Nonlinear Vibration of Multilayer Nonhomogeneous Moderately-Thick Cylindrical Shells on Three-Parameter Nonlinear Foundations

This study focuses on the analysis of the nonlinear vibration behavior of nonhomogenous isotropic (NHI) multilayered cylindrical shells resting on three-parameter nonlinear elastic foundations (Winkler-Pasternak type) within a theoretical framework based on Donnell-type shell theory, which considers von Kármán-type geometric nonlinearities and transverse shear deformation effects. The stress-displacement relations for each NHI layer are defined within the context of generalized Hooke's law, and based on this, the governing equations of the system are derived in the form of partial differential equations. These equations are reduced to second-order time-dependent nonlinear ordinary differential equations using the Galerkin approximation. The nonlinear frequency-amplitude relationship is established using the semi-inverse method, which establishes a variational formulation through an assumed functional representation and provides an approximate analytical solution to the nonlinear governing equations. Furthermore, the study comprehensively examined the effects of nonlinear elastic foundation parameters (Winkler and Pasternak coefficients), shear deformations, degree of nonhomogeneity, number and arrangement of layers, and shell geometric ratios on nonlinear frequency characteristics, and new findings are presented that contribute to the literature.