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Free and forced vibrations of shallow shells by boundary and interior elements

Providakis Konstantinos, Beskos, D. E

Πλήρης Εγγραφή

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Περίληψη

A direct boundary element method is developed for the dynamic analysis of thin elastic shallow shells of arbitrary geometry and boundary conditions. The integral formulation employs the static fundamental solution of thin elastic flat plates under combined flexural and membrane deformation. This creates not only boundary integrals, but surface integrals as well due to the presence of the inertia forces and the coupling between the flexural and membrane action in the shell. Thus the discretization involves boundary as well as interior elements, both of the quadratic isoparametric type. Both free and forced vibrations are considered. The free vibration problem is reduced to a generalized eigenvalue problem involving matrices with entries independent of frequency. The general 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 time domain response. The effect of the external viscous or internal viscoelastic damping on the response is also taken into account. Numerical examples are presented to illustrate the method and demonstrate its advantages.

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