A METHOD FOR SOLVING THE THREE DIMENSIONAL VIBRATION OF A UNIDIRECTIONAL COMPOSITE PARALLELEPIPED

Abstract

A semi-analytical method is proposed for solving the free vibration problem of a rectangular parallelepiped. The parallelepiped is made of a unidirectionally reinforced fiber composite, which is modeled to have rectangular orthotropy. The method is based on the Ritz approach, and accommodates arbitrary boundary conditions on the six faces by introducing the boundary indices into the displacement functions. Numerical results are given for the first several frequencies of isotropic and orthotropic parallelepipeds, including the cube, and are compared to the existing results obtained by other three dimensional and plate theories.