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Keywords: dynamic stiffness method, free vibration, arbitrary boundary conditions, classical plate theory, Wittrick-Williams algorithm..

Summary

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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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 106 PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: 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 doi:10.4203/ccp.106.36 purchase the full-text of this paper 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.. Summary 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. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £65 +P&P)
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