Free vibration of functionally graded carbon nanotube-reinforced conical panels integrated with piezoelectric layers subjected to elastically restrained boundary conditions:

摘要

This article presents the free vibration of piezoelectric functionally graded carbon nanotube-reinforced composite conical panels with elastically restrained boundary conditions. The material properties of carbon nanotube-reinforced composites are assumed to be temperature-dependent and are obtained using the extended rule of mixture. First-order shear deformation theory is adopted to obtain the kinematics of the hybrid panels, and the boundary spring technique is used to implement arbitrary boundary conditions. Meanwhile, two types of electrical boundary conditions, closed circuit and open circuit, are considered for the free surfaces of the piezoelectric layers. The complete sets of electro-mechanically coupled governing equations are obtained using the Rayleigh–Ritz procedure with the Chebyshev polynomial basis functions. The resultant eigenvalue problem is solved to obtain natural frequencies and mode shapes of the hybrid panels. Convergence and comparison studies have been conducted to verify the sta...