exact discrete time modelling of linear analogue systems abstract the discrete time minimum variance filtering of continuous time processes and the duality between the problems of discretized filtering and regulation are considered the discrete time optimal filter consists of a digital algorithm which is applied to the prefiltered sampled measurements this algorithm is based on the overall discrete time equivalent model i e the continuous time process the prefilter and the sampler for the first time different formulations of this discrete time equivalent model are presented in a comprehensive unified way a few prevailing misunder standings of the discretization issue are clarified and a few errors that appear in the literature are corrected the equations that govern the optimal linear quadratic discrete time regulation of continuous time systems are presented by comparing these equations to the equations that have been obtained for the optimal filtering problem we show that the optimal discretized filtering problem is not dual to the corresponding

sampled data observers with generalized holds for unstable plants optimality conditions are derived for reduced order sampled data estimation satisfying an observation constraint that involves a prespecified possibly unstable subspace of the system dynamics it is shown that a generalized hold device possessing a time varying exponential intersample profile is essential in order to account for the unstable dynamics in particular it is shown that with a continuous time quadratic performance measure a zero order hold device may result in an unbounded infinite cost an additional feature of the problem is the utilization of an averaging a d device within the continuous time discrete time conversion which results in averaged measurements depending upon delayed samples of the state

implicit runge kutta nystrom methods for general second order volterra integro differential equations abstract in this paper we derive m stage runge kutta nystrom methods for the numerical solution of general second order volterra integro differential equations these implicit methods are based on collocation techniques in certain polynomial spline spaces the question concerning the attainable order of convergence of such one step methods is completely answered

subgrid modeling in a galerkin method for the helmholtz equation abstract we improve the accuracy of finite element acoustic wave solutions without introducing additional degrees of freedom with physically inspired subgrid models the models explored here will not adversely impact system matrix storage or bandwidth can be used for structured or unstructured meshes do not require the solution of any auxiliary value problems and have minimal marginal overall computational cost one interpretation of the new models is as momentum transferred to and from modes at length scales below the local mesh dimension we show a method to approximate the effects of all subgrid modes on the grid scale solution and the significant improvements in local accuracy that the new models provide the new subgrid models also improve global or pollution accuracy through a reduction in the element dispersion error in addition we draw comparisons between this proposed method and much of the alternative and related work in this area

canonical representations of complex vibratory subsystems time domain dirichlet to neumann maps large scale dynamic simulations can often be simplified by appropriately replacing large portions of the domain by a dirichlet to neumann or dtn map givoli 1992 numerical methods for problems on infinite domains 1st ed elsevier amsterdam here we consider the problem of representing a linear dynamical subsystem by such a map the exact dtn map is computed as a modal summation and its properties are studied bounds on the symbol of the dtn map in the laplace domain are obtained the exact map is then approximated in particular in the high modal density regime in the high modal density limit we obtain the result that a subsystem can be accurately represented with just three parameters within such an approximation we obtain representations based on a maximum entropy representation self similar or fractal representation and a rational function representation the rational function representation leads to the interesting result that any complicated dynamical subsystem with a large number of degrees of freedom is asymptotically equivalent in the limit of infinite modal density to a single mass dashpot spring system we end with numerical examples showing the efficiency of the rational function approximation

a general model reduction with primal assembly in structural dynamics abstract a new formulation of general model reduction in structural dynamics is presented the proposed method consists of four attributes a hybrid method combining dynamic condensation and component mode synthesis that are arguably the most popular model reduction techniques a precise model reduction taking the inertia effect into consideration primal assembly at the boundary interface of substructures and general formulations of model reduction with primal assembly comparisons of the proposed model reduction method with the conventional methods are provided as well as an efficient model reduction procedure of the proposed method in particular its advantages and performance of the proposed method are thoroughly investigated with various numerical examples

time stepping schemes for systems of volterra integro differential equations linear volterra type systems of integro differential equations sides with kernels in the form of sums of complex exponentials are considered such systems arise for example in the semi discrete finite element model of dynamic viscoelasticity and of some dispersive wave equations and in the representation of dynamic subsystems on interfaces several new families of time stepping schemes are proposed here for the solution of this class of sides the accuracy stability and efficiency properties of these schemes are demonstrated via both theoretical analysis using a scalar model problem and numerical experiments applied to first and second order sides

equipartition and mean square responses in large undamped structures it is shown that the smoothed spectral energy density at one point in a large complex structure may be approximated in a simple manner as proportional to the frequency smoothed admittance at the receiver and at the source and inversely proportional to the global modal density thus the mean square response may be estimated with little computational burden knowing only the local properties at source and receiver and the size of the system the approximate predictions are compared with the results of direct numerical simulations and found to be accurate except in the presence of anderson localization work supported by nsf

a trigonometric interpolation approach to mixed type boundary problems associated with permeameter shape factors 1 hydraulic conductivity is a fundamental hydrogeological parameter whose in situ measurement at a local scale is principally performed through injection tests from screened probes or using impermeable packers in screened wells the shape factor f l is a proportionality constant required to estimate conductivity from observed flow rate to injection head ratios and it depends on the geometric properties of the flow field existing approaches for determination of f are either based on geometric or mathematical simplifications and are limited to particular assumptions about the flow domain s external boundaries the present work presents a general semianalytical solution to steady state axisymmetric flow problems where external boundaries may be nearby and of arbitrary combinations of impermeable and constant head type the inner boundary along the probe or well may consist of an arbitrary number of impermeable and constant head intervals resulting in a mixed type boundary value problem for which a novel and direct solution method based on trigonometric interpolation is presented the approach is applied to generate practical nondimensional charts of f for different field and laboratory situations results show that f is affected by less than 5 if a minimum distance of 10 probe or well diameters is kept between the injection screen and a nearby boundary similarly minimum packer lengths of two well diameters are required to avoid increasing f by more than 10 furthermore f is determined for laboratory barrel experiments giving guidelines for achieving equal shape factors as in field situations without nearby boundaries f for the theoretical case of infinitely short packers is shown to be infinitely large

