Exact mathematical solution for free vibration of thick laminated plates

In this paper, the modified form of shear deformation plate theories is proposed. First, the displacement field geometry of classical and the first order shear deformation theories are compared with each other. Using this comparison shows that there is a kinematic relation among independent variables of the first order shear deformation theory. So, the modified forms of rotation functions in shear deformation theories are proposed. Governing equations for rectangular and circular thick laminated plates, having been analyzed numerically so far, are solved by method of separation of variables. Natural frequencies and mode shapes of the plate are determined. The results of the present method are compared with those of previously published papers with good agreement obtained. Efficiency, simplicity and excellent results of this method are extensible to a wide range of similar problems. Accurate solution for governing equations of thick composite plates has been made possible for the first time.