Exact analysis of vibration of layered orthotropic plates on pasternak foundation

摘要

Based on three dimensional theory of orthotropic elasticity, an appropriate re-arrangement is carried on the basic equations, and, the state equation, in which only six physical quantities are involved including three components of displacement and three stress components on the surface parallel to the plane of the plate, is obtained. Therefore, the state space method is very suitable to deal with problems of laminated structures. For problem of free vibration of a simply supported plate, the Fourier series is applied and a first-order ordinary differential equation set is obtained. By employing Hamilton-Cayley theorem, the solution of the set can be obtained directly and the inverse operation of matrix is then avoided. The problem of free vibration of laminated orthotropic plates on Pasternak foundation finally turns to be an algebraic eigenvalue problem of a 3 x 3 matrix. A numerical example is given in the end of this paper.