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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 106
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Paper 36

An Analytical Solution for Free Transverse Vibration of Plates with Arbitrary Boundary Conditions

X. Liu1, S. Papkov2 and J.R. Banerjee1

1School of Engineering and Mathematical Sciences, City University London, United Kingdom
2Department of Mathematics, Sevastopol National Technical University, Ukraine

Full Bibliographic Reference for this paper
X. Liu, S. Papkov, J.R. Banerjee, "An Analytical Solution for Free Transverse Vibration of Plates with Arbitrary Boundary Conditions", in , (Editors), "Proceedings of the Twelfth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 36, 2014. doi:10.4203/ccp.106.36
Keywords: dynamic stiffness method, free vibration, arbitrary boundary conditions, classical plate theory, Wittrick-Williams algorithm..

This paper presents an exact dynamic stiffness method for free vibration analysis of a rectangular plate with general boundary conditions. The formulation is based on series solutions achieved from the governing differential equation, which provides complete flexibility to describe any arbitrary boundary conditions. Essentially the dynamic stiffness matrix for a rectangular plate is formulated through a mixed variable procedure to relate the amplitudes of harmonically varying forces to corresponding displacements on the plate boundaries. The natural frequencies are extracted from the dynamic stiffness matrix by applying theWittrick-Williams algorithm. The main contributions made in this paper are that the applicability of the DSM has been broadened by removing the restrictions of all previous dynamic stiffness theories which were restricted to plates with simply supported boundaries of opposite sides. Numerical results from the present theory for a wide range of boundary conditions are given. The comparisons between the numerical results and published ones by other methods wherever possible demonstrate the fast convergent rate, the high accuracy as well as the much better computational efficiency of the proposed method.

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