随机激励的非线性Markov跳变系统的响应分析

来源 :第九届全国随机振动理论与应用学术会议暨第三届全国随机动力学学术会议 | 被引量 : 0次 | 上传用户：xuanwuba

【摘要】

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【作者】

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宦荣华朱位秋

【机构】

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浙江大学应用力学研究所,杭州,310027

【出处】

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第九届全国随机振动理论与应用学术会议暨第三届全国随机动力学学术会议

【发表日期】

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2014年8期

【关键词】

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Markov跳变随机激励非线性随机平均法

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　　大量实际工程问题需要用同时包含连续和离散变量的Markov跳变系统来描述。本文介绍了研究一类随机激励的(强)非线性单自由度Markov跳变系统的响应的理论方法。首先，运用随机平均法对系统方程进行简化，导出了平均Markov跳变It(o)随机微分方程，原系统方程的维数得到降低。接着，建立和求解相应的广义Fokker-Planck-Kolmogorov (GFPK)方程，得到系统振幅和Markov跳变参数的稳态联合概率密度。最后，以一个高斯白噪声激励的跳变Duffing振子为例，计算得到不同跳变规律下系统的稳态响应及其统计量。研究结果表明，该方法对随机激励的非线性单自由度Markov跳变系统的响应求解比较有效。

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