Nonlinear vibration of a nanobeam elastically bonded with a piezoelectric nanobeam via strain gradient theory

Abstract

Nonlinear vibration of a nanobeam (NB) coupled with a piezoelectric nanobeam (PNB) is investigated in this article based on the strain gradient theory. The two nanobeams are coupled by an enclosing elastic medium which is simulated as Pasternak foundation. The PNB is subjected to an external electric voltage in thickness direction and a uniform temperature change. Considering the Von-Kármán geometric nonlinearity and charge equation for coupling of electrical and mechanical fields, the motion equations are derived using strain gradient theory and Hamilton׳s principle. The differential quadrature method (DQM) is applied to obtain the nonlinear frequency of NB for clamped–clamped mechanical boundary condition. Research results reveal that the dimensionless frequency of NB reduction results from increasing the external electric voltage. Furthermore, at higher values of small scale parameters, the difference between the results obtained by modified couple stress and strain gradient theories become considerable.