Comments on “Vibration Analysis of Arbitrary Shaped Membranes Using Non-Dimensional Dynamic Influence Function”

Chen, J.T.; Kuo, Shyh‐Rong; Chen, K.H.; Cheng, Yongling

doi:10.1006/jsvi.1999.2870

Cited by 20 publications

(17 citation statements)

References 19 publications

(36 reference statements)

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“…Simply speaking, their method took the response at any point inside the domain of interest as a linear combination of many non-singular point sources located on the selected boundary nodes. They claimed that their method worked very well and no numerical instability behaviours were reported, which was later criticized by Chen et al [11]. Kang's method is an indirect method such that it can represent mode shape easily.…”

Section: Introductionmentioning

confidence: 97%

Application of symmetric indirect Trefftz method to free vibration problems in 2D

Chang

Liu

Kuo

et al. 2003

Numerical Meth Engineering

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SUMMARYA symmetric indirect Tre tz method is developed to solve the free vibration problem of a 2D membrane. It is proved that in this approach the spurious eigensolution exists, and an auxiliary matrix is constructed to help extraction of the spurious solution using the generalized singular-value decomposition. In addition to the spurious eigensolution, this regular formulation su ers from its ill-posed nature, i.e. the numerical instability. In order to deal with the numerical instability, the Tikhonov's regularization method, in conjunction with the generalized singular-value decomposition, is suggested. The proposed approach has some merits when compared with other regular boundary element formulations reported so far; namely the capacity of representing eigenmodes and the ability to deal with a multiply connected domain of genus 1. Several numerical examples are demonstrated to show the validity of the current approach.

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Section: Introductionmentioning

confidence: 97%

Application of symmetric indirect Trefftz method to free vibration problems in 2D

Chang

Liu

Kuo

et al. 2003

Numerical Meth Engineering

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“…Recently, Kang et al (1999) employed the nondimensional dynamic in¯uence function (NDIF) method to solve the eigenproblem. Chen et al (2000b) commented that NDIF method is a special case of imaginary-part BEM. To deal with the ill-coditioned problem, Wu (1999) employed the generalized singular value decomposition (GSVD) in conjunction with the Tikhonov technique to regularize the ill-posed problem.…”

Section: Introductionmentioning

confidence: 98%

Analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using an efficient mixed-part dual BEM

Chen

Chung

Chen

2001

Computational Mechanics

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In this paper, we develop an ef®cient mixed-part dual BEM to solve the eigensolutions of a circular cavity analytically and numerically. The method is proposed by choosing a fewer number of equations from the dual BEM instead of all of the equations in the dual BEM developed by Chen and his coworkers. To solve this problem analytically, the spurious solution can be ®ltered out by adding constraints from the dual boundary integral equations. The proposed method is superior to the complex-valued BEM not only for half effort in constructing the in¯uence matrix, but also for its fewer size of dimension. Also, numerical experiments are performed to compare with the analytical results and the true eigensolutions can be easily extracted out in conjunction with the singular value decomposition technique (SVD). The optimum number of collocation point and appropriate collocating positions for the additional constraints are discussed.

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“…Recently, Kang and Lee [15] employed the non-dimensional dynamic influence function (NDIF) method to solve the eigenproblem of an acoustic cavity. Chen et al [16] commented that the NDIF method is a special case of the MFS with imaginary-part kernel and later further revisited this method in a series of works [17,18]. Later, Kang and Lee [19] extended the NDIF for plate vibrations with clamped boundary condition.…”

Section: Introductionmentioning

confidence: 99%

Method of Fundamental Solutions for Plate Vibrations in Multiply Connected Domains

2006

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This paper develops the method of fundamental solutions (MFS) to solve eigenfrequencies of plate vibrations of multiply connected domains. The complex-valued MFS combined with the mix potential method are utilized in order to avoid the spurious eigenvalues. The benchmarked problems of annular plates with clamped, simply supported and free boundary conditions are studied analytically as well as numerically. Wherein the results demonstrate that all true eigenvalues are contained and no spurious eigenvalues are included. In the analytical studies, the continuous version of the MFS is utilized to obtain the eigenequation by applying the degenerate kernels and Fourier series. The proposed numerical method is free from singularities, meshes, and numerical integrations and thus can be easily utilized to solve plate vibrations free from spurious eigenvalues in multiply connected domains.

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Comments on “Vibration Analysis of Arbitrary Shaped Membranes Using Non-Dimensional Dynamic Influence Function”

Cited by 20 publications

References 19 publications

Application of symmetric indirect Trefftz method to free vibration problems in 2D

Application of symmetric indirect Trefftz method to free vibration problems in 2D

Analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using an efficient mixed-part dual BEM

Method of Fundamental Solutions for Plate Vibrations in Multiply Connected Domains

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