Stochastic dynamics of an electromagnetic energy harvesting suspension with time-delayed feedback and fractional damping

Electromagnetic energy harvesting suspension (EMEHS) systems can convert mechanical energy into electrical energy, which has attracted much attention in the field of automotive energy harvesting. This paper aims to examine the stochastic dynamics of the EMEHS system with time-delayed feedback and fractional derivative damping under random road excitation. The equivalent system can be obtained by variable transformation, followed by the derivation of the steady-state probability density function using stochastic averaging method. The consistency between numerical simulation and analytical results verifies the effectiveness of the proposed method. Results indicate the existence of stochastic bifurcation phenomenon. The influences of fractional order, delayed time, fractional coefficient, and nonlinear damping coefficient on the stochastic P-bifurcation of the system are discussed individually in detail. Then the output performance of the EMEHS system is illustrated by presenting the mean square current and mean output power. The conclusions demonstrate that adjusting parameters such as fractional order, delayed time, and noise intensity can enhance the energy harvested from road vibrations. This article provides a theoretical reference for the future design of high-performance EMEHS.