a general method for fdtd modeling of wave propagation in arbitrary frequency dispersive media a general formulation is presented for finite difference time domain fdtd modeling of wave propagation in arbitrary frequency dispersive media two algorithmic approaches are outlined for incorporating dispersion into the fdtd time stepping equations the first employs a frequency dependent complex permittivity denoted form 1 and the second employs a frequency dependent complex conductivity denoted form 2 a pade representation is used in z transform space to represent the frequency dependent permittivity form 1 or conductivity form 2 this is a generalization over several previous methods employing either debye lorentz or drude models the coefficients of the pade model may be obtained through an optimization process leading directly to a finite difference representation of the dispersion relation without introducing discretization error stability criteria for the dispersive fdtd algorithms are given we show that several previously developed dispersive fdtd algorithms can be cast as special cases of our more general framework simulation results are presented for a one dimensional 1 d air muscle example considered previously in the literature and a three dimensional 3 d radiation problem in dispersive lossy soil using measured soil data

high modal density approximations for equipment in the time domain this article considers modeling the effect of complex subsystems on the dynamics of the main structure to which they are attached it is proposed that the substructure say a piece of equipment be replaced by an equivalent set of forces which react back on the main structure these forces are given as time convolutions of the displacements at the equipment attachment points the convolution integral which represents a time domain dtn dirichlet to neumann map is approximated in the high modal density limit with determined error bounds this approximation leads to a family of equipment representations the simplest requires few measured equipment properties though more information can lead to greater accuracy our approximate dtns are demonstrated numerically in finite element simulations

which are the important modes of a subsystem a linearly behaving vibrational substructure or more generally a linear dynamic subsystem attached to a main structure or a main dynamic system is considered after discretization the substructure is represented by afinite typically large number of degrees of freedom n and hence also by n s eigenmodes in order to reduce the computational effort it is common to apply modal reduction to the subsystem such that only n r modes out of the total number of n modes are retained where n r n s the following question then arises which n r modes should be retained in structural dynamics it is traditional to retain those modes associated with the lowest frequencies in this paper the question is answered by solving an appropriate optimization problem the most important modes of the subsystem are shown to be those whose coupling matrices which are defined in a particular way have the highest norm this leads to a simple and effective algorithm for optimal modal reduction the new criterion for modal importance is explained both mathematically and physically and is demonstrated by numerical examples

ensemble energy average and energy flow relationships for nonstationary vibrating systems abstract this paper attempts to introduce a new point of view on energy analysis in structural dynamics with particular emphasis to its link with uncertainty and complexity a linear elastic system undergoing free vibrations is considered the system is subdivided into two subsystems and their respective energies together with the shared energy flow are analysed first the ensemble energy average of the two subsystems assuming uncertain the natural frequencies is investigated it is shown how the energy averages follow a simple law when observing the long term response of the system obtained by a suitable asymptotic expansion the second part of the analysis shows how the ensemble energy average of a set of random samples is representative even of the single case if the system is complex enough the two previous points combined produce a result that applies to the energy sharing between two subsystems even independently of uncertainty for complex systems a simple energy sharing law is indeed stated moreover in the case of absence of damping a nonlinear relation between the energy flow and the energy weighted difference between the two subsystems is derived on the other hand when damping is present this relationship becomes linear including two terms one is proportional to the energy weighted difference between the two subsystems the other being proportional to its time derivative therefore the approach suggests a way for deriving a general approach to energy sharing in vibration with results that in some cases are reminiscent of those met in statistical energy analysis finally computational experiments performed on systems of increasing complexity validate the theoretical results

a theoretical formulation of the dynamical response of a master structure coupled with elastic continuous fuzzy subsystems with discrete attachments we present the formulation of the dynamic response of a master structure coupled with a locally homogeneous and orthotropic structural fuzzy with discrete attachment composed of elastic continuous fuzzy subsystems as introduced by soize the master structure is the part of the coupled system which is accessible by classical modeling whereas the structural fuzzy represents systems connected to the master structure whose characteristics are imprecisely known a deterministic formulation of the boundary impedance of a general continuous structural fuzzy which models its action on the master structure is derived it is shown that the formulation is different from the solution proposed by soize in the context of the type i fuzzy law established from the deterministic model of a linear oscillator excited by its support finally the general boundary impedance is applied to the special situation of a structural fuzzy composed of elastic bars whose geometrical parameters are randomly defined and numerical results are presented

backscattering from a baffled finite plate strip with fuzzy attachments a formulation for predicting the effect of fuzzy attachments on the response of a master structure was originally provided by the fuzzy structure theory of soize an extension of soize s theory was recently developed by pierce et al asme 1993 winter meeting new orleans la this new formulation is applied to a finite plate strip simply supported in an infinite rigid baffle an incident plane wave pulse is incident upon the plate and the effect of the fuzzy attachments on the target strength is determined the primary effect of a large number of 1 dof fuzzy attachments is an apparent added mass and an apparent added damping to the plate both of these effects depend directly on the mass distribution of the 1 dof attachments with respect to their natural frequencies a representative distribution is considered it is found that if the most probable natural frequency of the fuzzy attachments coincides with a plate resonance the amplitude at the target frequency is significantly reduced the amount of re

a combined analytic finite element method for elastic shells abstract a method is devised for the numerical analysis of structures that include semi infinite circular cylindrical shells the so called edge stiffness coefficients of the cylinder are used to eliminate the semi infinite domain only a small region is thus left for discretization in this computational domain a finite element scheme is used which incorporates transverse shear deformation numerical examples demonstrate the superiority of the suggested method to the standard one

