Browse > Article
http://dx.doi.org/10.5050/KSNVN.2007.17.6.531

Free Vibration Analysis of Clamped Plates with Arbitrary Shapes Using Series Functions  

Kang, Sang-Wook (한성대학교 기계시스템공학과)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.17, no.6, 2007 , pp. 531-538 More about this Journal
Abstract
A new method for free nitration analysis using series functions is proposed to obtain the eigenvalues of arbitrarily shaped, polygonal plates with clamped edges. Since a general solution used in the method satisfies the equation of motion for the transverse vibration of a plate, the method offers very accurate eigenvalues, compared to FEM or BEM results. In addition, the method can minimize the amount of numerical calculation because it has the advantage of not needing to divide the plate of interest. Two case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed method are compared to those by FEM (NASTRAN) or another analytical method.
Keywords
Series Function; Clamped Plate; Free Vibration; Arbitrarily Shaped Polygonal Plate; Eigenvalue; Clamped Boundary Condition;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Conway, H. D. and Farnham, K. A., 1965, 'The Free Flexural Vibration of Triangular, Rhombic and Parallelogram Plates and Some Analogies', International Journal of Mechanical Sciences, Vol. 7, pp. 811-816   DOI   ScienceOn
2 Mclachlan, N. W., 1947, 'Vibrational Problems In Elliptical Coordinates', Quarterly Applied Mathematics, Vol. 5, pp. 289-297   DOI
3 Conway, H. D., 1961, 'The Bending, Buckling, and Flexural Vibration of Simply Supported Polygonal Plates by Point-matching', American Society of Mechanical Engineers Journal of Applied Mechanics, Vol. 28, pp. 288-291   DOI
4 Bathe, K., 1982, Finite Element Procedures in Engineering Analysis. New Jersey: Prentice-Hall
5 Mavriplis, D. J., 1990, 'Accurate Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes', AIAA Journal, Vol. 28, No.2, pp. 213-221   DOI
6 Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C., 1984, Boundary Element Techniques, New York: Springer-Verlag
7 Kang, S. W. and Lee, J. M., 1999, 'Vibration Analysis of Arbitrarily Shaped Membrane Using Non-dimensional Dynamics Influence Function', Journal of Sound and Vibration, Vol. 221, pp. 117-132   DOI   ScienceOn
8 Blevins, R. D., 1979, 'Formulas for Natural Frequency and Mode Shape', New York: Litton Educational Publishing
9 Kang, S. W., et. al., 2003, 'Free Vibration Analysis of Arbitrarily Shaped Plates With Free Edges Using Non-dynamic Influence Functions', Transactions of the Korea Society for Noise and Vibration Engineering, Vol. 13, No. 10, pp. 821-827   과학기술학회마을   DOI   ScienceOn
10 Kim, Y. Y. and Kim, D. K., 1999, 'Applications of Waveguide-Type Base Functions for the Eigenproblems of Two-dimensional Cavities', J. Acoust. Soc. Amer. Vol. 106, pp. 1704-1711   DOI
11 Meirovitch, L., 1967, Analytic Methods in Vibrations, New York: Nacmillan Publishing, pp. 179-182
12 Kang, S. W., 2007, 'Free Vibration Analysis of Arbitrarily Shaped Polygonal Plates with Free Edges by Considering the Phenomenon of Stress Concentration at Comers', Transactions of the Korea Society for Noise and Vibration Engineering, Vol. 17, No. 3, pp. 220-225   과학기술학회마을   DOI   ScienceOn
13 Dickinson, S. M., 1978, 'The Buckling and Frequency of Flexural Vibration of Rectangular, Isotropic and Orthotropic Plates Using Rayleigh's Method', Journal of Sound and Vibration Vol. 61, pp. 1-8   DOI   ScienceOn
14 Kim, Y. Y. and Kang, J. H., 1996, 'Free Vibration Analysis of Membranes Using Wave-Type Base Functions', J. Acoust. Soc. Amer., Vol. 99, No. 5, pp, 2938-2946   DOI   ScienceOn
15 Kang, S. W. and Lee, J. M., 2001, 'Free Vibration Analysis of Arbitrarily Shaped Plates with Clamped Edges Using Wave-type Functions', Journal of Sound and Vibration, Vol. 242, No. 1, pp. 9-26   DOI   ScienceOn
16 Singh, B. and Chakraverty, S. 1992, 'Transverse Vibration of Simply Supported Elliptical and Circular Plates Using Boundary Characteristic Orthogonal Polynomials in Two Variables', Journal of Sound and Vibration, Vol. 152, No.1, pp. 149-155   DOI   ScienceOn
17 Kang, S. W. and Lee, J. M. 2000, 'Application of Free Vibration Analysis of Membranes Using the Non-dimensional Dynamics Influence Function', Journal of Sound and Vibration, Vol. 234, No. 3, pp. 455-470   DOI   ScienceOn
18 Kang, S. W. 2002, 'Free Vibration Analysis of Arbitrarily Shaped Plates with a Mixed Boundary Condition Using Non-dimensional Dynamic Influence Functions', Journal of Sound and Vibration, Vol. 256, No. 3, pp. 533-549   DOI   ScienceOn