Free vibration response of functionally graded carbon nanotube double curved shells and panels with piezoelectric layers in a thermal environment

This paper presents free vibration of the double-curved shells and panels with piezoelectric layers in a thermal environment. Vibration characteristics of elliptical, spherical, cycloidal, and toro circular shells of revolution are studied in detail. Vibration behavior of carbon nanotubes (CNTs) reinforced composite shells embedded with piezoelectric layers at the upper and lower surfaces is scrutinized. It is supposed that temperature changes linearly through-thickness direction. Reissner- Mindlin and the first order shear deformation (FSDT) theories are implemented to derive the governing equations of the considered structures. The distribution of nanotubes is assumed to be linear along the thickness direction. For solving the equation, the General Differential Quadrature (GDQ) method is used to obtain a numerical analysis for the dynamics of the objective structures. Finally, the effects of boundary conditions, the thickness of piezoelectric layers, functional distribution of CNTs, thermal environment and kinds of the circuit (opened-circuit and closed-circuit) are analyzed. Eigenvalue system is solved to obtain natural frequencies. It is delineated that the obtained fundamental frequency by the closed -circuit is smaller than those obtained by the opened-circuit. Another interesting result is that the natural frequency is decreased by increasing temperature.