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研究了单自由度非线性干摩擦系统在窄带随机噪声参数激励下的主共振响应问题.用Krylov-Bogoliubov平均法得到了关于慢变量的随机微分方程.在没有随机扰动情形,得到了系统响应幅值满足的代数方程.在有随机扰动情形,用线性化方法和矩方法给出了系统响应稳态矩计算的近似计算公式.讨论了系统阻尼项、非线性项、随机扰动项和干摩擦项等参数对于系统响应的影响.理论计算和数值模拟表明,当非线性强度增大时系统的响应显著变小,系统分岔点滞后;随着激励频率的增大系统响应变大,而当激励频率小于一定的值时,系统响应为零;增加干摩擦强度或者阻尼,可以减少系统的响应,并且使得系统分岔滞后.随机扰动可以使得系统的响应从一个极限环变为一扩散的极限环.数值模拟表明该方法是有效的.
The main resonance response of a single degree of freedom nonlinear dry friction system under the excitation of narrow-band random noise parameters is studied. The stochastic differential equations for slow variables are obtained by using the Krylov-Bogoliubov average method. In the absence of random perturbation, the response of the system is obtained The algebraic equations are satisfied.When there are stochastic disturbances, the approximate formulas for calculating the steady-state moments of the system are given by means of the linearization method and the moment method.The damping terms, the nonlinear terms, the random disturbances and the dry friction terms The theoretical calculation and numerical simulation show that the response of the system becomes smaller and the branch point of the system lags behind when the nonlinear strength increases. The response of the system becomes larger as the excitation frequency increases, When the frequency is less than a certain value, the system response is zero; increasing the dry friction or damping can reduce the response of the system and make the system stagger.Stochastic disturbance can make the system response change from a limit cycle to a diffusion limit cycle Numerical simulation shows that this method is effective.