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

Nano/micro actuators are widely used in micro/ nano electro mechanical systems (NEMS/MEMS) and the study on its nonlinear oscillation is of great significance. This paper begins with a wrong variational principle ([19] Appl Nanosci, 2016, 6: 309-317) 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, we establish the genuine variational principle. Then a simple method so called He’s frequency formulation is applied to solve the problem, where it only needs one-step to get the approximate amplitude-frequency relationship. Comparing with the existing method, it shows that the proposed method is simple but effective, which is helpful to be of significance to the study of the nonlinear oscillation in micro/nano electro mechanical systems.

He’s frequency formula to fractal undamped Duffing equation

Nonlinear oscillation is an increasingly important and extremely interesting topic in engineering. This article completely reviews a simple method proposed by Ji-Huan He and successfully establishes a fractal undamped Duffing equation through the two-scale fractal derivative in a fractal space. Its variational principle is established, and the two-scale transform method and the fractal frequency formula are adopted to find the approximate frequency of the fractal oscillator. The numerical result shows that He’s frequency formula is a unique tool for the fractal equations.