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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。
Under the background that the damping coefficients, natural frequencies and excitation signals of viscous damped second-order linear systems with one degree of freedom are all affected by Gaussian white noise, linear system-related theory and mathematical methods are used to derive the average output amplitude gain of the system expression. At the same time, MATLAB software is used to simulate the second-order under-damped linear system. The simulation results show that as long as the system parameters are adjusted to the proper range, the average output amplitude gain will reach a maximum value at a certain position, that is, the phenomenon of stochastic resonance exists. Therefore, as long as the system is in a stochastic resonance resonance region, Weak Signal Detection of Damped Second Order Linear Systems.