Geometrical nonlinear free vibration responses of FG-CNT reinforced composite annular sector plates integrated with piezoelectric layers

Abstract

The objective of this research is to scrutinize large amplitude vibration response of functionally graded carbon nanotube reinforced composite (FG-CNTRC) annular sector plates with surface-bonded piezoelectric layers. A nonlinear formulation is derived based on the first-order shear deformation theory (FSDT), von Karman geometrical nonlinearity along with the Hamilton principle. The distribution of electric potential through the thickness of the piezoelectric layers is simulated by a sinusoidal function. The closed circuit electrical boundary condition is taken into consideration for the top and bottom surfaces of the piezoelectric layers. The nonlinear dynamic equations, boundary conditions and Maxwell equation are discretized using the generalized differential quadrature method and direct iterative method is then employed to solve the nonlinear system of equations. The variation of nonlinear frequency versus the vibration amplitude is highlighted considering various influential parameters such as distribution and volume fraction of the CNTs, geometrical parameters, boundary conditions and the thickness of the piezoelectric layers. It is found that the dynamic responses of the CNTRC sector plate may be noticeably enhanced by adjusting values of the CNT volume fraction and distribution. The numerical results reveal that the increase in the nonlinear frequency descents at certain vibration amplitude owing to vibration mode redistribution.