional beam like repetitive pin jointed structure with point masses located at nodal cross sections the displacement force transfer matrix g and the displacement displacement transfer matrix h similarity matrices are introduced to relate g and h together with their respective metrics symplectic orthogonality relationships for the eigenvectors of both g and h are derived together with relationships between their respective sets of eigenvectors new expressions for the group velocity are derived for repetitive structures of finite length natural frequency equations are derived employing both g and h including phase closure and the direct application of boundary end conditions besides an exposition of the theory some familiar but much new the focus of the present paper is on the relationships between the two forms of transfer matrix including their respective dis advantages numerical results together with further theory necessary for interpretation are presented in companion papers

statistical origins of fractional derivatives in viscoelasticity many linear viscoelastic materials show constitutive behavior involving fractional order derivatives linear time invariant systems without memory have exponential decay in time but contradictorily not the power law decay associated with fractional derivatives the physics literature has noted that apparently non exponential decays can be observed when several simultaneously decaying processes have closely spaced exponential decay rates many engineer researchers interested in viscoelastic damping however seem unaware of these observations in this letter i give an unoriginal explanation but with a fresh engineering flavor for the appearance of these fractional order derivatives by this explanation fractional order damping can be expected from many materials with sufficiently disordered dissipation mechanisms

mobilities of periodic structures in terms of asymptotic modal properties the natural frequencies of periodic structures lie in distinct frequency bands and become densely spaced when the number of periodic segments is large this paper shows that within such frequency bands the structure has modal properties with asymptotic characteristics this feature of periodic structures is used to develop an asymptotic integral expression for the mobility function

nonlinear vibration of viscoelastic beams described using fractional order derivatives abstract the problem of non linear steady state vibration of beams harmonically excited by harmonic forces is investigated in the paper the viscoelastic material of the beams is described using the zener rheological model with fractional derivatives the constitutive equation which contains derivatives of both stress and strain significantly complicates the solution to the problem the von karman theory is applied to take into account geometric nonlinearities amplitude equations are obtained using the finite element method together with the harmonic balance method and solved using the continuation method the tangent matrix of the amplitude equations is determined in an explicit form the stability of the steady state solution is also examined a parametric study is carried out to determine the influence of viscoelastic properties of the material on the beam s responses

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

formulation and integration of the standard linear viscoelastic solid with fractional order rate laws abstract a physically sound three dimensional anisotropic formulation of the standard linear viscoelastic solid with integer or fractional order rate laws for a finite set of the pertinent internal variables is presented it is shown that the internal variables can be expressed in terms of the strain as convolution integrals with kernels of mittag leffler function type a time integration scheme based on the generalized midpoint rule together with the grunwald algorithm for numerical fractional differentiation for integration of the constitutive response is developed the predictive capability of the viscoelastic model for describing creep relaxation and damped dynamic responses is investigated both analytically and numerically the algorithm and the present general linear viscoelastic model are implemented into the general purpose finite element code abaqus the algorithm is then used together with an explicit difference scheme for integration of structural responses in numerical examples the quasi static and damped responses of a viscoelastic ballast material that is subjected to loads simulating the overrolling of a train are investigated