基于离散呼吸子理论的靶能量传递研究

摘要

研究了一个具有非线性能量阱的两自由度线性振子耦合系统，确定了其产生靶能量传递的条件和传递频率。建立了无量纲形式的振动方程，利用复变量———平均法推导了保守系统的慢变动力流和哈密顿函数。基于哈密顿力学和相空间中的离散呼吸子理论确定了系统产生靶能量传递的质量比条件和初值条件，并采用椭圆积分计算得到靶能量传递的频率。通过数值仿真验证了有阻尼系统中靶能量传递的不可逆性。%Analytic conditions and transmitting frequency for targeted energy transfer were investigated on a 2-dof system comprising of a linear oscillator coupled with a nonlinear energy sink.The vibration equations were formulated in a dimensionless form,then the dynamic flow and Hamiltonian function for the underlined conservative system were derived by the complex-averaging method.Based on the Hamiltonian and discrete breather theory in phase space dynamics,the mass ratio and initial value condition linked to a complete energy transfer in the conservative system were determined,and the frequency of the targeted transfer was calculated by the Jacobian elliptic integral.As a result of numerical simulation, the irreversibility of targeted energy transfer in damped system was demonstrated.