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Free and forced vibrations of plates by boundary and interior 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 and interior elements," Intern. J. for Numerical Meth. in Eng., vol. 28,no.9 pp. 1977-1994, 1989.doi: 10.1002/nme.1620280902
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A direct boundary element method is developed for the dynamic analysis of thin elastic flexural plates of arbitrary planform and boundary conditions. The formulation employs the static fundamental solution of the problem and this creates not only boundary integrals but surface integrals as well owing to the presence of the inertia force. Thus the discretization consists of boundary as well as interior elements. Quadratic isoparametric elements and quadratic isoparametric or constant elements are employed for the boundary and interior discretization, respectively. Both free and forced vibrations are considered. The free vibration problem is reduced to a matrix eigenvalue problem with matrix coefficients independent of frequency. 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. The effect of external viscous or internal viscoelastic damping on the response is also studied. The proposed method is compared against the direct boundary element method in conjunction with the dynamic fundamental solution as well as the finite element method primarily by means of a number of numerical examples. These examples also serve to illustrate the use of the proposed method.