Size‐dependent continuum‐based model of a flexoelectric functionally graded cylindrical nanoshells

Abstract

Flexoelectricity is dependent on the strain gradient, which is high in microscale and nanoscale, leading to its considerable effect on the electromechanical behavior of structures in microscale and nanoscale. Using the Love's theory for thin shells and the modified flexoelectricity theory, governing coupled equations of the functionally graded magneto‐electro‐elastic (FGMEE) cylindrical nanoshells were formulated along with their boundary conditions using the Hamilton's principle and variation method. It is worth noting that the governing coupled equations of FGMEE cylindrical nanoshell with an electric potential‐independent polarization parameter, where the polarization is independent of the electric potential, are considered the major novelty of this study. To show the ability and uniqueness of the formulation, free vibrations of the shell were examined in a specific state, regardless of the magnetic field effect under the clamped–clamped boundary condition. The effects of different parameters including geometry, size effect, and external voltage on the vibration frequency of the nanoshell were investigated. According to the results, the vibration behavior of the flexoelectric nanoshell is largely dependent on the size effect. Given the application of this structure in sensors and actuators, the external voltage has a considerable effect on the electromechanical behavior of the structure in the presence of the flexoelectric effect.