frequency weighted model reduction via optimal projection the problem of order reduction with frequency weighting is considered necessary conditions characterizing the reduced order model which minimizes a quadratic error criterion in the frequency domain with either input or output frequency weighting are given the problem is transformed to the time domain where the weighting matrix is expressed as a shaping filter that generates colored noise at the input when the weighting matrix is singular at infinity the reduced order model has a direct transmission term even if the original system is strictly proper this additional degree of freedom can be used to obtain better approximation over a prespecified frequency range

mst mems model order reduction requirements and benchmarks the needs for model reduction in microsystem technology mst are described from an engineering perspective two representative mst model reduction benchmarks are presented in order to facilitate further development in this area the first benchmark application is from the area of electro thermal simulation the second one considers an electrostatically actuated beam as found in radio frequency applications model reduction is contrasted with compact modeling which currently enjoys widespread use among engineers and important challenges to be addressed are listed

optimal modal reduction of vibrating substructures optimal modal reduction of vibrating substructures a structure which consists of a main part and a number of attached substructures is considered a model reduction scheme is developed and applied to each of the discrete substructures linear undamped transient vibrational motion of the structure is assumed with general external forcing and initial conditions the goal is to replace each discrete substructure by another substructure with a much smaller number of degrees of freedom while minimizing the effect this reduction has on the dynamic behaviour of the main structure the approach taken here involves ritz reduction and the dirichlet to neumann map as analysis tools the resulting scheme is based on a special form of modal reduction and is shown to be optimal in a certain sense for long simulation times the performance of the scheme is demonstrated via numerical examples and is compared to that of standard modal reduction copyright c 2003 john wiley sons ltd

an integral transform approach for a mixed boundary problem involving a flowing partially penetrating well with infinitesimal well skin 1 a flowing partially penetrating well with infinitesimal well skin is a mixed boundary because a cauchy condition is prescribed along the screen length and a neumann condition of no flux is stipulated over the remaining unscreened part an analytical approach based on the integral transform technique is developed to determine the laplace domain solution for such a mixed boundary problem in a confined aquifer of finite thickness first the mixed boundary is changed into a homogeneous neumann boundary by substituting the cauchy condition with a neumann condition in terms of well bore flux that varies along the screen length and is time dependent despite the well bore flux being unknown a priori the modified model containing this homogeneous neumann boundary can be solved with the laplace and the finite fourier cosine transforms to determine well bore flux screen length is discretized into a finite number of segments to which the cauchy condition is reinstated this reinstatement also restores the relation between the original model and the solutions obtained for a given time the numerical inversion of the laplace domain solution yields the drawdown distributions well bore flux and the well discharge this analytical approach provides an alternative for dealing with the mixed boundary problems especially when aquifer thickness is assumed to be finite

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

time reversal with partial information for wave refocusing and scatterer identification time reversal is a well known procedure in application fields involving wave propagation among other uses it can be applied as a computational tool for solving certain inverse problems the procedure is based on advancing the solution of the relevant wave problem backward in time one important use of numerical time reversal is that of refocusing where a reverse run is performed to recover the location of a source applied at an initial time based on measurements at a later time usually only partial noisy information is available at certain measurement locations on the field values that serve as data for the reverse run in this paper the question concerning the amount and characterization of the available data needed for a successful refocusing is studied for the scalar wave equation in particular a simple procedure is proposed which exploits multiple measurement times and is shown to be very beneficial for refocusing a tradeoff between availability of spatial and temporal information is discussed the effect of measurement noise is studied and the technique is shown to be quite robust sometimes even in the presence of very high noise levels the use of the technique as a basis for scatterer identification is also discussed a numerical study of these effects is presented employing finite elements in space and a standard explicit marching scheme in time in contrast to some previous studies the propagation medium is taken to be homogeneous

induced damping by a nearly continuous distribution of nearly undamped oscillators linear analysis abstract the induced damping in a master oscillator contributed by a set of satellite oscillators is obtained in terms of a summation over a discrete distribution of the set the distribution is with respect to the resonance frequencies of the satellite oscillators in the set the distribution is cast in an ascending order and is assumed to be centered about the resonance frequency of the master oscillator in isolation if the modal overlap parameters are less than unity significant undulations are present in the induced damping the less the modal overlap parameters are compared with unity the more prominent are the undulations the undulations are largely suppressed when the local modal overlap parameters exceed unity moreover appropriately averaging the undulations yields values for the induced damping that coincide with those obtained when the modal overlap parameters exceed unity further it transpires that these common values are independent of the individual modal overlap parameters when the summation is replaced by an integration the first order results are undulations free and the values so obtained again coincide with those pertaining to modal overlap parameters that exceed unity without defining the excursions in the undulations the transition from a discrete to a continuous distribution that is implied by a summation to an integration must assume that the modal overlap parameters exceed unity in particular without careful and meaningful qualifications it may be misleading to assume a priori that the modal overlap parameters are equal to zero

considering the higher order effect of residual modes in the craig bampton method in this paper the accuracy of the craig bampton method one of the most widely used component mode synthesis methods is improved considering the higher order effect of residual modes that are si

reduced models for modal analysis of fluid structure systems taking into account compressibility and gravity effects abstract it is proposed to investigate and discuss from theoretical point of view various reduced order variational formulations for modal analysis of linear vibrations of bounded fluid structure systems with free surface taking into account possible gravity compressibility interactions in a non homogeneous fluid situation those formulations are based on substructural synthesis techniques and various modal reduction schemes are then obtained in a previous paper various original formulations have been exhibited associated to numerical validation the present paper starts from those formulations in order to construct theoretically various reduced order models

