Elasticity solution for the free vibration analysis of functionally graded cylindrical shell bonded to thin piezoelectric layers

Based on the three-dimensional theory of elasticity, free vibration analysis of a functionally graded cylindrical shell embedded in piezoelectric layers is performed by using an analytical method for simply supported boundary conditions and a semi-analytical method for non-simply supported conditions. Material properties are assumed to vary along the thickness according to an exponential law with Poisson's ratio held constant. For non-simply supported conditions, this method can give an analytical solution along the graded direction using the state space method (SSM) and an effective approximate solution along the axial direction using the one dimensional differential quadrature method (DQM). Numerical results are compared to those available in the literature to validate the convergence and accuracy of the present approach. The effects of material property gradient index, edge conditions, midradius to thickness ratio, length to mid-radius ratio and the piezoelectric thickness on vibration behavior of shell are investigated. (C) 2011 Elsevier Ltd. All rights reserved.