Nonlinear free vibration of shear deformable orthotropic functionally graded cylindrical shells

Abstract

This paper investigates the non-linear free vibration of functionally graded (FG) orthotropic cylindrical shells taking into account the shear stresses. The formulation is based on the shear deformation theory (SDT) and von Karman-type strain displacement relationships. The material properties of FG orthotropic cylindrical shell are assumed to vary exponentially through the thickness. The equations of motion of the FG orthotropic cylindrical shells are derived from the Donnell’s non-linear shell theory, and then the superposition and Galerkin methods are adopted to convert the equation of motion into a non-linear ordinary differential equation. The expressions for the non-linear frequency parameters and non-linear to linear frequency ratios depending on the amplitude within the SDT are obtained in the form of Jacobian elliptic function. In addition, the non-linear ordinary differential equation is solved using the homotopy perturbation method (HPM) and one another expressions for the non-linear frequency parameters and non-linear to linear frequency ratio are obtained. The results are compared and validated with the results available in the literature. The influences of non-linearity, shear stresses, FG profiles as well as the cylindrical shell characteristics on the non-linear frequencies depending on the amplitude of vibration are investigated through a comprehensive parametric study.