Forced nonlinear vibrations of circular cylindrical sandwich shells with cellular core using higher-order shear and thickness deformation theory

A geometrically nonlinear forced vibration analysis of circular cylindrical sandwich shells with open/closed cellular core using higher-order thickness and shear deformation theory is presented. The proposed sandwich shell comprises two thin face-sheets perfectly bonded to a functionally graded porous core. The face-sheets are made of carbon nanotubes (CNTs) reinforced composites. Three different types of porosity distribution, including two non-uniform and a uniform variation through the thickness, are considered. The effective mechanical properties of the core material, having open cells or closed cells, are determined using the Gibson and Ashby model. The rule-of-mixture, which includes efficiency parameters to account for scale-dependent properties of nanocomposite media, is adopted to obtain the mechanical properties of the face-sheets. The in-plane and transverse displacements of a generic point are assumed as a third and fourth-order polynomials of the through-the-thickness coordinate. The model is derived within the framework of an equivalent single layer (ESL) theory. Hamilton's principle is employed to obtain the nonlinear governing differential equations and further discretised by adopting the Galerkin method. Finally, the incremental harmonic balance (IHB) method, in conjunction with the arc-length continuation method, is used to solve the nonlinear system of coupled ordinary differential equations and compute the frequency-amplitude response. An extensive numerical study is carried out to examine the effects of the porosity coefficient, porosity distribution, core-to-face ratio and the volume fraction of CNTs in the face-sheets on the frequency-amplitude response of circular cylindrical sandwich shells.