Efficacy of Harmonic Differential Quadrature method to vibration analysis of FGPM beam

The priority of this paper is to explore the computational characteristics of Harmonic Differential Quadrature (HDQ) method for free flexural vibration analysis of functionally graded piezoelectric material (FGPM) beam. The modified Timoshenko beam theory is used in this study where electric potential is assumed to have sinusoidal variation across the depth. The equations of motion and boundary conditions are derived by employing Hamilton's principle. The material properties are assumed to have a power law or sigmoid law variation across the depth. The available equations of motion are then solved using the Harmonic Differential Quadrature (HDQ) method to obtain the natural frequencies of the FGPM beam. The efficacy of the present method is validated by comparing the results with the previous published work. It is observed that the results obtained by HDQ method are at the same level of accuracy than those of previous analysis using GDQ method.