Eigensolutions of multiply connected membranes using the method of fundamental solutions

Chen, Jeng‐Tzong; Chen, I. L.; Lee, Ying‐Te

doi:10.1016/j.enganabound.2004.10.005

Cited by 59 publications

(36 citation statements)

References 22 publications

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“…Since the MFS is highly ill conditioned, the determinant is very small. So, using this technique in the 2D case, one operates with values of the order ∼ 10 −50 -10 −500 , see [24,37] for more detailed information.…”

Section: One-dimensional Casementioning

confidence: 99%

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The Methods of External Excitation for Analysis of Arbitrarily-Shaped Hollow Conducting Waveguides

Reutskiy¹

2008

PIER

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Abstract-A new numerical technique is proposed for analyzing arbitrary shaped hollow waveguides.The method is based on mathematically modelling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. The results of the numerical experiments justifying the method are presented. The method is validated by circular waveguide, rectangular waveguide an equilateral triangular waveguide. We apply the method for multi connected domains and for waveguides with boundary singularities like the Lshaped waveguide. Good agreements between the simulated and the published results have been obtained. The method does not generate spurious eigenfrequencies.

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Section: One-dimensional Casementioning

confidence: 99%

“…This equation must be investigated analytically or numerically to get the eigenvalues This technique is described in [19][20][21][22][23][24] in more details. In the three latest papers there is a complete bibliography on the subject considered.…”

Section: Introductionmentioning

confidence: 99%

The Methods of External Excitation for Analysis of Arbitrarily-Shaped Hollow Conducting Waveguides

Reutskiy¹

2008

PIER

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“…Detailed descriptions and comparisons of the MQ method and the MFS can be found in [9]. Specially, the MFS performed better for eigenproblems [10,11].…”

Section: Introductionmentioning

confidence: 99%

The Method of Fundamental Solutions with Dual Reciprocity for thin Plates on Winkler Foundations with Arbitrary Loadings

Tsai

2008

J. mech.

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This paper describes the combination of the method of fundamental solutions (MFS) and the dual reciprocity method (DRM) as a meshless numerical method to solve problems of thin plates resting on Winkler foundations under arbitrary loadings, where the DRM is based on the augmented polyharmonic splines constructed by splines and monomials. In the solution procedure, the arbitrary distributed loading is first approximated by the augmented polyharmonic splines (APS) and thus the desired particular solution can be represented by the corresponding analytical particular solutions of the APS. Thereafter, the complementary solution is solved formally by the MFS. In the mathematical derivations, the real coefficient operator in the governing equation is decomposed into two complex coefficient operators. In other words, the solutions obtained by the MFS-DRM are first treated in terms of these complex coefficient operators and then converted to real numbers in suitable ways. Furthermore, the boundary conditions of lateral displacement, slope, normal moment, and effective shear force are all given explicitly for the particular solutions of APS as well as the kernels of MFS. Finally, numerical experiments are carried out to validate these analytical formulas.

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“…The slope (θ ), normal moment (m) and effective shear force (v), are also obtained as reference (Ref. [7]). In order to derive the exact eigensolution, degenerate kernel and circulant are considered for an annular plate.…”

Section: Analytical Derivation Of Free Vibration For Annular Plate Usmentioning

confidence: 99%

“…The two kernels (P and Q) are obtained from either the two of the kernel U (s, x) and the other three kernels, (s, x), M(s, x) and V (s, x) (Ref. [7]). The slope (θ ), normal moment (m) and effective shear force (v), are also obtained as reference (Ref.…”

Section: Analytical Derivation Of Free Vibration For Annular Plate Usmentioning

confidence: 99%

Free Vibration Analysis of Multiply Connected Plates Using the Method of Fundamental Solutions

Lee

Chen

Computational Methods

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In this paper, the method of fundamental solutions (MFS) for solving the eigenfrequencies of multiply connected plates is proposed. The coefficients of influence matrices are easily determined when the fundamental solution is known. True and spurious eigensolutions appear at the same time. It is found that the spurious eigensolution using the MFS depends on the location of the inner boundary where the fictitious sources are distributed. To verify this finding, mathematical analysis for the appearance of spurious eigenequations using degenerate kernels and circulants is done by demonstrating an annular plate with a discrete model. In order to obtain the true eigensolution, the Burton & Miller method is utilized to filter out the spurious eigensolutions. One example is demonstrated analytically and numerically to see the validity of the present method.

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Eigensolutions of multiply connected membranes using the method of fundamental solutions

Cited by 59 publications

References 22 publications

The Methods of External Excitation for Analysis of Arbitrarily-Shaped Hollow Conducting Waveguides

The Methods of External Excitation for Analysis of Arbitrarily-Shaped Hollow Conducting Waveguides

The Method of Fundamental Solutions with Dual Reciprocity for thin Plates on Winkler Foundations with Arbitrary Loadings

Free Vibration Analysis of Multiply Connected Plates Using the Method of Fundamental Solutions

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