Natural vibration of circular and annular thin plates by Hamiltonian approach
Author(s)
Author(s)
Zhou, Z. H.
Wong, K. W.
Xu, X. S.
Date Issued
2011
Publisher
Elsevier
Journal
Journal of Sound and Vibration
Volume
330
Issue
5
Start page
1005
End page
1017
Abstract
The present paper deals with the natural vibration of thin circular and annular plates using Hamiltonian approach. It is based on the conservation principle of mixed energy and is constructed in a new symplectic space. A set of Hamiltonian dual equations with derivatives with respect to the radial coordinate on one side of the equations and to the angular coordinate on the other side are obtained by using the variational principle of mixed energy. The separation of variables is employed to solve Hamiltonian dual equations of eigenvalue problem. Analytical frequency equations are obtained based on different cases of boundary conditions. The natural frequencies are the roots of the frequency equations and corresponding mode functions are in terms of the dual variables q1(r, θ). Three basic edge-constraint cases for circular plates and nine edge-constraint cases for annular plates are calculated and the results are compared well with existing ones.
SFU Affiliated Publication
No
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