Free vibration of functionally graded carbon nanotube reinforced composite plates integrated with piezoelectric layers.

In the present research, free vibration behavior of carbon nanotube reinforced composite (CNTRC) plates integrated with piezoelectric layers at the bottom and top surfaces is analyzed. Plate is modeled according to the first order shear deformation plate theory. Distribution of CNTs across the plate thickness may be functionally graded (FG) or uniformly distributed (UD). Properties of the composite media are obtained according to a modified rule of mixtures approach which contains efficiency parameters. Distribution of electric potential across the piezoelectric thickness is assumed to be linear. The complete set of motion and Maxwell equations of the system are obtained according to the Ritz formulation suitable for arbitrary in-plane and out-of-plane boundary conditions. Besides, two types of electrical boundary conditions, namely, closed circuit and open circuit are considered for the free surfaces of the piezoelectric layers. Chebyshev polynomials are used as the basis functions in Ritz approximation. The resultant eigenvalue system is solved to obtain the frequencies of the system as well as the mode shapes. It is shown that, fundamental frequency of a closed circuit plate is always higher than a plate with open circuit boundary conditions.