有界随机噪声激励下一类非线性系统的共振与饱和现象

Saturation and Resonance in a Class of Non-linear Systems Under Bounded Noise Excitation

研究了二自由度非线性系统在有界随机噪声激励下,系统响应的共振与随机饱和现象。用多尺度法分离了系统的快变项,用线性化方法求出了系统响应幅值的一、二阶矩,并给出了系统优化设计的一些建议。数值模拟表明本文提出的方法是有效的。

The principal resonance of a two-degree-of-freedom non-linear oscillator to bounded noise excitations is investigated,the phenomenon of random saturation is found.The method of multiple scales is used to separate the rapidly varying items in the modulation equations,and the linearization process is carried out to determine the steady state moments of the amplitude of the system response.Some suggestions for system optimum design are proposed.The theoretical analyses are verified with numerical simulation.