Journal of Applied Nonlinear Dynamics 14(3) (2025) 657--683 | DOI:10.5890/JAND.2025.09.011

Sayyid H. Hashemi Kachapi$^{1}$, S. Gh. Hashemi Kachabi$^{2}$

$^1$ Department of Mechanical Engineering, Faculty of Engineering and Technology, University of Mazandaran, Babolsar, Iran

$^{2}$ Department of Physics, University of Kashan, Kashan, Iran

Abstract

In current study, nonlinear vibration and frequency response analysis of double walled piezoelectric nanoresonator (DWPENR), simultaneously subjected to visco-Pasternak medium, nonlinear van der Waals force and electrostatic excitation is investigated using the Gurtin--Murdoch surface/interface (S/I) and nonlocal theories. For this analysis, Hamilton's principle is used to obtain the governing equations and boundary conditions and Galerkin technique is used to solve the equation of motion. Complex averaging method combined with arc-length continuation is used to achieve the influences of the small-scale, surface effects, elastic medium, van der Waals force, electrostatic and piezoelectric voltages and other parameters on dimensionless natural frequency (DNF), nonlinear frequency response and stability analysis of the DW piezoelectric nanoresonator. It is concluded that ignoring surface and small-scale effects lead to inaccurate results in vibrational response of the DWPENR. It is found that with increasing or decreasing of dimensionless nonlocal parameter and surface/interface parameters, due to increasing or decreasing of DWPENR stiffness, lead to increasing or decreasing DNF, the resonance amplitude and frequency, the range of instability with saddle-node bifurcations and nonlinear softening or hardening behavior and all nonlinear behavior of DWPENR. The obtained results of this study may be useful for designing of nano/micro electro mechanical system and other nano-/micro-smart structures.

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