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. These structures are made of a based carbon nanotubes (CNTs) core and piezoelectric layers at the upper and lower surfaces. It is supposed that temperature changes linearly through the 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 implemented to investigate the dynamic behavior of the structures. Finally, the effects of the boundary conditions, the thickness of piezoelectric layers, the functional distribution of CNTs, thermal environment and kinds of the circuit (opened-circuit and closedcircuit) 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.

Flexoelectric and piezoelectric effects have attracted the attention of researchers, owing to their applications in sensing systems and actuators. In this paper, the vibration of functionally graded material (FGM) conical nanoshell is studied, taking into account both piezoelectricity and flexoelectricity. The nanoshell has a sandwich-type structure with a FGM core and two layers of piezoelectric materials on its top and bottom. With the combination of the first order shear deformation and Eringen’s nonlocal theories, the vibration equation of the nanoshell is developed. In order to study the governing equations and the frequency of vibrations of nanoshell, the generalized differential quadrature method is implemented. Based on the developed numerical solution procedure, the effect of different parameters, such as flexoelectricity, piezoelectricity, nonlocal term and Pasternak foundation, are shown on the vibrations of conical nanoshell. The presented analysis provides a better insight into the behavior of conical nanoshells, which are highly applicable in bio-sensing and optical devices.