Numerical Solution of Vibrating Double and Triple-Panel Stepped Thickness Plates
Mohamed A. El-Sayad* and Ahmed M. Farag
Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria, Egypt
- *Corresponding Author:
- Mohamed A. El-Sayad
Department of Engineering Mathematics and Physics
Faculty of Engineering, Alexandria University, Alexandria, Egypt
E-mail: [email protected]
Received Date: April 17, 2012; Accepted Date: May 19, 2012; Published Date: May 22, 2012
Citation: El-Sayad MA, Farag AM (2012) Numerical Solution of Vibrating Double and Triple-Panel Stepped Thickness Plates. J Appl Computat Math 1:110. doi: 10.4172/2168-9679.1000110
Copyright: © 2012 El-Sayad MA, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The main objective of the present paper is to achieve a modified numerical method for investigating the vibration characteristics of the stepped thickness plate with many types of boundary conditions surrounding certain number of panels. The presented technique relies on dividing the entire plate into several regions of uniform thickness separated by sudden steps. Each region is divided to number of strips which are assembled and solved numerically by the Finite Strip-Transition Matrix method FSTM. A convenient basic function is applied to reduce the partial differential equation of motion of plate inside a single region into an ordinary differential one. Step continuity conditions are applied to achieve the final solution of plate. Regional rigidities of plates and mass per unit area are changed due to the change of plate thickness from a region to another. Consequently, new straining actions are occurred and then compatibility conditions become necessary to modify the nodal vector at each step. Various types of restrained boundary conditions against rotation are included in the present paper. The validity of present method is checked and the accuracy of the results is compared with those available in literature showing a good agreement.