理论力学机械的振动基础18.ppt

1 　 1 b 随? 增大而减小； where b decreases with increasing ? : If w goes to , b goes to b0. If w goes to , b goes to zero. ? — 振幅比或称动力系数 ? — 频率比 ?—? 曲线 幅频响应曲线 （幅频特性曲线） is the amplitude ratio (or the dynamic coefficient). ? is the frequency ratio. This is the ? - ? curve, the dependence of the amplitude on the frequency. 　 4. Resonance 4、共振现象 b is the infinite( ), this phenomenon is called resonance. then n w w =  If ，这种现象称为共振。 At resonance we get 此时， 　 §18-5 Damped forced vibration of a system with one degree of freedom §18-5 单自由度系统的有阻尼强迫振动 1. Differential equation of a damped forced vibration and its solution. 一、有阻尼强迫振动微分方程及其解 Dividing both sides of the last equation by m and introducing the notations 将上式两端除以m ，并令 　 we obtain 有阻尼强迫振动微分方程的标准形式，二阶常系数非齐次微分方程。 This equation is the differential equation of a damped forced vibration in standard form. It is a linear inhomogeneous differential equation of second order. Its solution is 　 where x1 is the general solution of the corresponding linear homogeneous equation x1是齐次方程的通解 in the case of small resistance 小阻尼： （A、? 积分常数，取决于初始条件） and x2 is a particular solution of the complete equation Substituting this expression into the differential equation in standard form we obtain x2 是特解： 代入标准形式方程并整理 　 — 强迫振动的振幅 — 强迫振动相位滞后激振力相位角 — the amplitude of the forced vibration. e is the phase shift of the forced vibration, the difference to the phase of the disturbing force. 振动微分方程的全解为 The total solution of the differential equation of the vibration is 衰减振动 强迫振动 damped vibration forced vibration 　 At the beginning of the vibration, the process with both the natural and the forced vibration simultaneously, is called the transient process. 振动开始时，二者同时存在的过程——瞬态过程。 The other process of forced vibration after the transient process, is called the stable state process. It is the