Three-dimensional vibration of thick plate

By the method of initial functions(MIF) and based upon the basic equations of three dimensional theory of elasto dynamics,the governing differential equations of plate with arbitrary thickness are formulated in this paper.The dynamic response of stress and displacement of thick plate subjected to the transverse forces is obtained.It is shown that the vibration characteristics of thick plate consist of three modes: thickness shear mode, symmetric mode and anti symmetric mode.The characteristic equations of simply supported thick plate are derived and the comparison of the free vibration frequencies of moderate thick plate theory and three dimensional elasticty theory with the classical theory is made.