Mathematical modeling and solution of nonlinear vibration problem of laminated plates with CNT originating layers interacting with two-parameter elastic foundation

Abstract Generalizing the first-order shear deformation plate theory (FOPT) proposed by Ambartsumyan (Theory of anisotropic plates, Nauka, Moscow, 1967 ( in Russian )) to heterogeneous laminated nanocomposite plates and nonlinear vibration problem is analytically solved taking into account an elastic medium this study for first time. The Pasternak-type foundation model (PT-EF) used as model. After creating mathematical models rectangular with CNT originating layers on PT-EF, large amplitude stress–strain relationships motion equations are derived form partial differential (PDEs) within FOPT. Then, applying Galerkin's method equations, it reduced a ordinary equation (NL-ODE) containing second- third-order terms deflection function composed layers. NL-ODE semi-inverse method, frequency–amplitude relationship consisting resting PT-EF established FOPT From these relations, similar relations can be obtained particularly unconstrained monolayer patterns plates. comparing accuracy formulas reliable results literature, comprehensive numerical analyses performed.