悬臂梁结构单点非高斯激励动态位移响应分析

The Displacement Response Analysis of Cantilever Beam Subjected to Non-Gaussian Random Loadings

针对非高斯随机载荷的复杂性,研究了悬臂梁结构在单点非高斯激励下的位移响应问题。通过定性分析非高斯随机载荷的统计特性和频谱特征指出基于功率谱的频域方法对于非高斯过程不完全适用,并进一步说明基于高阶谱的分析方法很难展开应用。通过理论研究建立了悬臂梁结构时域非高斯激励位移响应计算公式,并确定了影响结构位移响应峭度值的不同因素。通过仿真计算具体分析了激励位置、平稳性和阻尼比对结构位移响应非高斯性的影响。

The non-Gaussian random loading is complicated to characterize. In this study, the displacement response of the cantilever beam under the single-point non-Gaussian excitation is investigated. Firstly, the statistical characteristics and spectral properties are analyzed qualitatively, and it shows that the spectral method based on power spectrum is not quite suitable for non-Gaussian process and it is difficult to apply the method based on higher-order spectrum in the response analysis. Secondly, the time-domain formulae for the response analysis of a cantilever beam excited by non-Gaussian input are established. Then the factors that will affect the kurtosis value of the displacement response are determined. Finally, the influence of the excitation point, steady properties and damping ratio to the kurtosis value is examined by numerical simulations.