硬弹簧滑移系统稳态随机响应的等效化预测及适用性分析

Equivalent prediction and its applicability analysis of steady state random responses of hardening springs sliding system

以高斯白噪声作用下的刚性滑动摩擦体系为例,利用相对刚度硬化系数指标同时定义了系统位移响应的峰值与差值累计量指标。基于蒙特卡洛模拟结果,对比分析了硬弹簧滑移系统对高斯白噪声作用稳态响应的几种等效化预测方法的精度。分析表明:对于取定的相对刚度硬化系数η,当其值较小时,阻尼等效线性化法的峰值差和差值累计量一般较其它两种等效化法的相应值大;当η值增大时,等效非线性系统法的峰值差和差值累计量最大,而完全等效线性化法的峰值差和差值累计量最小。与数字模拟的失效概率相比,等效非线性系统法将低估不同阈值下滑移系统的滑移失效概率,完全等效线性化法在预测阻尼弱非线性系统及噪声强度较高的滑移系统的滑移失效概率时,与数字模拟的结果吻合较好。

Taking rigid sliding friction system under action of Gauss white noise as an example, and by use of rela- tive rigidity displacement hardening coefficient,the peak displacement response and difference accumulation indiees were defined simultaneously. Based on Monte Carlo simulation results, the accuracy of several equivalent prediction methods for determing response of hardening spring sliding system to Guass while noise input was analyzed comparatively. The results show that, for the taken relative stiffness hardening coefficient η, when its value is small peak differnce and difference, cumulative amount of damping equivalent linearization method are larger than those of other two equivalent linearization method; when the η value increases, the peak difference and diffevence cumulalive a- mount of equivalent nolinear system method are largest,and those of completely equivalent linearization method are smallest. Compared with failure probability from digital simulation, equivalent nonlinear system method understi-mates sliding failure probaility of sliding system under different threshold. In predicting sliding failure probability of weak damping nonlinear system and sliding system with more intensive noise, the simulated results from complete equivalent linearization method conincied with that from diglal simulation.