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Dynamic stiffness matrix of a rectangular plate for the general case

Banerjee, J. R., Papkov, S. O., Liu, X. and Kennedy, David 2015. Dynamic stiffness matrix of a rectangular plate for the general case. Journal of Sound and Vibration 342 , pp. 177-199. 10.1016/j.jsv.2014.12.031

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Abstract

The dynamic stiffness matrix of a rectangular plate for the most general case is developed by solving the bi-harmonic equation and finally casting the solution in terms of the force–displacement relationship of the freely vibrating plate. Essentially the frequency dependent dynamic stiffness matrix of the plate when all its sides are free is derived, making it possible to achieve exact solution for free vibration of plates or plate assemblies with any boundary conditions. Previous research on the dynamic stiffness formulation of a plate was restricted to the special case when the two opposite sides of the plate are simply supported. This restriction is quite severe and made the general purpose application of the dynamic stiffness method impossible. The theory developed in this paper overcomes this long-lasting restriction. The research carried out here is basically fundamental in that the bi-harmonic equation which governs the free vibratory motion of a plate in harmonic oscillation is solved in an exact sense, leading to the development of the dynamic stiffness method. It is significant that the ingeniously sought solution presented in this paper is completely general, covering all possible cases of elastic deformations of the plate. The Wittrick–Williams algorithm is applied to the ensuing dynamic stiffness matrix to provide solutions for some representative problems. A carefully selected sample of mode shapes is also presented.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Additional Information: Available online 27 January 2015
Publisher: Elsevier
ISSN: 0022-460X
Date of Acceptance: 22 December 2014
Last Modified: 11 Mar 2019 12:34
URI: http://orca-mwe.cf.ac.uk/id/eprint/76323

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