The method of fundamental solutions for eigenfrequencies of plate vibrations

Computers, Materials and Continua

Volumn 4, Issue 1, 2006, Pages 1-10

  Young, D L ^a   Tsai, C C ^b   Lin, Y C ^a   Chen, C S ^c  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^b TOKO UNIVERSITY   (Taiwan)

^c University of Southern Mississippi   (United States)

Author keywords

Circular plate; Clamped; Free boundary conditions; Method of fundamental solutions; Plate vibration analysis; Simply supported; Spurious eigenvalues

Indexed keywords

CIRCULAR PLATE; METHOD OF FUNDAMENTAL SOLUTIONS; PLATE VIBRATION ANALYSIS; SPURIOUS EIGENVALUES;

BOUNDARY CONDITIONS; NUMERICAL METHODS; PLATES (STRUCTURAL COMPONENTS); PROBLEM SOLVING; VIBRATIONS (MECHANICAL);

EIGENVALUES AND EIGENFUNCTIONS;

EID: 33749837530     PISSN: 15462218     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Abramowitz, M.; Stegun, I.A. (1972): Handbook of mathematical functions with formulation, graphs and mathematical tables. Dover, New York.
2. Atluri, S.N.; Han, Z.D.; Rajendran, A.M. (2004): A new implementation of the meshless finite volume method, through the MLPG "Mixed" approach. CMES: Computer Modeling in Engineering & Sciences, Vol. 6(6), pp. 491-513.
3. th order ODE: illustration of various primal & mixed MLPG methods. CMES: Computer Modeling in Engineering & Sciences, Vol. 7(3), pp. 241-268.
4. Chen, C.W.; Fan, C.M.; Young, D.L.; Murugesan, K.; Tsai, C.C. (2005): Eigenanalysis for membranes with stringers using the methods of fundamental solutions and domain decomposition. CMES: Computer Modeling in Engineering and Sciences, vol. 8, pp. 29-44.
5. Chen, J.T.; Lin, S.Y.; Chen, K.H.; Chen, I.L. (2004): Mathematical analysis and numerical study of true and spurious eigenequations for free vibration of plates using real-part BEM. Comput. Mech., vol. 34, pp. 165-180.
6. Chen, J.T.; Kou, S.R.; Chen, K.H.; Cheng, Y.C. (2003): Comments on "Free vibration analysis of arbitrary shaped plates with clamped edges using wave-type functions". J. Sound Vibr., vol. 262, pp. 370-378.
7. Chen, J.T.; Chen, I.L.; Chen, K.H.; Lee, Y.T.; Yeh, Y.T. (2004): A meshless method for free vibration analysis of circular and rectangular clamped plates using radial basis function. Eng. Anal. Bound. Elem., vol. 28, pp. 535-545.
8. Cho, H.A.; Golberg, M.A.; Muleshkov, A.S.; Li, X. (2004): Trefftz methods for time dependent partial differential equations. CMC: Computers, Materials, and Continua, vol. 1, pp. 1-37.
9. Fairweather, G.; Karageorghis, A. (1998): The method of fundamental solutions for elliptic boundary value problems. Adv. Comput. Math., vol. 9, pp. 69-95.
10. Fairweather, G.; Karageorghis, A.; Martin, P.A. (2003): The method of fundamental solutions for scattering and radiation problems. Eng. Anal. Bound. Elem., vol. 27, pp. 759-769.
11. Golberg, M.A.; Chen, C.S. (1998): The method of fundamental solutions for potential, Helmholtz and diffusion problems. In: Boundary integral methods: numerical and mathematical aspects, M.A. Golberg, (ed.), Computational Mechanics Publications, Boston, pp. 103-176.
12. Han, Z.D.; Atluri, S.N. (2004): A meshless local Petrov-Galerkin (MLPG) approach for 3-dimensional elasto-dynamics. CMC: Computers, Materials, & Continua, vol. 1(2), pp. 129-140.
13. Hutchinson, J.R. (1988): Vibration of plates, In: Boundary elements X, C.A. Brebbia (ed.) Springer, Berlin, pp. 413-430.
14. Hutchinson, J.R. (1991): Analysis of plates and shells by boundary collocation, In: Boundary elements analysis of plates and shells, D.E. Beskos (ed.) Springer, Berlin, pp. 314-368.
15. Ito, K.; Crandall, S.H. (1979): Natural modes and natural frequencies of uniform, circular, free-edge plates. J. App. Mech., vol. 46, pp. 448-453.
16. Kang, S.W.; Lee, J.M. (2001): Free vibration analysis of arbitrary shaped plates with clamped edges using wave-type functions. J. Sound Vibr., vol. 242, pp. 9-26.
17. Kang, S.W. (2002): Free vibration analysis of arbitrary shaped plates with a mixed boundary condition using non-dimensional dynamic influence functions. J. Sound Vibr., vol. 256, pp. 533-549.
18. Karageorghis, A. (2001): The method of fundamental solutions for the calculation of the eigenvalues of the Helmholtz equation. Appl. Math. Letters, vol. 14, pp. 837-842.
19. Kitahara, M. (1985): Boundary integral equation methods in eigenvalue problems of elastodynamics and thin plates, Elsevier, Amsterdam.
20. Kondapalli, P.S.; Shippy, DJ.; Fairweather, G. (1992): Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions. J. Acoust. Soc. Am., vol. 91, pp. 1844-1854.
21. Kupradze, V.D.; Aleksidze, M.A. (1964): The method of functional equations for the approximate solution of certain boundary value problem. USSR Comut. Math. Math. Phys., vol. 4(4), pp. 82-126.
22. Leissa, A.W. (1969) Vibration of Plates, NASA SP-160, U.S. Government Printing Office, Washington, D.C. (Reprinted by the Acoustical Society of America, 1993)
23. Leissa, A.W.; Laura, P.A.A.; Gutierrez, R.H. (1979): Transverse vibrations of circular plates having nonuniform edge constraints. J. Acoust. Soc. Am., vol. 66, pp. 180-184.
24. Leissa, A.W.; Narita, Y. (1980): Natural frequencies of simply supported circular plates. J. Sound Vibr., vol. 70, pp. 221-229.
25. Li, Q.; Soric, J.; Jarak, T.; Atluri, S.N. (2005): A locking-free meshless local Petrov-Galerkin formulation for thick and thin plates. J. Comput. Phys., vol. 208(1), pp. 116-133.
26. Soric, J.; Li, Q.; Jarak, T.; Atluri, S.N. (2004): Meshless local Petrov-Galerkin (MLPG) formulation for analysis of thick plates. CMES: Computer Modeling in Engineering & Sciences, Vol. 6(4), pp. 349-357.
27. Young, D.L.; Hu, S.P.; Chen, C.W.; Fan C.M.; Murugesan, K. (2005): Analysis of elliptical waveguides by method of fundamental solutions. Microwave and Optical Technology Letters, vol. 44, pp. 552-558.
28. Young, D.L.; Ruan, J.W. (2005): Method of fundamental solutions for scattering problems of electromagnetic wave. CMES: Computer Modeling in Engineering and Sciences, vol. 7, pp. 223-232.