A non–Poisson model for the vibration analysis of uncertain dynamic systems
A non–Poisson model for the vibration analysis of uncertain dynamic systems
复制标题
不确定动态系统振动分析的非泊松模型
DOI：
10.1098/rspa.1999.0453
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
R. Langley
中科院分区：
文献类型：
--
作者：
R. Langley
动态系统对中频或高频激励的响应对系统物理特性的微小变化非常敏感。以前的工作通过采用系统固有频率的泊松模型来研究这个问题；其他研究已经进行了数值模拟，揭示了不能包括在泊松模型中的参数的影响。本工作将包含泊松模型的固有频率的点过程模型视为极限情况，但也允许考虑统计重叠因子等关键参数的影响。导出了一些一般性的结果，并将其应用于高斯型固有频率的特殊情况。推导了频率响应函数的方差的闭合形式解，该解依赖于单个参数：该参数是统计重叠系数、振型重叠系数和固有频率之间的相关程度的组合。对自然频率间隔的统计分布也给予了关注，并根据点过程模型的累积量函数得出了各种结果。通过与仿真结果的比较，验证了分析结果的正确性。
The response of a dynamic system to medium– or high–frequency excitation can be very sensitive to small changes in the physical properties of the system. Previous work has investigated this issue by adopting a Poisson model of the system natural frequencies; other studies have performed numerical simulations that reveal the effect of parameters that cannot be included in the Poisson model. The present work considers a point–process model of the natural frequencies that encompasses the Poisson model as a limiting case but also allows the influence of key parameters such as the statistical–overlap factor to be considered. A number of general results are derived and these are then applied to the special case of Gaussian natural frequencies. A closed–form solution for the variance of a frequency–response function is derived that depends upon a single parameter: this parameter is a combination of the statistical–overlap factor, the modal overlap factor, and the degree of correlation between the natural frequencies. Attention is also directed at the statistical distribution of the natural frequency spacing, and various results are derived in terms of the cumulant functions of the point–process model. The analytical results obtained are confirmed by comparison with simulation results.