Non-linear dynamic stability of piezoelectric functionally graded carbon nanotube-reinforced composite plates with initial geometric imperfection

• We investigate the non-linear dynamic stability of imperfect piezoelectric CNTRC plate.
• Plate initial imperfection introduces coupling of in-plane and lateral response.
• Distribution patterns of SWCNTs affect the size of stability regions significantly.
• Increasing the CNTs volume fraction will increase the size of stability regions.
• The amplitude of vibration decreases with increasing the CNTs volume fraction.

This paper deals with non-linear dynamic stability of initially imperfect piezoelectric functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates under a combined thermal and electrical loadings and interaction of parametric and external resonance. The excitation, which derives from harmonically varying actuators voltage, results in both external and parametric excitation. The governing equations of the piezoelectric CNTRC plates are derived based on first order shear deformation plate theory (FSDT) and von Kármán geometric non-linearity. The material properties of FG-CNTRC plate are assumed to be graded in the thickness direction. The single-walled carbon nanotubes (SWCNTs) are assumed aligned, straight and a uniform layout. The linear buckling and vibration behavior of perfect and imperfect plates are obtained in the first step. Then, Galerkin's method is employed to derive the non-linear governing equations of the problem with quadratic and cubic non-linearities associated with mid-plane stretching. Periodic solutions and their stability are determined by using the harmonic balance method with simply supported boundary conditions. The effect of the applied voltage, temperature change, plate geometry, imperfection, the volume fraction and distribution pattern of the SWCNTs on the parametric resonance, in particular the positions and sizes of the instability regions of the smart CNTRC plates as well as amplitude of steady state vibration are investigated through a detailed parametric study.