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Free and forced vibrations of plates by boundary elements

Providakis Konstantinos, Beskos, Dimitri E

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Year 1989
Type of Item Peer-Reviewed Journal Publication
Bibliographic Citation C.P.Providakis , D.E. Beskos, "Free and forced vibrations of plates by boundary elements", Comp. Methods in Ap. Mechanics and Eng., vol. 74,no.3 pp.231-250, 1989.doi:10.1016/0045-7825(89)90050-9
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A direct boundary element methodology is developed for the dynamic analysis of thin elastic flexural plates of arbitrary planform and boundary conditions. The formulation employs the frequency domain dynamic fundamental solution of the problem and this essentially creates only boundary integrals. Thus only the plate perimeter has to be discretized and this is accomplished with the aid of quadratic isoparametric boundary elements for increased accuracy. Both free and forced vibration problems are considered. The free vibration problem is reduced to a matrix eigenvalue problem wherein the matrix coefficients are complex Bessel functions of the frequency parameter. The forced vibration problem is solved with the aid of the Laplace transform with respect to time and this requires a numerical inversion of the transformed solution to obtain the plate dynamic response to arbitrary transient loading. Numerical examples are presented to illustrate the proposed methodology and demonstrate its advantages.