Modal analysis of shear-induced flexural vibration of FGPM beam using Generalized Differential Quadrature method

Present investigation is concerned with modal analysis of functionally graded piezoelectric material (FGPM) beam excited using the d15 effect. In the piezoceramic actuators, the d15 effect is found more attractive for application, as the shear piezoelectric coefficient is much higher than other piezoelectric coefficients d31 and d33. A modified Timoshenko beam theory is used in this study where the electric potential is assumed to vary sinusoidal along the thickness direction. Material properties of the beam are assumed to vary continuously across the thickness according with power law distribution. The governing equations and boundary conditions are obtained by using Hamilton's principle. The available governing equations are then solved using the Generalized Differential Quadrature (GDQ) method to obtain the natural frequencies of the FGPM beam. As no prior solution exists for this type of problem, so the results are compared with the results obtained by COMSOL Multiphysics (version 4.2) software and also with the results obtained in previous investigation for the special case. It is found that results obtained by GDQ method are in good agreement with the results obtained by COMSOL software. The effect of slenderness ratios, volume fraction indices and boundary conditions on natural frequencies are also examined.