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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.

The effects of surface energy on the non-linear frequency response and stability analysis of piezoelectric cylindrical nano-shell as piezoelectric nanoresonator are investigated in the current paper using Gurtin–Murdoch surface elasticity and von Karman–Donnell’s theory. The nanoresonator is embedded in visco-Pasternak medium and electrostatic excitation. The governing equations and boundary conditions are derived using Hamilton’s principle and also the assumed mode method is used for changing the partial differential equations into ordinary differential equations. Complex averaging method combined with arc-length continuation is used to achieve an approximate solution for the steady-state vibrations of the system. The validation of the mentioned system is achieved with excellent agreements by comparison with numerical results. The parametric studies such as the effects of geometrical and material properties, different boundary conditions, the ratio of length to radius $L/R$ for different values of the voltages ${V_{{\rm{DC}}}}$ and ${V_{{\rm{AC}}}}$, the gap width of the nanoresonator $b/L$, the effect of the voltages ${V_{{\rm{DC}}}}$ and ${V_{{\rm{AC}}}}$ and also the effect of piezoelectric voltage ${V_p}$ are conducted on the non-linear frequency response and stability analysis of the piezoelectric nanoresonator.