非线性耦合振子间产生靶能量传递的初始条件

Initial conditions for targeted energy transfer in coupled nonlinear oscillators

摘要:

针对线性振子连接非线性能量阱的系统中产生靶能量传递需要一定的初始条件,首先说明最优靶能量传递同其非保守系统中完全能量传递存在一致性,之后建立该非保守系统的慢变力学模型,并针对该系统提出引发最优靶能量传递的初始能量同系统中立方刚度存在精确比例关系的假设和推论,通过数值仿真验证了该假设及推论的正确性．最后将该结论应用于线性振子连接非线性能量阱系统的立方刚度设计,提出了设计可实现靶能量传递的立方刚度的方法．

Abstract:

The initial conditions for targeted energy transfer in coupled nonlinear oscillators are investigated. First it is shown that optimal targeted energy transfer and complete energy exchange in non-conservative systems are basically the same in the system of a linear oscillator coupled with a nonlinear energy sink. An assumption and an inference are proposed that there is a proportional relationship between initial energy for inducing optimal targeted energy transfer and the cubic stiffness based on the research of slow-flow dynamics of the non-conservative system. The assumption and inference are verified by numerical simulations. The result can be applied for design of the cubic stiffness for inducing optimal targeted energy transfer in the system of a linear oscillator coupled with a nonlinear energy sink, and the method is also given in the paper.