摘要:
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.
Abstract:
The resonance response of a single-degree-of-freedom nonlinear dry oscillator of Coulomb type to narrow-band random parameter excitation is investigated. The analysis is based on the Krylov-Bogoliubov averaging method. The averaged equations are solved exactly and the algebraic equation of the amplitude of the response is obtained in the case without random disorder. Linearization method and moment method are used to obtain the mean square response amplitude for the case with random disorder. The effects of damping, nonlinear intensity, detuning, bandwidth, dry intensity, and magnitudes of random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak amplitudes may be strongly reduced and the bifurcation of the system will be delayed when intensity of the nonlinearity increases. The peak amplitudes will also be reduced and the bifurcation of the system will be delayed when damping and dry intensity of the system increases.
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