The nonlinear vibration of orthotropic functionally graded cylindrical shells surrounded by an elastic foundation within first order shear deformation theory

Abstract The non-linear free vibration behavior of functionally graded (FG) orthotropic cylindrical shell interacting with the two-parameter elastic foundation is investigated. The major goal of this research was to obtain a solution for the non-linear frequencies associated with the problem outlined above. The dynamic stability and compatibility equations of FG orthotropic cylindrical shells surrounded by an elastic foundation are derived within the first order shear deformation theory (FSDT) and von Karman strain displacement relationships, and then superposition and Galerkin methods are adopted to convert the above equations into a nonlinear ordinary differential equation. The expression for non-linear frequency of FG orthotropic cylindrical shell surrounded by an elastic foundation within the FSDT is obtained using the homotopy perturbation method (HPM). In particular, similar expression in the framework of the classical shell theory (CST) is obtained, also. The results are compared and validated with the results available in the literature. Finally, the calculation and presentation of the effect of many parameters included in the analysis conclude the goals to be reached in the study.