numerical techniques for the treatment of quasistatic viscoelastic stress problems in linear isotropic solids abstract for quasistatic stress problems two alternative constitutive relationships expressing the stress in a linear isotropic viscoelastic solid body as a linear functional of the strain are available in conjunction with the equations of equilibrium these form the mathematical models for the stress problems these models are first discretized in the space domain using a finite element method and semi discrete error estimates are presented corresponding to each constitutive relationship through the use respectively of quadrature rules and finite difference replacements each semi discrete scheme is fully discretized into the time domain so that two practical algorithms suitable for the numerical stress analysis of linear viscoelastic solids are produced the semi discrete estimates are then also extended into the time domain to give spatially h 1 error estimates for each algorithm the numerical schemes are predicated on exact analytical solutions for a simple model problem and finally on design data for a real polymeric material

the optimal projection equations for model reduction and the relationships among the methods of wilson skelton and moore first order necessary conditions for quadratically optimal reduced order modeling of linear time invariant systems are derived in the form of a pair of modified lyapunov equations coupled by an oblique projection which determines the optimal reduced order model this form of the necessary conditions considerably simplifies previous results of wilson 1 and clearly demonstrates the quadratic extremality and nonoptimality of the balancing method of moore 2 the possible existence of multiple solutions of the optimal projection equations is demonstrated and a relaxation type algorithm is proposed for computing these local extrema a component cost analysis of the model error criterion similar to the approach of skelton 3 is utilized at each iteration to direct the algorithm to the global minimum

a component mode selection method based on a consistent perturbation expansion of interface displacement abstract a mode selection method is presented for the reduced order modeling rom of structural systems in conjunction with the craig bampton component mode synthesis technique the proposed method is derived by using a consistent expansion of the interface displacement in terms of a frequency dependent small parameter as applied to a craig bampton like rom formulation it is found that this procedure yields a coupling mechanism of the modes of the full model to those of substructures the present mode selection method employs this coupling mechanism as an indicator labeled as the cms method for the substructural modal contributions to the full model the performance of the proposed method is demonstrated by various numerical examples and compared favorably with existing method such as the cms method

fuzzy structure theory modeling of sound insulation layers in complex vibroacoustic uncertain systems theory and experimental validation the fuzzy structure theory was introduced 20 years ago in order to model the effects of complex subsystems imprecisely known on a master structure this theory was only aimed at structural dynamics in this paper an extension of that theory is proposed in developing an elastoacoustic element useful to model sound insulation layers for computational vibroacoustics of complex systems the simplified model constructed enhances computation time and memory allocation because the number of physical and generalized degrees of freedom in the computational vibroacoustic model is not increased however these simplifications introduce model uncertainties in order to take into account these uncertainties the nonparametric probabilistic approach recently introduced is used a robust simplified model for sound insulation layers is then obtained this model is controlled by a small number of physical and dispersion parameters first the extension of the fuzzy structure theory to elastoacoustic element is presented

trax an approach for the time rational analysis of complex dynamic systems this paper introduces a theoretical and algorithmic reduced model approach to efficiently evaluate time responses of complex dynamic systems the proposed approach combines four main components analytical expressions of the average of the system s transfer functions in the frequency domain precise and convergent rational approximations of these exact expressions exact evaluation of these approximations through model reduction in rational krylov subspaces and semi analytical interpolation at just a few frequency points the resulting algorithmic principles to evaluate the time response of a particular system are relatively straightforward one first evaluates the response of the system with slight additional damping at a few frequencies and one then projects or reduces the system in the subspace spanned by these responses the time response of the reduced model implicitly provides a precise evaluation of that of the original system the properties of the reduced models and the precision of the proposed approach are studied and applications on complex matrix systems are presented and discussed while the theory and numerical algorithms are presented in a matrix context they are also transposable in a continuous functional context

vibration of a master plate with attached masses using modal sampling method at medium frequencies several problems deal with systems having a large number of modes where classical modal methods must cope with the solution of large linear systems the objective of the modal sampling method is to reduce these systems of equations in order to obtain a simplified model the vibration response of a structure is reconstructed using a limited number of modes called a sample to interpolate the response of other modes the accuracy of the prediction can be improved by increasing the size of the sample the method which has been developed in the case of a long beam is presented here in the case of a nonhomogeneous structure such as a large thin plate where point masses have been added the structure is excited by a harmonic point force or a planar acoustic wave a study of the convergence of the method shows that global quantities such as space and or frequency averaged energy converge quickly thus predictions can be obtained with models having few degrees of freedom moreover resu

mean and mean square responses of a prototypical master fuzzy structure analytical estimates are made for mean and mean square transient responses of a single degree of freedom master oscillator attached to an undamped n degree of freedom random substructure the ensemble averaged response is found to be asymptotically for a large number of substructural degrees of freedom in accord with the predictions of the pierce sparrow russell theory in particular the mean response of the master oscillator manifests an apparent damping corrections to this behavior are also predicted but are found to lie well below the root mean square level of the fluctuations the corrections are therefore for practical purposes unimportant the ensemble average of the square of the response is also investigated and found to take a value at later times that is in accord with simple equipartition arguments advanced in an earlier paper the power spectral density of the late time behavior is shown to be proportional to the square of the power spectrum of the early time response and thus to be a n

reduced order design oriented stress analysis using combined direct and adjoint solutions a new method for extracting accurate stress information from reduced order structural and aeroelastic models is presented the method has second order accuracy when approximate reduced order direct and adjoint solutions based on different reduced order bases are used simultaneously to obtain approximate stresses the method is applicable to both static and dynamic linear analysis a review of four common methods for structural model order reduction two variants of the mode displacement method standard mode displacement and the fictitious mass method the mode acceleration method and the ritz vector method identifies sources of difficulty and causes of errors in stress behavior sensitivity calculations considerations used for selection of the reduced order direct and adjoint bases are discussed a series of static and dynamic test cases is used to assess accuracy of the new method in an analysis mode accuracy studies of sensitivity calculations follow we hope to contribute to the field of design oriented structural dynamics in terms of both insight and practice

