Stochastic Averaging of Energy Envelope
Stochastic Averaging of Energy Envelope
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DOI：
10.1061/(asce)0733-9399(1991)117:8(1890
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发表时间：
1991-08
期刊：
影响因子：
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通讯作者：
W. Zhu;Y. Lin
中科院分区：
文献类型：
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作者：
W. Zhu;Y. Lin
将先前用于分析非线性系统在独立理想高斯白噪声随机激励下的能量包络的随机平均方法推广到包含相关物理白噪声的情况。激励可以是加性的或乘性的，或两者兼而有之。推广的关键是将众所周知的Wong - Zakai校正项分成两部分，并分别将它们确定为阻尼和恢复力的附加贡献。结果表明，对于位移和速度，这种广义方法与另一种称为耗散能量平衡的方法得到的联合概率密度相同。此外，对于一个简化的线性系统，所得到的二阶矩稳定性条件是精确的。给出了两个例子来说明。
The method of stochastic averaging, as applied previously to analyze the energy envelope of a nonlinear system under random excitations of independent ideal Gaussian white noises, is generalized to include the case of correlated physical white noises. The excitations can be additive or multiplicative, or both. The key to the generalization is to separate the well‐known Wong‐Zakai correction terms into two parts and identify them as additional contributions to damping and restoring force, respectively. It is shown that this generalized procedure yields the same stationary joint probability density for the displacement and velocity as that obtained from another procedure, called dissipation energy balancing. Furthermore, the second‐moment stability conditions obtained for a reduced linear system are exact. Two examples are given for illustration.