摘要
以相平面、时域响应辅以FFT等方法研究了同时具有二次和三次非线弹性的振动系统的超谐共振数值模拟问题.在一般初值条件下,无阻尼系统的共振响应含一长拍,弱阻尼系统的共振响应有一长过渡过程.本文提供了时域响应立即进入周期态的方法,从而大大提高了工程应用中FFT的精度和可实现性.
The superharmonic resonant responses of the vibrating Systems with nonlinear elasticity of the 2nd and 3rd powers are numerically studied on the phase plane and in the original coordinates in time domain, supplemented with FFT.The resonant responses for general initial conditions are found being accompanied by long beats in the undamped systems and by long transient in the weakly-damped systems.A method is examined for immediately entering essentially-periodic responses.The feasibility and accuracy of FFTare greatly achieved in engineering.
关键词
非线性
周期响应
超谐共振
nonlinearity
periodic response
superharmonic resonance
numerical simulation
beat
