Dynamic Analysis of Functionally Graded Piezoelectric Material Beam Using the Hybrid Fourier-Laplace Transform Method

This paper presents an analytical solution for transient response of a simply supported functionally graded piezoelectric material (FGPM) beam under mechanical loads. The beam’s material properties are assumed to vary through the thickness direction following a power law distribution in terms of the volume fractions of the constituent materials. Based on higher-order shear deformation theory the governing equations, equations of motion and Maxwell equation, are derived using Hamilton’s principle. The resulting system of differential equations of vibration is solved using the finite Fourier transformation method. Using the Laplace transform, the unknown variables are obtained in the Laplace domain. Applying the analytical Laplace inverse method, the solution in the time domain is derived. Initially the efficiency of the proposed method is investigated by comparing present results with FEM and Newmark method. Then the effects of material composition, slenderness ratio, and shear deformation on the transient response are investigated.