Combined effects of transverse shear stresses and nonlinear elastic foundations on the nonlinear dynamic response of heterogeneous orthotropic cylindrical shells

The present work aims to provide a detailed study regarding the nonlinear dynamic response of heterogeneous (HT) orthotropic cylinders resting on the nonlinear elastic foundations. The problem is formulated on the basis of the shear deformation theory (SDT) using von Karman type geometric nonlinearity in the framework of the Donnell's shell theory. Material properties of the cylinders vary continuously in the thickness direction according to the exponential-law distribution. Nonlinear ordinary differential equation is obtained with the use of superposition and Galerkin methods and solved applying the homotopy perturbation method (HPM). The validity of the present method is demonstrated by comparing the present results with existing results in the literature in the limit cases. Numerical simulations are performed to discuss the influences of the nonlinear elastic foundations, vibration amplitude, shear stresses, heterogeneity and cylinder characteristics on the nonlinear frequency parameters.