保守系统中非线性耦合振子间的能量传递

In this study，the slowly varying dynamic equation of the conservative system of the nonlinear coupled oscillator is established by using the complex variable-average method，and the expression of complete energy transfer between the two oscillators is deduced. Thus，the relationship between the critical mass of the nonlinear oscillator and the initial energy of the system is obtained. Finally，the numerical simulation is carried out and an interesting conclusion is obtained：the transient time of the two oscillators entering the energy transfer in the system is related to the mass of the oscillator. When the mass ratio is greater than or equal to 0.0557，the energy exchange between the two oscillators can occur directly without transient.The smaller the NES mass is，the longer the energy exchange time between the two oscillators is.When the NES mass is too small，properly increasing the initial energy of the nonlinear coupled oscillator can realize efficient energy transfer. The stiffness of nonlinear coupled vibration subsystem will affect the transient of energy transfer but has little effect on the energy exchange time. The form of the initial energy of the nonlinear coupled oscillator will affect the energy transfer of the system，and the potential energy is easier to cause the energy transfer of the system than the kinetic energy.