Effect of porosity and characteristics of carbon nanotube on the nonlinear characteristics of a simply-supported sandwich plate

This paper presents geometric-based nonlinear formulation of a composite sandwich plate on the elastic foundation based on first-order shear deformation theory. The composite sandwich plate is fabricated from a porous core integrated with two carbon-nanotubes-reinforced face sheets. After developing the kinematic relations based on first-order shear deformation theory, the geometric nonlinearity is accounted based on von-Karman-type nonlinearity. Porosity of the core is modeled based on two known models in terms of porosity coefficient. After presentation of the effective material properties of the core and the carbon nanotube reinforcement in terms of porosity coefficient, volume fraction of carbon nanotube, and basic material properties, the nonlinear governing equations are derived using Hamilton's principle. Galerkin's approach is applied to reduce nonlinear governing equations of motion to an ordinary time-dependent differential equation. The nonlinear frequency is analytically found based on linear frequency and initial boundary conditions. Before presentation of full numerical results, a comprehensive comparative study is presented for verification of the derivation and solution procedure. The nonlinear to linear frequency ratio is computed based on significant input parameters of porous core and carbon-nanotube-reinforced face sheets such as type of porosity, porosity coefficient, volume fraction, and type of reinforcement's distribution.