【摘要】 将参数变换法和随机多尺度法结合起来,研究窄带随机噪声激励下强非线性Duffing-Rayleigh振子的响应及稳定性问题.首先借助参数变换思想引入小参数,然后用多尺度法分离了系统的快变量,最后由摄动法和矩方程法得到了系统的稳态响应.并利用Routh-Hurwitz准则得到了稳态解稳定的充要条件.理论分析与数值计算表明:在一定条件下,系统存在两个稳定的稳态解.数值模拟的结果表明:参数变换法结合随机多尺度法研究强非线性随机系统的响应、稳定性等问题是有效的.更多还原

【Abstract】 A technique combining the parameter transformation method with the multiple scales method was presented to determine the primary resonance response of a strongly non-linear EXiffing-Rayleigh oscillator to random narrow-band excitation. First, we introduced a new expansion parameter α=α(ε,μ0),and then we employed the multiple scales method to determine the equations, which described the modulation of the amplitude and phase, finally we analyzed the dynamical behaviors of the primary resonance response. The effect of the random excitation on the stable periodic response was analyzed as a perturbation, and the stationary meansquare response was obtained by the moment method. The sufficient and necessary condition for the stability of the steady-state response was obtained by the Routh-Hurwitz criterion. Theoretical analyses and numerical calculation showed that under some conditions the system may have two steady-state solutions, and that the technique was effective to study the strongly non-linear oscillator.更多还原