S_1-ZGV Modes of a Linear and Nonlinear Profile for Functionally Graded Material Using Power Series Technique

The present work deals with functionally graded materials (FGM) isotropic plates in the neighborhood of the first-order symmetric zero group velocity (S 1 -ZGV) point. The mechanical properties of functionally graded material (FGM) are assumed to vary continuously through the thickness of the plate and obey a power law of the volume fraction of the constituents. Governing equations for the problem are derived, and the power series technique (PST) is employed to solve the recursive equations. The impact of the FGM basic materials properties on S 1 -ZGV frequency of FGM plate is investigated. Numerical results show that S 1 -ZGV frequency is comparatively more sensitive to the shear modulus. The gradient coefficient p does not affect the linear dependence of ZGV frequency f o as function of cut-off frequency f c ; only the slope is slightly varied.