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http://dx.doi.org/10.5050/KSNVE.2015.25.11.779

Extraction of Accurate Eigenvalues of Plates Using a Meshless Method  

Kang, Sangwook (Hansung University)
Woo, Yoonhwan (Hansung University)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.25, no.11, 2015 , pp. 779-786 More about this Journal
Abstract
The Kansa method, which is used for various free vibration problems of arbitrarily shaped plates including membranes, discretizes the domain of a plate using only nodes without elements unlike FEM. The method requires a small amount of computation relative to FEM thanks to this discretization scheme but has limit in the accuracy of its solution. This paper reveals the reason of the limit and, to overcome the limit, proposes the practical method of calculating the singularity of a system matrix and extracting accurate natural frequencies. Case studies for a rectangular plate and an arbitrarily shaped plate validate the proposed method.
Keywords
Meshless Method; Kansa Method; Natural Frequency; Plate; Simply Supported;
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Times Cited By KSCI : 3  (Citation Analysis)
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1 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, No. 1, pp. 117-132.   DOI
2 Bathe, K., 1982, Finite Element Procedures in Engineering Analysis, Prentice-Hall, New Jersey.
3 Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C., 1984, Boundary Element Techniques, Springer-Verlag, New York.
4 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
5 Kang, S. W., 2007, Free Vibration Analysis of Arbitrarily Shaped Polygonal Plates with Free Edges by Considering the Phenomenon of Stress Concentration at Corners, Transactions of the Korea Society for Noise and Vibration Engineering, Vol. 17, No. 3, pp. 220-225.   DOI
6 Kang, S. W., Kim, I. S. and Lee, J. M., 2008, Free Vibration Analysis of Arbitrarily Shaped Plates with Smoothly Varying Free Edges using NDIF Method, Journal of Vibration and Acoustics, Vol. 130, No. 4, pp. 041010.1-041010.8.
7 Kang, S. W. and Kim, J. G., 2009, A Formulation of NDIF Method to the Algebraic Eigenvalue Problem for Efficiently Extracting Natural Frequencies of Arbitrarily Shaped Plates with the Simply Supported Boundary Condition, Transactions of the Korean Society for Noise and Vibration Engineering. Vol. 19, No. 6, pp. 607-613.   DOI
8 Kang, S. W., Kim, S. H. and Atluri, S., 2012, Application of the Nondimensional Dynamic Influence Function Method for Free Vibration Analysis of Arbitrarily Shaped Membranes, Journal of Vibration and Acoustics, Vol. 134, No. 4, pp. 041008.1-041008.8.
9 Kang, S. W. and Yon, J. I., 2013, New Formulation of MNDIF Method for Extracting Accurate Natural Frequencies of Plates, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 23, No. 8, pp. 725-733.   DOI
10 Kang, S. W. and Atluri, S., 2015, Improved Non-dimensional Dynamic Influence Function Method Based on Two-domain Method for Vibration Analysis of Membranes, Advances in Mechanical Engineering, Vol. 7, No. 2, pp. 1-8.
11 Tiago, C. M. and Leitao, V. M. A., 2006, Application of Radial Basis Functions to Linear and Nonlinear Structural Analysis Problems, Computers and Mathematics with Applications, Vol. 51, No. 8, pp. 1311-1334.   DOI
12 Misra, R. K., 2012, Free Vibration Analysis of Isotropic Plate using Multiquadric Radial Basis Function, International Journal of Science, Environment and Technology, Vol. 1, No. 2, pp. 99-107.
13 Leitao, V. M. A. and Tiago, C. M., 2002, The Use of Radial Basis Functions for One-dimensional Structural Analysis Problems, Proceedings of the Twenty-fourth International Conference on the Boundary Element Method, pp. 165-179.
14 Liu, X., Liu, G. R., Tai, K. and Lam, K. Y., 2005, Radial Point Interpolation Collocation Method (RPICM) for Pratial Differential Equations, Computers and Mathematics with Applications, Vol. 50, No. 8-9, pp. 1425-1442.   DOI
15 Li, J., Cheng, H. D. and Chen, C. S., 2003, A Comparison of Efficiency and Error Convergence of Multiquadric Collocation Method and Finite Element Method, Engineering Analysis with Boundary Elements, Vol. 27, No. 3, pp. 251-257.   DOI
16 Meirovitch, L., 1967, Analytical Methods in Vibrations, Macmillan Publishing, New York.
17 Blevins, R. D., 1979, Formulas for Natural Frequency and Mode Shape, Litton Educational Publishing, New York.