Free vibration and buckling analysis of third-order shear deformation plate theory using exact wave propagation approach

In this paper, wave propagation approach is used to analysis the free vibration and buckling analysis of the thick rectangular plates based on higher order shear deformation plate theory. From wave viewpoint, vibrations can be considered as traveling waves along structures. Waves propagate in a waveguide and reflect at the boundaries. It is assumed that the plate has two opposite edge simply supported while the other two edges may be simply supported or clamped. It is the first time that the wave propagation method is used for thick plates. In this study, firstly the matrices of propagation and reflection are derived and by combining them, the characteristic equation of the plate is obtained. Comprehensive results on dimensionless natural frequencies and dimensionless buckling loads of rectangular thick plates with different boundary conditions for various values of aspect ratio and thickness to length ratio are presented. It is observed that obtained results of wave propagation method with considerable accuracy are so close to obtained values by literature.