Nonlinear vibration characteristics of graphene/piezoelectric sandwich films under electric loading based on nonlocal elastic theory

•The nonlinear electric resonant of grapheme/piezoelectric films is described.•Effect of small scale on the nonlinear frequency of laminated films is presented.•The nonlinear resonant of laminated films is controlled by the electric loading.

This paper reports the result of an investigation into the nonlinear vibration frequencies of graphene/piezoelectric sandwich films under electrical loading based on nonlocal elastic theory by utilizing a global residual harmonic balance method. Based on the Galerkin method and global residual harmonic balance method, the nonlinear resonant frequencies of graphene/piezoelectric sandwich films under electric exciting loads are obtained with a set of factors: the ratio of the oscillating amplitude to the thickness of sandwich films, small scale effect, electric loading exerted on piezoelectric layer, mode number and size length. Results indicate that the electric exciting load enhances the nonlinear resonant frequency of graphene/piezoelectric sandwich films, the nonlinear resonant frequency decreases as the scale effect increases, the scale effect has a more significant effect on higher mode resonant frequency and linear resonant frequency, and the effect of scale on the nonlinear resonant frequency is independent on the electric exciting load and the boundary conditions exerted on the sandwich films.

Graphical abstractEffect of the ratio of amplitude to thickness A   on the characteristics of nonlinear vibration frequency under different boundary conditions, where scale effect μ⁎=μ/aμ⁎=μ/a.Figure optionsDownload full-size imageDownload as PowerPoint slide