A fast insight into the nonlinear oscillation of nano-electro-mechanical resonators considering the size effect and the van der Waals force

School of Physics and Electronic Information Engineering, Henan Polytechnic University - Jiaozuo, 454003, China

^(a) konka05@163.com (corresponding author)

Received: 5 September 2021
Accepted: 24 November 2021

Abstract

Nano/micro actuators are widely used in micro/nano-electro-mechanical systems (NEMS/MEMS) and the study on their nonlinear oscillation is of great significance. This paper begins with a wrong variational principle (Ghalambaz M., Appl. Nanosci., 6 (2016) 309) of the reduced governing partial differential equation of the resonator which is used to describe the nonlinear oscillation of nano-electro-mechanical resonators that takes into account the size effect and the van der Waals force. By using the semi-inverse method,the we establish the genuine variational principle. Then a simple method, the so-called He's frequency formulation, is applied to solve the problem, where only one step is needed to get the approximate amplitude-frequency relationship. Comparing with the existing method, we show that the proposed method is simple but effective, which is helpful for the study of the nonlinear oscillation in micro/nano-electro-mechanical systems.