vibration modeling of structural fuzzy with continuous boundary from experiments it is well known that the vibration response of a main structure with many attached substructures often shows more damping than structural losses in the components can account for in practice these substructures which are not attached in an entirely rigid manner behave like a multitude of different sprung masses each strongly resisting any motion of the main structure master at their base antiresonance the theory of structural fuzzy is intended for modeling such high damping in the present article the theory of fuzzy structures is briefly outlined and a method of modeling fuzzy substructures examined this is done by new derivations and physical interpretations are provided further the method is extended and simplified by introducing a simple deterministic approach to determine the boundary impedance of the structural fuzzy by using this new approach the damping effect of the fuzzy with spatial memory is demonstrated by numerical simulations of a main beam structure with fuz

efficient modeling of flat and homogeneous acoustic treatments for vibroacoustic finite element analysis direct field formulations abstract this paper is concerned with the development of a simplified model for noise control treatments to speed up finite element analysis in vibroacoustic applications the methodology relies on the assumption that the acoustic treatment is flat and homogeneous moreover its finite lateral extent is neglected this hypothesis is justified by short wavelength and large dissipation which suggest that the reflected field emanating from the acoustic treatment lateral boundaries does not substantially affect its dynamic response under these circumstances the response of the noise control treatment can be formally obtained by means of convolution integrals involving simple analytical kernels i e green functions such fundamental solutions can be computed efficiently by the transfer matrix method however some arbitrariness arises in the formulation of the mathematical model resulting in different baffling conditions at the two ends of the treatment to be considered thus the paper investigates the possibility of different formulations i e baffling conditions within the same hybrid finite element transfer matrix framework seeking for the best strategy in terms of tradeoff between efficiency and accuracy numerical examples are provided to show strengths and limitations of the proposed methodology

an adaptive strategy for the bivariate solution of finite element problems using multivariate nested pade approximants most engineering applications involving solutions by numerical methods are dependent on several parameters whose impact on the solution may significantly vary from one to the other at times an ev

uncertainty in structural dynamics experimental validation of a wishart random matrix model in the modeling of complex dynamical systems high resolution finite element models are routinely adopted to reduce the discretization error such an approach may fail to enhance the confidence in simulation based predictions when the dynamical systems exhibit significant variability in the parameterization and description of the mathematical model due to parametric data uncertainty and model uncertainty in contrast to parametric uncertainty model uncertainty poses significant challenges as no explicit parameter is available a priori to characterize its behavior in the current investigation a set of sprung mass oscillators randomly attached to a baseline system namely a homogeneous cantilever plate gives rise to model uncertainty contrary to model parametric uncertainty traditionally tackled using stochastic finite element method sfem the model uncertainty arising from randomly attached sprung masses gives rise to a new variant of dynamical system for every sample the feasibility of adopting a wishart random matrix to represent such ensemble of dynamical systems derived from model perturbation is investigated in this paper the experiments conducted on a vibrating plate with randomly attached sprung mass oscillators demonstrate that the wishart random matrix model may provide a reasonable representation of model uncertainty in linear dynamical systems in the medium and high frequency region

statistical energy analysis and structural fuzzy the concepts and derivations of the effects of a minor or secondary structure on the dynamics of a well defined major or primary structure have been recently presented as a fuzzy structure interacting with a deterministic one on the face of it this appears like a halfway sea system in that one of the two systems is well defined while the other is probabilistic in the sea sense it is therefore interesting to see if a full sea treatment of the system would lead to difference in at least some of the quoted results the second and more important purpose of this paper is to relate the dynamics of potential minor structures to the properties of the fuzzy system since these properties have been presented in some of the fuzzy literature in rather general terms

multiple scattering theory for mean responses in a plate with sprung masses diagrammatic multiple scattering theory is applied to the case of an infinite homogeneous plate in flexure attached to a random distribution of sprung masses this system is a prototypical example of a wave bearing master structure with a locally reacting fuzzy substructure results for mean fields are obtained from the first order smoothing approximation the foldy average t matrix approximation and soven s coherent potential approximation the study of mean square responses is reserved to a later paper it is found that the attenuation as calculated by pierce et al j vib acoustics 117 339 348 1995 differs from that of the multiple scattering theory by a fractional amount which is small if the individual sprung masses are weak

uncertainty propagation in sea for structural acoustic coupled systems with non deterministic parameters abstract considering limited available information on uncertainties in structural acoustic coupled systems two methods namely the vertex method and the legendre orthogonal polynomial based method for predicting their dynamic behavior are developed based on the statistical energy analysis sea approach for the vertex method an efficient program for determining coordinates of all vertices of the rectangular spanned by entries of the involved interval input vector is coded which is well suited for an interval input vector in arbitrary dimension instead of calculating the extremum of the response of interest a method for determining its minimal and maximal point vectors dimension by dimension with respect to uncertain parameters is proposed based on the legendre orthogonal polynomial approximation following the theoretical analysis of the accuracy and efficiency of the proposed methods their validation is performed by one numerical example and two applications

a global local probabilistic approach for reduced order modeling adapted to the low and mid frequency structural dynamics abstract the research presented here is devoted to the construction of a probabilistic reduced order computational model adapted to the low and mid frequency structural dynamics the methodology presented here is based on a global local separation of the space of admissible displacements by solving two separated eigenvalue problems in which the kinetic energy is modified this paper presents a general framework for constructing the modified kinetic energy by introducing classes of kinematic reductions the global local separation allows the construction of a probabilistic model of uncertainties for which the fluctuations of the global displacements and the fluctuations of the local displacements can be controlled separately

