Non-reciprocity of energy transfer derived from cubic stiffness-induced nonlinear phenomena

• The effects of cubic stiffness-induced nonlinear phenomena in constructing strongly non-reciprocity are explored. • The variation of reciprocity with excitation amplitude is elaborated. • A trigger method for constructing non-reciprocity using an impulse is proposed. Introducing purely nonlinear elastic elements can induce rich dynamic behaviors, such as bifurcations, jumps and isolated resonance curves, to linear systems. Therefore, these elements are suitable for constructing strong non-reciprocity of vibration energy transfer. First, the energy transfer along reciprocal directions in a three-degree-of-freedom system is investigated, where three oscillators are connected by cubic springs. The semi-analytical solutions of the system are obtained using the complexification-averaging method and the least squares method. The results are compared against numerical solutions obtained by the Runge-Kutta method. The excitation amplitude range that produces strong non-reciprocity of vibration energy is analyzed. The jump phenomenon under combined excitation is investigated, and a trigger method for constructing non-reciprocity using an impulse is proposed. Then, an oscillator chain with cubic stiffness and scaling parameters is embedded into a multi-degree-of-freedom linear oscillator system to further explore the effect of cubic stiffness. Energy transfer along two directions is compared by exciting the leftmost oscillator and the rightmost oscillator. Moreover, the trigger effect of the impulse on non-reciprocity is demonstrated. The results show significant differences in vibration energy transfer within three distinct frequency bands. The critical points between reciprocal and non-reciprocal states are obtained, and the three stages of reciprocity related to excitation amplitude are analyzed. Lastly, the modulation effect of the cubic stiffness on non-reciprocity is conducted by comparing the energy of the output oscillator.