用形状记忆合金控制转子振动的非线性动力学研究

考虑了形状记忆合金控制器作用力的软非线性，给出了具有形状记忆合金控制器和弹性支承转子系统的动力学方程。运用非线性动力学理论求出了系统在主共振时的二阶非线性近似解，运用运动稳定性理论求出了系统振幅跳跃区间表达式，通过对系统的解和跳跃区间的表达式的分析和讨论，得出了系统诸参数对系统动力学特性的影响，并通过仿真验证了理论结果；提出了用形状记忆合金控制器结合挤压油膜阻尼器降低系统在非定常状态下最大振幅的构想，并探讨了加装挤压油膜阻尼器后系统动力学特性的变化。

Study on Nonlinear Dynamics of Rotors under Vibration Control Using SMA

The equation of motion of a rotor system supported by shape memory alloy (SMA)controller and elastic bearing is given in this paper after the soft nonlinear characteristics of the controlling force are considered.Using the nonlinear dynamic theory,one obtain the second order nonlinear approximate solution of the system in main resonance.Using dynamic stability theory,one also obtain the function of the jump range of the vibration amplitude of the system.By analyzing the solution and the jump range,the effects of the system parameters on dynamic characteristics of the system are determined.Theoretical results are supported by simulating results.A conception is suggested to reduce the maximum vibration amplitude of system in uncertain state by SMA controller and SFD(squeeze film damper,and investigate the variation of system characteristics when SFD was equipped.