Numerical investigation of a fractal oscillator arising from the microbeams-based microelectromechanical system

Abstract

In this paper, we consider a electrically excited microbeams-based microelectromechanical system (MEMS) on a fractal time space. This MEMS problem can be modelled by a fractal nonlinear oscillator. A numerical approach by combining the fractal complex transformation and the spreading residue harmonic balance method is proposed for finding the approximations to the fractal vibration system. The approximated solutions and frequencies with high accuracy are given, and compared with the approximations by the existing methods such as Runge–Kutta method, energy balance method and Li-He’s modified homotopy perturbation method. Sensitivity analysis of the approximations concerning different amplitudes and other parameters is also investigated for understanding the numerical behaviour. Numerical results confirm the efficiency of the proposed approach over some existing methods.