Analytical solution for free vibration analysis of composite plates with layer-wise displacement assumptions

This paper presents an analytical closed form solution for free vibration analysis of multilayered plates by using a layer-wise displacement assumption based on Carrera’s Unified Formulation. A wide range of boundary conditions are analysed by using a Levy type solution. By using such a solution, the number of the differential equations of motion depends on the number of plies. This means that for plates with different number of plies the equations of motion need to be re-derived and re-solved. In this paper, a procedure has been devised to overcame this problem and the equation of motions can be automatically obtained and solved to obtain natural frequencies and mode shapes for plates with any number of layers. This procedure has been called “L-matrix method”. The novel solutions have been validated by analytical 3D and 2D Navier type solutions for plates simply supported at all edges. A comparison of the results with 2D and 3D NASTRAN finite element models is also carried out showing the superiority of the analytical solution. Furthermore, benchmark solutions have been obtained for plates with different boundary conditions. The presented Levy type solution can be easily extended to static, buckling and response analysis.