THE FREE VIBRATION ANALYSIS OF THICK FUNCTIONALLY GRADED BEAMS ACCOUNTING HIGHER ORDER SHEAR DEFORMATION THEORY WITH DIFFERENTIAL TRANSFORM METHOD

This work aims to study the free vibration of thick beams accounting higher-order shear deformation, the material properties are those of functionally graded material. The Hamilton's principle is used to come up with the governing equations and boundary conditions. The solution is assumed to be as a product of two functions: a geometric function and a temporal one in exponential form. This leads to an ordinary system of differential equations where the axial and transverse displacements of bending and shear displacement are the functions to be determined. These are assumed to be Taylor´s series expansion. Afterwards, the differential transformation method is applied to obtain a system of recurrent sequences. To form the system of Eigen functions to be solved the boundary conditions for clamped-clamped beam are expressed using the previous recurrent sequences. A numerical resolution gives nondimensional natural frequencies and vibration mode shapes. A comparison with the previous results with those already presented in the literature is performed.