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泊松脉冲激励的多自由度耗散哈密顿系统平稳响应

发表时间:2008-05-15  浏览量:1960  下载量:878
全部作者: 吴禹,朱位秋
作者单位: 浙江大学航空航天学院应用力学研究所
摘 要: 本文研究了随机脉冲激励下的多自由度耗散哈密顿系统的平稳概率与统计特性。随机脉冲采用Poisson白噪声模型。通过用摄动法求解四阶广义Fokker-Planck方程,得到Poisson白噪声激励的多自由度耗散哈密顿系统的近似平稳响应概率密度函数和均方值。作为例子,考察了两自由度线性与非线性刚度耦合的Duffing振子,证明了其响应的非高斯特性依赖于脉冲平均到达率和系统弛豫时间的乘积,并用Monte Carlo模拟验证了该方法的可行性。
关 键 词: 工程力学;泊松白噪声;摄动法;耗散的哈密顿系统;概率密度函数;广义Fokker-Planck 方程
Title: Stationary response of multi-degree-of-freedom dissipated Hamiltonian systems under Poisson pulses
Author: WU Yu, ZHU Weiqiu
Organization: Institute of Applied Mechanics, School of Aeronantics and Astronautics, Zhejiang University
Abstract: The paper studied the stationary probabilistic and statistical characteristics of multi-degree-of-freedom (MDOF) dissipated Hamiltonian systems driven by random pulses. The pulse model adopted is Poisson white noise. The approximate stationary probability density functions and mean square values for the response of MDOF dissipated Hamiltonian systems to Poisson white noise are obtained by solving the four-order generalized Fokker-Planck equation using perturbation approach. As an example, two Duffing oscillators coupled with linear and nonlinear stiffness terms are investigated. It is shown that the non-Gaussian behavior depends on the product of the average arrival rate of the impulses and the relaxation time of the oscillator. The validity of this approach is confirmed by experimental results obtained by Monte Carlo simulation.
Key words: engineering mechanics;Poisson white noise;perturbation approach;dissipated Hamiltonian system;probability density function;generalized Fokker-Planck equation
发表期数: 2008年9月第9期
引用格式: 吴禹,朱位秋. 泊松脉冲激励的多自由度耗散哈密顿系统平稳响应[J]. 中国科技论文在线精品论文,2008,1(9):973-980.
 
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