黏弹性系统随机响应分析

发布时间：2018-01-31 04:31

本文关键词： 黏弹性系统随机响应等效非线性化方法广义谐和变换稳态概率密度函数　出处：《振动工程学报》2016年05期 　论文类型：期刊论文

【摘要】：应用等效非线性化方法分析了高斯白噪声激励作用下强非线性黏弹性系统随机响应。首先,通过广义谐和变换,黏弹性作用力可近似等效为拟线性阻尼和拟线性刚度两部分,进而原系统简化为无黏弹性项的非线性随机系统。其次,选取一类具有待定参数的等效非线性系统类。该等效非线性系统类具有精确稳态解,且和简化后的非线性随机系统具有相同的特性。然后,根据简化系统和等效非线性系统类之差的均方值最小原则,最终确定等效非线性系统类中的待定参数。最后以该系统的精确稳态随机响应近似表示原系统的随机响应。本文所提方法得到的解析结果与蒙特卡洛模拟方法得到的结果符合较好,证实了该方法的正确性。
[Abstract]:The stochastic response of strongly nonlinear viscoelastic system under the excitation of Gao Si white noise is analyzed by using the equivalent nonlinear method. Firstly, the generalized harmonic transformation is used. The viscoelastic force can be approximately equivalent to two parts of quasilinear damping and quasilinear stiffness, and then the original system can be simplified as a nonlinear stochastic system with no viscoelastic term. A class of equivalent nonlinear systems with undetermined parameters is selected. The class of equivalent nonlinear systems has exact steady-state solutions and has the same characteristics as simplified nonlinear stochastic systems. According to the principle of minimum mean square of difference between simplified system and equivalent nonlinear system. Finally, the undetermined parameters in the class of equivalent nonlinear system are determined. Finally, the exact steady-state stochastic response of the system is approximated to the stochastic response of the original system. The analytical results obtained by the proposed method and the Monte Carlo simulation method are obtained. The results are in good agreement. The correctness of the method is verified.
【作者单位】：中国计量大学计量测试工程学院;中国计量大学浙江省流量计量技术研究重点实验室;
【基金】：国家自然科学基金青年基金资助项目(11402258)
【分类号】：O343
【正文快照】： 引言诸如聚合物、复合材料、生物材料等黏弹性材料广泛应用于结构和机械工程[1]。与传统弹性材料相比,黏弹性材料不仅可以储存弹性势能,而且类似阻尼可耗散能量。此外,黏弹性材料具有黏弹性特性——应力松弛和蠕变特性[2]。由于黏弹性材料的独特性质,它们已被应用于机器人,高

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