Large amplitude vibration of FG-CNT reinforced composite annular plates with integrated piezoelectric layers on elastic foundation

Abstract

The aim of the present study is to investigate the applications of piezoelectric layers and carbon nanotubes (CNTs) in enhancing nonlinear vibration behaviors of functionally graded carbon nanotube reinforced composite (FG-CNTRC) annular plates. A nonlinear formulation is developed with regard to the first-order shear deformation theory, von Karman geometrical nonlinearity in conjunction with the Hamilton principle. A Pasternak elastic foundation is assumed to be in contact with the annular plate during deformation. The distribution of electric potential across the thickness of piezoelectric layers is simulated via a combination of sinusoidal and linear functions. Both closed and open circuit electrical boundary conditions are taken into account for the bottom and top surfaces of piezoelectric layers. Generalized differential quadrature method is utilized to discretize the nonlinear equations of motion, Maxwell equation and boundary conditions, and then direct iterative method is used to solve the nonlinear system of equations. An extensive parametric study is directed to provide an insight into effects of the thickness of piezoelectric layers, piezoelectric materials, volume fraction and distribution of CNTs, geometrical parameters, elastic foundation coefficient, and mechanical/electrical boundary conditions on the nonlinear dynamic responses of the annular plate. It is found that both distribution and volume fraction of CNTs have a remarkable effect on nonlinear natural frequencies of FG-CNTRC annular plates. It is also revealed that the type of piezoelectric materials, thickness of piezoelectric layers and electrical boundary condition play a pivotal role in improving dynamic responses of FG-CNTRC annular plates. It is also found that presence of elastic foundation increases hardening responses of FG-CNTRC annular plates.