Nonlinear vibration analysis of multilayer heterogeneous orthotropic cylindrical shells on nonlinear Winkler foundation using extended shear deformation theory

Abstract

In this study, nonlinear vibration of multilayered cylindrical shells consisting of heterogeneous orthotropic (HTO) layers on the nonlinear Winkler foundation (NL-WF) is investigated using extended shear deformation theory (ESDT). In order to establish the basic relations, the basic assumptions used in the formation of the theory of homogeneous (HOM) orthotropic cylindrical shells are generalized for multilayered HTO cylindrical shells. Extended shear deformation theory, von Karman type nonlinearity and modified Donnell type shell theory are used in the formation of basic relations and equations. By applying Galerkin method to the fundamental equations system and transforming it into a second-order time dependent nonlinear ordinary differential equation, the analytical expression for the frequency-amplitude relationship is obtained using by semi-inverse method. The accuracy of the present work is verified by comparing with other solutions available in the literature. Also, some new results are presented to study the effects of nonlinear elastic foundation, shear strains, heterogeneous orthotropic profiles, number of layers, layer arrangement and shell properties on the dimensionless nonlinear frequency parameter (DNLFP).