关于线性系统避免共振的条件

ON THE CONDITIONS FOR LINEAR SYSTEMS TO AVOID RESONANCE

对于无阻尼线性系统,外力频率不等于或不接近于系统的任一固有频率一直被认为是避免共振的条件.本文对此作了进一步的探讨,建立并统一了线性系统避免共振的条件,还尝试回答下面问题:外力频率等于系统的某阶固有频率,是否一定发生共振?有阻尼系统情况又怎样?

It is widely accepted that the frequencies of external forces are neither equal nor near to any eigenvalue of a linear system without damping, so as to prevent it from resonance. Based upon further investigation in the paper, a more general statement has been made, through which the authors try to answer such questions as follows: Must a resonance occur for the non-damped linear system when a frequency of the forces equals to some eigenvalue? How aboutdamped linear system?