光线示波器振子非线性动力学分析

A Nonlinear Dynamic Analysis of the Ray Oscilloscope Vibrator

通过引入光线示波器振子系统中的非线性恢复力偶矩建立非线性振动方程,分析可以诱发振子系统主共振的条件。应用多尺度法得到振子系统满足主共振情况下的近似解,并进行数值计算。讨论磁感应强度、电流信号强度、阻尼对振子系统的影响,表明增大振子系统的磁感应强度或电流信号的强度可以增大系统主共振的振幅和共振区,增大振子系统阻尼可以减小系统主共振的振幅和共振区,反之亦然。

Through introducing the nonlinear restoring couple moment in the ray vibrator oscillo-scope system,a nonlinear vibration equation is established and conditions that can bring out the primary resonance of the vibrator system are analyzed.The method of multiple scales is employed to obtain the approximate solution for the primary resonance of the vibrator system and numerical calculation is made.The authors of this paper discuss the influence of the magnetic induction in-tensity,current signal strength,the damping on the vibration system,which shows that the in-crease of the magnetic induction intensity or the current signal strength of the vibration system will lead to the rise in the primary resonance amplitude and primary resonance region of the sys-tem and that the increase of the damping of the vibration system will lead to the decrease of the primary resonance amplitude and primary resonance region of the system and vice versa.