随机噪声激励下的一类相对转动系统的响应

Response of a Relative-Rotation Nonlinear System Under Random Noise Excitationr

探讨一类相对转动非线性动力系统在随机噪声作用下的响应问题,将多尺度法运用到含有随机扰动的相对转动系统中,利用线性化法、矩方法讨论了该系统的阻尼项、随机项对系统的二阶矩的影响并应用Routh-Harwitz准则给出了系统解的稳定性条件,理论分析了较小的随机强度对系统解的稳定性影响不大,系统的二阶矩随着阻尼项的增大而减小,随着随机强度的增大而增大,最后得出理论分析与数值模拟是一致的.

The steady-state response of a relative-rotation system under random noise excitation is investigated.The method of multiple scales is applied to this system.The method of linearization and moment means are used to discuss that damping term and random item have a great influence on secondary moment of the system,rule is utilized to give the condition of stability of system.It is theoretically illustrated that the small random intensity has little influence on the stability of solution,and the second moment of system will decrease with the increase of the damping and increase with the increase of the random intensity.Finally,the theoretical analysis is consistent with numerical simulation.