Free and transient vibration analysis of an un-symmetric cross-ply laminated plate by spectral finite elements

Abstract

In this study, a spectral finite element formulation for free and transient vibration analysis of a rectangular un-symmetric cross-ply laminated composite plate of Levy-type is developed. Plate kinematics obeys classical lamination plate theory. The formulation is based on dynamic shape functions in frequency-domain derived from the exact solution of the governing wave equations. Based on Levy-type solution and finite strip method, 2/D space-time partial differential equations (PDEs) of motion are transformed to 1/D space-time PDEs. Spectral elements are used to transform 1/D space-time PDEs to temporal ordinary differential equations. For investigating validity and accuracy of the model presented, numerical solutions are established for both free and transient vibrations. Comparison of spectral finite element method (SFEM) time responses with an exact analytical method demonstrates the superiority of SFEM in both reducing computational cost and increasing numerical accuracy. It is correct especially for excitations of high-frequency contents. A comparison of SFEM and FEM shows the same result.