Vibration Analysis of Arbitrarily Shaped Membranes Using Non-Dimensional Dynamic Influence Function

Kang, Sang Wook; Lee, J.M.; Kang, Yeon June

doi:10.1006/jsvi.1998.2009

Cited by 90 publications

(91 citation statements)

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“…This inconsistency is due to that our formulations are of the direct type BEM. Kang's method [23] will not encounter such di$culties since their method is not of the direct BEM. The above BEM formulations, no matter they are singular or regular, are incomplete.…”

Section: Construction Of Various Bem Formulationsmentioning

confidence: 99%

“…They pointed out that some incorrect answers would appear and they also explained this phenomenon as incompleteness of base functions. Later, Kang et al [23] proposed another regular formulation using the so-called non-dimensional dynamic in#uence function. 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.…”

Section: Introductionmentioning

confidence: 99%

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Applications of the Generalized Singular-Value Decomposition Method on the Eigenproblem Using the Incomplete Boundary Element Formulation

Kuo

Yeih

2000

Journal of Sound and Vibration

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In this paper, four incomplete boundary element formulations, including the real-part singular boundary element, the real-part hypersingular boundary element, the imaginary-part boundary element and the plane-wave element methods, are used to solve the free vibration problem. Among these incomplete boundary element formulations, the real-part singular and the hypersingular boundary elements are of the singular type and the other two are of the regular type. When the incomplete formulation is used, the spurious eigensolution may be encountered. An auxiliary system, whose boundary conditions are linearly independent of those of the original system, is required in the proposed method in order to eliminate the spurious eigensolution. A mathematical proof is given to show that the spurious eigensolution will appear in both the original and auxiliary systems. As a result, one can eliminate spurious eigensolution by means of the generalized singular-value decomposition method. In addition to the spurious eigensolution problem, the regular boundary element formulation further su!ers ill-conditioned behaviors in the problem solver. It is explained analytically using a circular domain why ill-conditioned behaviors exist. Two main ill-conditioned problems are the numerical instability of solution and the nonexistence of solution. To solve the numerical instability of solution problem existing in these proposed regular formulations, the Tikhonov's regularization technique is used to improve the condition number of the leading coe$cient matrix; further, the generalized singular-value decomposition method is used to eliminate spurious eigensolutions. Numerical examples are given to verify the performance of these proposed methods, and the results match the analytical values well.

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Section: Construction Of Various Bem Formulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Applications of the Generalized Singular-Value Decomposition Method on the Eigenproblem Using the Incomplete Boundary Element Formulation

Kuo

Yeih

2000

Journal of Sound and Vibration

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“…In these homogeneous problems can be solved by using n's function method. The problem of oscillation of a regular shaped system is solved by using approximate (numerical) methods [5]. The method of fundamental solutions can be used as an example of such media of regular shapes (rectangle, circle), an exact solution to…”

Section: Introductionmentioning

confidence: 99%

Chiral Wave Modes in Elliptical Region

Torres-Silva¹,

Cabezas²

2016

IJAERS

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“…1,2,7 However, a survey of the literature performed by the authors reveals that only a very few articles of them dealt with concavely shaped membranes and plates.…”

Section: Introductionmentioning

confidence: 99%

Improved non-dimensional dynamic influence function method based on tow-domain method for vibration analysis of membranes

Kang

Atluri

2015

Advances in Mechanical Engineering

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This article introduces an improved non-dimensional dynamic influence function method using a sub-domain method for efficiently extracting the eigenvalues and mode shapes of concave membranes with arbitrary shapes. The nondimensional dynamic influence function method (non-dimensional dynamic influence function method), which was developed by the authors in 1999, gives highly accurate eigenvalues for membranes, plates, and acoustic cavities, compared with the finite element method. However, it needs the inefficient procedure of calculating the singularity of a system matrix in the frequency range of interest for extracting eigenvalues and mode shapes. To overcome the inefficient procedure, this article proposes a practical approach to make the system matrix equation of the concave membrane of interest into a form of algebraic eigenvalue problem. It is shown by several case studies that the proposed method has a good convergence characteristics and yields very accurate eigenvalues, compared with an exact method and finite element method (ANSYS).

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Vibration Analysis of Arbitrarily Shaped Membranes Using Non-Dimensional Dynamic Influence Function

Cited by 90 publications

References 0 publications

Applications of the Generalized Singular-Value Decomposition Method on the Eigenproblem Using the Incomplete Boundary Element Formulation

Applications of the Generalized Singular-Value Decomposition Method on the Eigenproblem Using the Incomplete Boundary Element Formulation

Chiral Wave Modes in Elliptical Region

Improved non-dimensional dynamic influence function method based on tow-domain method for vibration analysis of membranes

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