Dynamic analysis of polygonal Mindlin plates on two-parameter foundations using classical plate theory and an advanced BEM

摘要

Forced vibrations of moderately thick plates on two-parameter, Pasternak-type foundations are considered. Influence of plate shear and rotatory inertia are taken into account according to Mindlin. Excitations are of the force as well as of the support motion type. Formulation is in the frequency domain. An analogy to thin plates without foundations is given. This analogy to classical plate theory is complete in the case of polygonal plan-forms and hinged support conditions. In that case the higher order Mindlin-problem is reduced to two (second order) Helmholtz-Klein- Gordon boundary value problems. An advanced BEM using Green's functions of rectangular domains is applied to the latter, thereby satisfying boundary conditions exactly as far as possible. This problem oriented strategy provides the frequency response functions for the deflection of the undamped Mindlin plate with high numerical accuracy. Structural damping is built in subsequently, and Fast Fourier Transform is applied for calculation of the transient response.