a model and numerical method in the medium frequency range for vibroacoustic predictions using the theory of structural fuzzy in linear dynamical analysis of complex mechanical systems the structural fuzzy is defined as the set of minor subsystems that are connected to the master structure but are not accessible by classical modeling the notion of master structure is presently extended to others elements such as an external dense compressible fluid strongly coupled with the primary structure for the low frequency lf dynamical analysis the modeling of the structural fuzzy is commonly made with a system of masses if the lf modeling of the structural fuzzy is applied in the medium frequency mf domain there are some large differences between calculations and experiment it is therefore necessary to take into account internal degrees of freedom of the structural fuzzy a global probabilistic modeling of the structural fuzzy is proposed to improve the calculated estimates of the mf vibrations into the master structure and of the far field radiated by itself in or out of context of the acoustic scattering this paper reviews the author s previous work and introduces the type ii probabilistic constitutive law in this paper 1 a probabilistic modeling of the structural fuzzy is presented 2 two probabilistic constitutive laws of the structural fuzzy are constructed 3 the modeling in the mf range for vibroacoustic predictions using theory of structural fuzzy is developed 4 the fuzzy solution in the mf range is studied and 5 numerical simulations on standard structures and on a submerged complex industrial structure are shown

simple vibration modeling of structural fuzzy with continuous boundary by including two dimensional spatial memory many complicated systems of practical interest consist basically of a well defined outer shell like master structure and a complicated internal structure with uncertain dynamic properties using the fuzzy structure theory for predicting audible frequency vibration the internal structure is considered as one or more fuzzy substructures that are known in some statistical sense only experiments have shown that such fuzzy substructures often introduce a damping in the master which is much higher than the structural losses account for a special method for modeling fuzzy substructures with a one dimensional continuous boundary was examined in a companion paper l friis and m ohlrich vibration modeling of structural fuzzy with continuous boundary j acoust soc am 123 718 728 2008 in the present paper this method is extended such that it allows modeling of fuzzy substructures with a two dimensional continuous boundary additionally a simple method for determining the so called equivalent cou

model reduction and perturbation analysis of wave finite element formulations for computing the forced response of coupled elastic systems involving junctions with uncertain eigenfrequencies abstract the wave finite element method is investigated for computing the low and mid frequency forced response of coupled elastic systems involving straight structures with junctions the relevance of the method is discussed when a component mode synthesis procedure is used for modeling the junctions a norm wise selection criterion is proposed so as to reduce efficiently the number of junction modes retained in the wave based formulations component wise perturbation bounds of the wave based displacement force solutions are also derived to address slight uncertainties for the junction eigenfrequencies numerical comparisons with standard finite element solutions as well as monte carlo simulations highlight the relevance of the formulation

pade approximants and the modal connection towards increased robustness for fast parametric sweeps summary in order to increase the robustness of a pade based approximation of parametric solutions to finite element problems an a priori estimate of the poles is proposed the resulting original approach is shown to allow for a straightforward efficient subsequent pade based expansion of the solution vector components overcoming some of the current convergence and robustness limitations in particular this enables for the intervals of approximation to be chosen a priori in direct connection with a given choice of pade approximants the choice of these approximants as shown in the present work is theoretically supported by the montessus de ballore theorem concerning the convergence of a series of approximants with fixed denominator degrees key features and originality of the proposed approach are i a component wise expansion which allows to specifically target subsets of the solution field and ii the a priori simultaneous choice of the pade approximants and their associated interval of convergence for an effective and more robust approximation an academic acoustic case study a structural acoustic application and a larger acoustic problem are presented in order to demonstrate the potential of the approach proposed this article is protected by copyright all rights reserved

energy equipartition and frequency distribution in complex attachments as reported in several recent publications an undamped simple oscillator with a complex attachment that consists of a set of undamped parallel resonators can exhibit unusual energy sharing properties the conservative set of oscillators of the attachment can absorb nearly all the impulsive energy applied to the primary oscillator to which it is connected the key factor in the ability of the attachment to absorb energy with near irreversibility correlates with the natural frequency distribution of the resonators within it the reported results also show that a family of optimal frequency distributions can be determined on the basis of a variational approach minimizing a certain functional related to the system response the present paper establishes a link between these optimal frequency distributions and the energy equipartition principle optimal frequency distributions are those that spread the injected energy as uniformly as possible over the degrees of freedom or over the modes of the system theoretical as well as numerical results presented support this point of view

dominant dynamic characteristics of built up structures abstract an approach for evaluating the dominant dynamic characteristics of built up structures is presented based on a division of substructures and couplings into two groups primary and subordinate the approach is established by treating the members of the former group as precisely as possible whereas the descriptions of those in the latter group are simplified substantially two generic built up structures are discussed to illustrate how the approach promotes the understanding of the dynamic behaviour of built up structures and also to illustrate its application a corroboration of the applicability is provided from comparisons with the measured response of a shell beam plate structure

on the standard deviation of change in impedance due to fuzzy subsystems the effects of attached multiple subsystems of uncertain properties on the behavior of a main system are investigated by modeling the natural frequencies of the subsystems as random points in the frequency domain both the mean and the standard deviation of the change in impedance attributable to the subsystems are computed without the usual assumption of modal overlap it is shown that the standard deviation which has been overlooked by most authors on this subject can sometimes be greater than the mean thus the knowledge of the mean alone is inadequate to make engineering decisions

optimal modal reduction of dynamic subsystems extensions and improvements the problem of optimal reduction of a linear dynamic subsystem is revisited the subsystem may represent for example a complex but minor part of a large elastic structure the goal is to drastically reduce the number of degrees of freedom of a subsystem attached through an interface to a main system in such a way as to affect the dynamic behavior of the main system in the least possible way in a recent publication the optimal modal reduction omr algorithm was developed to this end this algorithm seeks a reduction of the subsystem that will have minimal effect in the l2 norm on the dirichlet to neumann dtn map on the interface here this algorithm is extended and improved in a number of ways first a family of alternative formulations are derived for the dtn map which lead to alternative omr algorithms one of them called omr j 2 is shown to yield better results than the original formulation second the omr algorithm which was originally developed for undamped subsystems is extended to subsystems undergoing rayleigh damping in addition an enhanced derivation of the original omr algorithm is presented and the good pointwise performance of omr is explained by relating to minimization with respect to the h1 norm the extensions mentioned above are discussed theoretically as well as demonstrated via numerical examples experiments and discussion include comparison of the omr algorithm to simple coarsening of the subsystem discretization in all cases central finite difference discretization in space and explicit time stepping are employed to solve the scalar wave equation copyright 2010 john wiley sons ltd

