Free vibration analysis of functionally graded carbon nanotube-reinforced composite cylindrical panel embedded in piezoelectric layers by using theory of elasticity

In this paper free vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical panel embedded in piezoelectric layers with simply supported boundary conditions is investigated by using three-dimensional theory of elasticity. By using Fourier series expansion along the longitudinal and latitudinal directions and state space technique across the thickness direction, state space differential equations are solved analytically. The traction-free surface conditions then give rise to the characteristic equation for natural frequencies. Accuracy and convergence of the present approach are validated by comparing the numerical results with those found in literature. In addition, the effects of volume fraction of CNT, four cases of FG-CNTRC, piezoelectric layer thickness, mid radius to thickness ration and modes number on the vibration behavior of the hybrid cylindrical panel are also examined.