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Shock and Vibration
Volume 2017, Article ID 5905417, 10 pages
Research Article

A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

Department of Aerospace Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, M5B 2 K3, Canada

Correspondence should be addressed to Mohammad M. Elahi; ac.nosreyr@ihale.dieom

Received 6 July 2017; Revised 2 September 2017; Accepted 24 September 2017; Published 19 October 2017

Academic Editor: Yuri S. Karinski

Copyright © 2017 Mohammad M. Elahi and Seyed M. Hashemi. 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.


Dynamic Finite Element formulation is a powerful technique that combines the accuracy of the exact analysis with wide applicability of the finite element method. The infinite dimensionality of the exact solution space of plate equation has been a major challenge for development of such elements for the dynamic analysis of flexible two-dimensional structures. In this research, a framework for such extension based on subset solutions is proposed. An example element is then developed and implemented in MATLAB® software for numerical testing, verification, and validation purposes. Although the presented formulation is not exact, the element exhibits good convergence characteristics and can be further enriched using the proposed framework.