Electrostatically actuated double walled piezoelectric nanoshell subjected to nonlinear van der Waals effect: nonclassical vibrations and stability analysis

In this paper, nonlinear vibration and frequency response analysis of double walled piezoelectric nanoshell (DWPENS) is investigated using nonclassical approach of the Gurtin–Murdoch surface/interface (GMSIT) theory. The piezoelectric nanoshell is simultaneously subjected to visco-Pasternak medium, the nonlinear van der Waals and electrostatic forces. Hamilton’s principles, the assumed mode method combined with Lagrange–Euler’s are used for the governing equations and boundary conditions. Complex averaging method combined with Arc-length continuation is used to achieve the nonlinear frequency response and stability analysis of the DWPENS. It is found that the electrostatic and piezoelectric voltages, the length to radius ratio, the nanoshell gap width, van der Waals (vdW) coefficients and other parameters can effectively change the flexural rigidity of the system which in turn affects the nonlinear frequency response. And also, increasing or decreasing of some parameters lead to increasing or decreasing the resonance amplitude, resonant frequency, the system’s instability, nonlinear behavior, and bandwidth.