transient energy exchange between a primary structure and a set of oscillators return time and apparent damping in this paper we examine the conditions that influence the return time the time it takes before energy returns from a set of satellite oscillators attached to a primary structure two methods are presented to estimate the return time one estimate is based on an analysis of the reaction force on a rigid base by a finite number of oscillators as compared with an infinite number of continuously distributed oscillators the result gives a lower bound estimate for the return time a more accurate estimation results from considering the dynamic behavior of a set of oscillators as waves in a waveguide such an analogy explains energy flow between a primary structure and the oscillators in terms of pseudowaves and shows that a nonlinear frequency distribution of the oscillators leads to pseudodispersive waves the resulting approximate expressions show the influence of the natural frequency distribution within the set of oscillators and of their number on the return time as compared with the asymptotic case of a continuous set with infinite oscillators in the paper we also introduce a new method based on a hilbert envelope to estimate the apparent damping loss factor of the primary structure during the return time considering transient energy flow from the primary structure before any energy reflects back from the attached oscillators the expressions developed for return time and damping factor show close agreement with direct numerical simulations the paper concludes with a discussion of the return time and its relation to apparent damping and optimum frequency distribution within a set of oscillators that maximize these quantities

use of approximate discrete time models in filtering and regulation of continuous time processes a commonly used approximate discrete time model for the estimation of the states of linear continuous time invariant processes is analysed this analysis is performed by carefully defining and evaluating the true error covariance matrix of the estimate and by comparing it with what has been commonly believed to be the error covariance matrix it is shown that there exists a class of unstable processes for which the former error covariance matrix attains an unbounded norm in spite of the fact that the norm of the other error covariance matrix remains bounded it is also shown that for another class of processes the approximate model provides a particularly good estimation for short sampling periods based on the equations that govern the behaviour of the estimation error covariance matrices an alternative improved approximation is proposed that always leads to a true error covariance matrix with a bounded norm finally following similar lines of analysis it is shown that the approximate discrete time

time point relaxation methods for volterra integro differential equations abstract time point relaxation methods based on direct quadrature methods and on runge kutta methods for the numerical solution of volterra integro differential systems are proposed the convergence of the discrete time iterations is analyzed

estimation of fuzzy structure parameters for continuous junctions the fuzzy structure theory introduced 15 years ago is designed to predict the frequency response functions of structures and structural acoustic systems with structural complexity in the low and medium frequency ranges this paper constitutes a first validation of the fuzzy structure theory for continuous junctions between the master structure and the fuzzy substructures in addition a method to estimate the fuzzy structure parameters introduced in the fuzzy structure theory is presented and it is validated for the case of continuous junctions this validation obtained by numerical simulations opens the field of experimental identifications

convergence acceleration of fourier series by analytical and numerical application of poisson s formula a form of the poisson summation formula appropriate for the transformation of infinite fourier series is derived and shown to be applicable to slowly converging series arising in the solution of laplace s equation in a rectangular electrochemical cell the result is a rapidly convergent fourier series which is particularly useful in giving the potential close to the electrode surface results obtained from the analytical expression are found to be in close agreement with those resulting from numerical evaluation of the fourier integrals using simpson s rule and the euler transformation and direct summation by using goertzel s 1958 algorithm

response variance prediction for uncertain vibro acoustic systems using a hybrid deterministic statistical method imperfections during the manufacturing process can cause significant variations in the noise and vibration levels exhibited by nominally identical structures any response calculations employed during the design process should ideally take account of these uncertainties and predict the expected range in performance recently a hybrid method has been developed to predict the ensemble average response of a built up system by combining a deterministic model of parts of the system with a statistical model of other components shorter p j and langley r s 2005 j sound vib 288 669 700 in this paper the method is extended to predict the ensemble variance of the response expressions are derived for the variance of the vibrational energies in the statistical components and for the variance of the cross spectrum of the response of the deterministic components which augment the mean values of these quantities predicted by the original theory the method employs a nonparametric model of uncertainty in the sense that the statistical components are taken to carry diffuse wave fields and this obviates the requirement for a detailed description of the system uncertainties the method is validated by application to a range of coupled plate structures and good agreement with detailed monte carlo simulations is found

optimal discretization of continuous time linear filter and linear regulator and duality properties an algorithm for linear discretized filtering and its dual discretized quadratic coat optimal control for real time applications on continuous time systems is presented the algorithm is optimal in the sense of achieving the optimal approximation by discretized time processing to the ideal but non realizable continuous time processing it provides the possibility to choose the sampling rate beforehand by obtaining the corresponding error variance or the policy cost the problem s horizon can be finite properties and applications of the algorithm are explored the concept of duality is made apparent and given new insight

near irreversibility in a conservative linear structure with singularity points in its modal density through two complementary approaches using modal response and wave propagation the analyses presented here show the conditions under which a decaying impulse response or a nearly irreversible energy trapping takes place in a linear conservative continuous system the results show that the basic foundation of near irreversibility or apparent damping rests upon the presence of singularity points in the modal density of dynamic systems or analogously in the wave stopping properties associated with these singularities to illustrate the concept of apparent damping in detail a simple undamped beam is modified to introduce a singularity point in its modal density distribution simulations show that a suitable application of a compressive axial force to an undamped beam placed on an elastic foundation attenuates its impulse response with time and develops the characteristics of a nearly irreversible energy trap

