欠阻尼二阶线性系统中的随机共振

摘要

在单自由度粘滞阻尼二阶线性系统的阻尼系数、固有频率和激励信号三者均受高斯白噪声干扰的背景下,利用线性系统相关理论和数学方法,推导得到了系统平均输出幅度增益的表达式.同时,利用MATLAB软件对此二阶欠阻尼线性系统做了仿真研究.仿真结果表明:只要将系统参数调节至适当范围,平均输出幅度增益会在某个位置达到最大值,即存在随机共振现象,因而只要使系统处于随机共振的共振区域,就能实现噪声背景下欠阻尼二阶线性系统的微弱信号检测.%This paper deals with the phenomena of stochastic resonance in the under-damped secondorder linear system, whose damping coefficient, intrinsic frequency, and driving signal frequency are disturbed by the Gaussian white noise. Based on the related theories of linear systems and mathematical methods, the expression of output amplitude gain (OAG) was derived. This expression is a nonmonotonic function concerning the damping coefficient, intrinsic frequency, noise intensity, and driving signal frequency. Simultaneously, MATLAB software was used to simulate the under-damped second-order linear system. The simulation results show that as long as appropriate parameters are adjusted, the average output amplitude gain value will be the maximum at some location, namely,there exists the phenomenon of stochastic resonance. Therefore, if the system is in the resonance region, the weak signals in the under-damped second-order linear systems in the noise background can be detected.