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Journal of Applied Mathematics
Volume 2013, Article ID 284208, 7 pages
Research Article

Natural Frequencies of Shear Deformable Plates by Polyharmonic Splines

1Faculdade de Engenharia da Universidade do Porto, Porto, Portugal
2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3Department of Mathematics, Faculty of Science, Kafr El-Sheikh University, Kafr El-Sheikh 33516, Egypt

Received 10 July 2013; Accepted 16 September 2013

Academic Editor: Carla Roque

Copyright © 2013 A. J. M. Ferreira and A. M. Zenkour. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We use the third-order shear deformation theory and a collocation technique with polyharmonic splines to predict natural frequencies of moderately thick isotropic plates. The natural frequencies of vibration are computed for various plates and compared with some available published results. Through numerical experiments, the capability and efficiency of the present method for eigenvalue problems are demonstrated, and the numerical accuracy and convergence are thoughtfully examined.