Free vibration analysis of a plate with a slit by BEM.

Abstract

A boundary element method is developed for the free vibration analysis of a rectangular plate with a slit. The formulation employs a fundamental solution of a static problem of a plate and this creates not only boundary integrals but surface integrals as well, owing to the presence of an inertia force. Thus the discretization consists of boundary elements as well as interior elements. The boundary and interior are divided into constant elements, and all integrals are solved analytically. The method is applied to square plates having a slit, and the natural frequencies and the modes of vibrations are calculated numerically.