Journal of Applied Science and Engineering

Published by Tamkang University Press

1.30

Impact Factor

2.10

CiteScore

The plate is supported as all of edges are simply supported except one edge is simply supported with torsion spring.

Ming-Hung Hsu  1

1Department of Electronic Engineering National Penghu Institute of Technology Penghu, Taiwan 721, R.O.C.


 

Received: May 16, 2003
Accepted: October 23, 2003
Publication Date: December 1, 2003

Download Citation: ||https://doi.org/10.6180/jase.2003.6.4.05  


ABSTRACT


The vibration response of isotropic and orthotropic plates with mixed boundary conditions is numerically modeled using a solution that is based on the differential quadrature method (DQM). The DQM is applied to each region and with the imposition of appropriate boundary conditions; the problem is transformed into a standard eigenvalue problem. The δ technique is used to treat the various boundary conditions. The results also demonstrate the efficiency of the method in treating this class of engineering problem.


Keywords: Differential Quadrature Method, Plates, Numerical Methods, Vibration Analysis, Mixed Boundary Condition


REFERENCES


  1. [1] Bellman, R. E., Kashef, B. G. and Casti, J., “Differential Quadrature: a Technique for Rapid Solution of Nonlinear Partial Differential Equations,” Journal of Computational Physics, Vol. 10, pp. 40-52 (1972).
  2. [2] Civan, F. and Sliepcevich, C. M., “Application of Differential Quadrature to Transport Processes,” Journal of Mathematical Analysis and Applications, Vol. 93, pp. 206-221 (1983).
  3. [3] Civan, F., “Solving Multivariable Mathematical Models by the Quadrature and Cubature Methods,” Numerical Methods for Partial Differential Equations, Vol. 10, pp. 545-567 (1994).
  4. [4] Han, J. B. and Liew, K. M., “Axisymmetric Free Vibration of Thick Annular Plates,” International Journal of Mechanical Science, Vol. 41, pp. 1089-1109 (1999).
  5. [5] Chen, W. and Zhong, T., “The Study on the Nonlinear Computations of the DQ and DC Methods,” Numerical Methods for Partial Differential Equations, Vol. 13, pp. 57-75 (1997).
  6. [6] Bert, C. W., Wang, X. and Striz, A. G., “Convergence of the DQ Method in the Analysis of Anisotropic Plates,” Journal of Sound and Vibration, Vol. 170, pp. 140-144 (1994).
  7. [7] Bert, C. W., Wang, X. and Striz, A. G., “Differential Quadrature for Static and Free Vibration Analysis of Anisotropic Plates,” International Journal of Solids and Structures, Vol. 30, pp. 1737-1744 (1993).
  8. [8] Bert, C. W., Wang, X. and Striz, A. G., “Static and Free Vibration Analysis of Beams and Plates by Differential Quadrature Method,” Acta Mechanica, Vol. 102, pp. 11-24 (1994).
  9. [9] Malik, M. and Bert, C. W., “Implementing Multiple Boundary Conditions in the DQ Solution of Higher-order PDE’s: Application to Free Vibration of Plates,” International Journal for Numerical Methods in Engineering, Vol. 39, pp. 1237-1258 (1996).
  10. [10] Xiang, Y., Liew, K. M. and Kitipornchai, S., “Vibration Analysis of Rectangular Mindlin Plates Resting on Elastic Edge Supports,” Journal of Sound and Vibration, Vol. 204, pp. 1-16 (1997).
  11. [11] Laura, P. A. A. and Grossi, R. O., “Transverse Vibration of a Rectangular Plate Elastically Restrained Against Rotation Along Three Edges and Free on the Fourth Edge,” Journal of Sound and Vibration, Vol. 59, pp. 355-368 (1978).
  12. [12] Laura, P. A. A. and Gross, R. O., “Transverse Vibrations of Rectangular Plates with Edges Elastically Rrestrained Against Translation and Rotation,” Journal of Sound and Vibration, Vol. 75, pp. 101-107 (1981).
  13. [13] Grossi, R. O. and Nallim, L. G., “A Note on the Strain Energy Stored in Rotational Springs at the Plate Edges of Non-uniform Thickness,” Journal of Sound and Vibration, Vol. 206, pp. 448-452 (1997).
  14. [14] Gorman, D. J., “Accurate Free Vibration Analysis of Shear-deformable Plates with Torsional Elastic Edge Support,” Journal of Sound and Vibration, Vol. 203, pp. 209-218 (1997).
  15. [15] Omurtag, M. H. and Kadioglu, F., “Free Vibration Analysis of Orthotropic Plates Resting on Pasternak Foundation by Mixed Finite Element Formulation,” Computers and Structures, Vol. 67, pp. 253-265 (1998).
  16. [16] Malik, M., and Bert, C. W., “Implementing Multiple Boundary Conditions in the DQ Solution of Hogher-order PDE’s: Application to Free Vibration of Plates,” International Journal for Numerical Methods in Engineering, Vol. 39, pp. 1237-1258 (1996).
  17. [17] Leissa, A. W., Vibration of Plate, NASA SP-160, U.S.A. (1969).