Nonreciprocity of energy transfer in a nonlinear asymmetric oscillator system with various vibration states

Abstract

The nonreciprocity of energy transfer is constructed in a nonlinear asymmetric oscillator system that comprises two nonlinear oscillators with different parameters placed between two identical linear oscillators. The slow-flow equation of the system is derived by the complexification-averaging method. The semi-analytical solutions to this equation are obtained by the least squares method, which are compared with the numerical solutions obtained by the Runge-Kutta method. The distribution of the average energy in the system is studied under periodic and chaotic vibration states, and the energy transfer along two opposite directions is compared. The effect of the excitation amplitude on the nonreciprocity of the system producing the periodic responses is analyzed, where a three-stage energy transfer phenomenon is observed. In the first stage, the energy transfer along the two opposite directions is approximately equal, whereas in the second stage, the asymmetric energy transfer is observed. The energy transfer is also asymmetric in the third stage, but the direction is reversed compared with the second stage. Moreover, the excitation amplitude for exciting the bifurcation also shows an asymmetric characteristic. Chaotic vibrations are generated around the resonant frequency, irrespective of which linear oscillator is excited. The excitation threshold of these chaotic vibrations is dependent on the linear oscillator that is being excited. In addition, the difference between the energy transfer in the two opposite directions is used to further analyze the nonreciprocity in the system. The results show that the nonreciprocity significantly depends on the excitation frequency and the excitation amplitude.