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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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In current work, Gurtin–Murdoch surface/interface and nonlocal theories are presented to investigate nonlinear vibration and stability analysis of piezoelectric nanoresonator simultaneously subjected to direct and alternating voltages. Complex averaging method combined with arc-length continuation is used to achieve the nonlinear frequency response and stability analysis of the piezoelectric nanoresonator. It is concluded that ignoring surface and small-scale effects lead to inaccurate results in vibration response of the piezoelectric nanoresonator. Also, with increasing dimensionless nonlocal parameter and decreasing nanoshell stiffness, dimensionless natural frequency, the resonance amplitude, the range of instability with saddle-node bifurcations and nonlinear hardening behavior, and also resonance frequency decrease. In addition, it is found that when the surface/interface effects corresponding to higher surface/interface density are considered, natural frequency is increased. Also, regardless the Lamé’s constants lead to decreasing of piezoelectric nanoresonator stiffness, and as a result, the dimensionless natural frequency is lower than all cases. The rest of the surface/interface parameters do not have much effect on the dimensionless natural frequency. Also, with increasing electrostatic and piezoelectric voltages, the oscillation amplitude and range of the piezoelectric nanoresonator system’s instability and all nonlinear behavior of piezoelectric nanoresonator are increased.

In this paper, vibration analysis of double-walled piezo-viscoelastic cylindrical nanoshell integrated with piezoelectric layers is investigated using Gurtin–Murdoch surface/interface theory and Donnell's theory. Three parameters namely, shear modulus, damp coefficient, and Winkler modulus are used for simulation of visco-Pasternak model. Hamilton's principle is used for deriving the governing equations and boundary conditions and also the assumed mode method is used for changing the partial differential equations into ordinary differential equation. The effects of the surface energy, length and thickness of nanoshell and piezoelectric layer, boundary condition, van der Waals force, and visco-Pasternak effects on the undamped and damped natural frequencies of piezo-viscoelastic cylindrical nanoshell is studied. Also, the results show that on considering surface effects in the nanoscale system without considering the surface density, the maximum frequency will be obtained and this case will be considered as the critical state of the system. As a result, controlling the frequency of the system in this case is essential and it is quite clear that considering the effects of the surface energy will have a remarkable effect on the natural frequency of the piezo-viscoelastic nanoshell.

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