保守系统中非线性耦合振子间的能量传递

ENERGY TRANSFER BETWEEN NONLINEAR COUPLED OSCILLATORS IN CONSERVATIVE SYSTEMS

利用复变量-平均法建立了非线性耦合振子内在保守系统的慢变动力学方程,推导出了两振子间能量完全传递的表达式,从而得出了完全能量传递时非线性振子的临界质量和系统初始能量需满足的关系.最后进行数值仿真并得到以下结论:系统两振子进入能量传递的暂态时间与振子的质量有关,当质量比大于等于0.0557时,两振子可不经过暂态而直接发生能量交换;NES质量越小,两振子能量交换的时间越长,当NES质量过小时,适当提高非线性耦合振子的初始能量可实现能量高效传递;非线性耦合振子系统的刚度会影响能量传递的暂态而对能量交换时间影响不大;非线性耦合振子初始能量的形式会影响系统的能量传递,势能比动能更容易引发系统能量传递.

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.