the important modes of subsystems a moment matching approach substructure coupling methods such as the component mode synthesis cms method have been studied in structural dynamics analysis since 1960s the modes of subsystems associated with the lowest frequencies are typically retained in these methods in this paper we present a coupling matrix based mode selection scheme for the cms method referred to as the cms method this new scheme is derived using a moment matching principle defined on the interface between substructures it is compatible to the one in recently proposed optimal modal reduction omr method due to givoli et al the improvements of the cms method to the cms and omr methods are demonstrated by numerical examples from structural dynamics in both frequency and time domains copyright 2006 john wiley sons ltd

ritz volterra projections to finite element spaces and applications to integrodifferential and related equations the object of this paper is to investigate the convergence of finite element approximations to solutions of parabolic and hyperbolic integrodifferential equations and also of equations of sobolev and viscoelasticity type the concept of ritz volterra projection will be seen to unify much of the analysis for the different types of problems optimal order error estimates are obtained in l p for 2 leqq p infty and almost optimal order pointwise results given

an iterative substructuring approach to the calculation of eigensolution and eigensensitivity the eigensolutions and associated eigensensitivities of an analytical model are usually calculated at the global structure level which is time consuming or even prohibitive for large scale structures several substructuring approaches have been proposed that divide the global structure into some manageable substructures and assemble parts of the eigensolutions and eigensensitivities of the substructures to recover those of the global structure however these approaches are not usually accurate as only the lowest eigensolutions and eigensensitivities are retained and the higher modes are excluded in this paper a new iterative substructuring method is proposed to accurately obtain the eigensolutions and eigensensitivities of structures with this new approach the contribution of the higher modes to the reduced eigenequation is retained as a residual flexibility matrix in an iterated form which allows the eigenvalues and eigenvalue derivatives to be obtained from the previous results the eigenvectors and their derivative matrices can be calculated from a reduced eigenequation directly without iteration upon convergence the iterative scheme reproduces the eigensolutions and eigensensitivities of the original structure exactly the computational efficiency and numerical accuracy of the proposed method are verified by the applications to a cantilever plate structure and an actual super tall structure

a finite element method for domains with corners a new finite element method is devised for the numerical solution of elliptic boundary value problems with geometrical singularities in it the singularity is eliminated form the computational domain in an exact fashion this is in contrast to other common methods such as those which use a refined mesh in the singularity region or those which use special singular finite elements in them the singularity is treated as a part of the numerical scheme the new method is illustrated on an elliptic differential equation in a domain containing a re entrant corner numerical experiments show that the new method yields result which are generally much more accurate than those obtained by using the standard finite element method with mesh refinement in the singularity region both methods require about the same computing time

validity diagrams of statistical energy analysis abstract this paper is concerned with the validity domain of statistical energy analysis sea which is defined in terms of four criteria the mode count n and the modal overlap m must be high the normalized attenuation factor m and the coupling strength must be small the application of dimensional analysis on the governing equations of plates gives the space of dimensionless parameters in which the validity domain of sea must be delimited this domain is discussed on the basis of geometry of the surfaces delimiting it the diagrams of validity of sea are introduced and discussed a numerical simulation on a couple of rectangular plates coupled along one edge illustrates the theoretical approach

the modeling of a continuous structure as a fuzzy for a continuous structure with a deterministic drive it is suggested by example that 1 the loss factor invariance of its fuzzy limit is realized only when boundaries discontinuities away from the master structure measure many characteristic wavelengths so that the influence of their reflecting waves is negligible at the interface and 2 the value of the fuzzy limit depends on structural details as well as averaged or smoothed characteristics

dynamics of structures coupled with elastic media a review of numerical models and methods abstract this paper reviews issues and developments in the field of structure environment interaction problems in which the environment is an elastic body possibly unbounded it covers in particular the fields of soil structure interaction ground borne noise and vibration emitted by transportation systems and wave diffraction by obstacles in an elastic medium the general setting for a linear bounded structure coupled to an unbounded linear environment through a bounded interface is first recalled and the domain decomposition technique classically used for its description is put up extensions for the cases of nonlinear structure and uncertain environment are then discussed finally the ongoing research in the fields of unbounded interface moving interface and multiple interfaces are reviewed and summarized

shape factors for constant head double packer permeameters 1 local estimates of hydraulic conductivity are often obtained from constant head double packer tests the tests yield ratios of flow against head difference these are converted to values of hydraulic conductivity by dividing by a shape factor previously used shape factors have generally assumed that the packers are infinitely large such shape factors lead to overestimates of hydraulic conductivity as they ignore the effect of water flow around the packers a semianalytical solution is derived for a constant head double packer permeameter test the solution is compared with existing approximate techniques including the spheroidal equipotential solution the narrow packer approximation of rehbinder 1996 and the long packer approximation of rehbinder 2005 generally it is shown that ignoring the length of the packer and assuming a fully cased well lead to an overestimate of hydraulic conductivity the significance of this reduces with increasing well screen aspect ratio evaluation of the solution is nontrivial for this reason a polynomial relationship between shape factor well screen aspect ratio and packer length obtained by curve fitting with the semianalytical solution is provided

a hybrid method for the vibration analysis of complex structural acoustic systems a new method is presented for the analysis of complex dynamic systems which is based on partitioning the system degrees of freedom into a global set and a local set the global equations of motion are formulated and solved in a standard deterministic manner although due account is taken of the presence of the local degrees of freedom via an approach which is analogous to fuzzy structure theory the local equations of motion are formulated and solved by using statistical energy analysis sea with due account being taken of power input from the global degrees of freedom the method can be considered to encompass a number of existing analysis techniques and to form a flexible framework within which a number of detailed modeling strategies can be devised a simple rod system provides an initial application and it is shown that the method yields very good results from low to high frequency excitation