In this work, nonlinear vibration and frequency response analysis of a double-walled piezoelectric nanoresonator based on a cylindrical nanoshell is performed using the Gurtin–Murdoch surface/interface theory. The piezoelectric nanoresonator is simultaneously subjected to the visco-Pasternak medium and nonlinear van der Waals and electrostatic forces. It is found that the electrostatic and piezoelectric voltages, length to radius ratio, nanoresonator gap width, linear and nonlinear van der Waals coefficients and other parameters can effectively change the flexural rigidity of the system, which in turn affects the nonlinear frequency response. Also, increasing or decreasing of some parameters leads to increase or decrease in the resonance amplitude, resonant frequency, instability of the system, nonlinear behavior and bandwidth.

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