Initial conditions in frequency-domain analysis: the FEM applied to the scalar wave equation

Mansur, Webe João; Soares, Delfim; Ferro, M. A. C.

doi:10.1016/s0022-460x(03)00256-6

Cited by 28 publications

(19 citation statements)

References 12 publications

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“…This limitation is overcome in the present work by employing an original methodology denoted initial conditions by pseudoforces (ICPF). The ICPF was already successfully employed in a BEM formulation [13] and in a FEM formulation [14], both for the frequency-domain analysis of transient scalar wave propagation. Although the ICPF is a quite original methodology, it is based on a simple idea: the initial conditions, related to the potential and its time derivative, can be replaced by equivalent pseudo-forces without introducing any modification in the final results of the analysis.…”

Section: Introductionmentioning

confidence: 99%

Initial conditions contribution in a BEM formulation based on the convolution quadrature method

Abreu

Mansur

Carrer

2006

Int. J. Numer. Meth. Engng

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SUMMARYThis work presents a two-dimensional boundary element method (BEM) formulation for the analysis of scalar wave propagation problems. The formulation is based on the so-called convolution quadrature method (CQM) by means of which the convolution integral, presented in time-domain BEM formulations, is numerically substituted by a quadrature formula, whose weights are computed using the Laplace transform of the fundamental solution and a linear multistep method. This BEM formulation was initially developed for scalar wave propagation problems with null initial conditions. In order to overcome this limitation, this work presents a general procedure that enables one to take into account non-homogeneous initial conditions, after replacing the initial conditions by equivalent pseudo-forces. The numerical results included in this work show the accuracy of the proposed BEM formulation and its applicability to such kind of analysis.

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Section: Introductionmentioning

confidence: 99%

Initial conditions contribution in a BEM formulation based on the convolution quadrature method

Abreu

Mansur

Carrer

2006

Int. J. Numer. Meth. Engng

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“…One of the problems in using the Fourier transform method is how to deal with the nonzero initial conditions for structural systems with various damped models. Here by using the pseudo-force approach [31,58,59], we transform the original equations of motion with nonzero initial conditions into an equivalent one with zero initial conditions.…”

Section: Fourier Transform Methods For Structural Systems With Variousmentioning

confidence: 99%

Dynamics of structural systems with various frequency-dependent damping models

Deng

et al. 2015

Front. Mech. Eng.

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The aim of this paper is to present the dynamic analyses of the system involving various damping models. The assumed frequency-dependent damping forces depend on the past history of motion via convolution integrals over some damping kernel functions. By choosing suitable damping kernel functions of frequency-dependent damping model, it may be derived from the familiar viscoelastic materials. A brief review of literature on the choice of available damping models is presented. Both the mode superposition method and Fourier transform method are developed for calculating the dynamic response of the structural systems with various damping models. It is shown that in the case of non-deficient systems with various damping models, the modal analysis with repeated eigenvalues are very similar to the traditional modal analysis used in undamped or viscously damped systems. Also, based on the pseudo-force approach, we transform the original equations of motion with nonzero initial conditions into an equivalent one with zero initial conditions and therefore present a Fourier transform method for the dynamics of structural systems with various damping models. Finally, some case studies are used to show the application and effectiveness of the derived formulas.

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“…This method uses the existing FEM procedures to obtain the stiffness matrix, K, the mass matrix, M and damping matrix, C of the basis cell (or elements). Dynamic equation involved is then solved in the frequency domain using FFT method [2]- [4].…”

Section: Introductionmentioning

confidence: 99%

Lamb wave propagation using Wave Finite Element Method

Ahmad

Perez

Willberg

et al. 2009

Proc Appl Math and Mech

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Some of the available techniques for Lamb wave propagation simulation are the Finite Element Method (FEM), the Boundary Element Method and the Finite Difference Method. The FEM is the best method when complex damage, geometry or boundary is involved. However, high Lamb wave frequency requires very small element size thus high computational cost in FEM analysis. By using the existence of periodicity in plates, an attempt to reduce this computational cost is done using Wave FEM. The applicability of this method to model Lamb wave propagation in plate is first assessed in this paper for the 1-D wave propagation and compared with FEM explicit method.

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Initial conditions in frequency-domain analysis: the FEM applied to the scalar wave equation

Cited by 28 publications

References 12 publications

Initial conditions contribution in a BEM formulation based on the convolution quadrature method

Initial conditions contribution in a BEM formulation based on the convolution quadrature method

Dynamics of structural systems with various frequency-dependent damping models

Lamb wave propagation using Wave Finite Element Method

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