Browse > Article
http://dx.doi.org/10.5050/KSNVE.2016.26.5.602

Meshless Method Based on Wave-type Function for Accurate Eigenvalue Analysis of Arbitrarily Shaped, Clamped Plates  

Kang, Sang-wook (Hansung University)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.26, no.5, 2016 , pp. 602-608 More about this Journal
Abstract
The paper proposes a practical meshless method for the free vibration analysis of clamped plates having arbitrary shapes by extending the non-dimensional dynamic influence function (NDIF) method, which was developed by the author in 1999. In the proposed method, the domain and boundary of the plate of interest are discretized using only nodes without elements unlike FEM and the system matrices are obtained by making domain nodes and boundary nodes satisfy the governing differential equation and boundary conditions, respectively. However, since the above system matrices are not square ones, the problem of free vibrations of clamped plates is not reduced to an algebraic eigenvalue problem. An additional theoretical treatment is considered to produce an algebraic eigenvalue problem. It is revealed from case studies that the proposed method is valid and accurate.
Keywords
Meshless Method; Clamped Plate; Eigenvalue; Mode Shape; Natural Frequency; Free Vibration;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Kang, S. W. and Atluri, S. N., 2014, Application of Nondimensional Dynamic Influence Function Method for Eigenmode Analysis of Two-dimensional Acoustic Cavities, Advances in Mechanical Engineering, 363570, pp. 1~9.
2 Kang, S. W. and Atluri, S. N., 2015, Improved Non-dimensional Dynamic Influence Function Method based on Tow-domain Method for Vibration Analysis of Membranes, Advances in Mechanical Engineering, Vol. 7, No. 2, pp. 1~8.
3 Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C., 1984, Boundary Element Techniques, Springer-Verlag, New York.
4 Bathe, K., 1982, Finite Element Procedures in Engineering Analysis, Prentice-Hall, New Jersey.
5 Meirovitch, L., 1967, Analytical Methods in Vibrations, Macmillan Publishing, New York.
6 Leitao, V. M. A. and Tiago, C. M., 2002, The Use of Radial Basis Functions for One-dimensional Structural Analysis Problems, Boundary Elements XXIV (WIT Transactions on Modelling and Simulation), Vol. 18, pp. 165~179.
7 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.
8 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, Journal of Sound and Vibration, Vol. 242. No, 1, pp. 9~26.   DOI
9 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
10 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
11 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
12 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, Transaction of ASME, Vol. 130, No. 4, pp. 041010.1~041010.8.