Geometrical nonlinear free vibration analysis of laminated composite doubly curved shell panels embedded with piezoelectric layers

The nonlinear free vibration behaviour of laminated composite single/doubly curved shell panel embedded with the piezoelectric layer is investigated numerically in this article. For the analysis purpose, a general nonlinear mathematical model has been developed using higher-order shear deformation theory and Green-Lagrange nonlinearity including the quadratic variation of the electric potential across the thickness due to the piezoelectric layer. In order to capture the exact flexure of the shear deformable panel, all the nonlinear higher order terms are included in the present model. The nonlinear governing equation of free vibrated shell panel is derived using Hamilton’s principle and discretised through suitable finite element steps. The desired nonlinear responses are computed numerically using the direct iterative method. The developed nonlinear numerical model has been validated by comparing the responses with that to available published literature. Finally, the efficacy and applicability of the present nonlinear model has been checked by solving few numerical examples for different geometrical parameters (stacking sequence, thickness ratio, aspect ratio, curvature ratio, different support constraints and amplitude ratio) and number of piezo layers and discussed in details.