相关激励作用下随机结构振动响应的统计分析

Statistical analysis of vibrational response of uncertain dynamics structures based on correlated excitations

应用随机过程理论,以能量为变量,分析了随机结构振动响应的统计特性。结构受相关激励作用时,通过输入激励的解相关方法,将作用在结构上的相关激励转变为各个不相关激励的作用;分析结构的振动响应的统计特性时,计及响应特征频率的相关性,在响应特征频率满足高斯正交总体的假设下,推导出了随机结构振动响应分析的统计分析表达式。应用设计的实验件和试验验证了所提出的统计分析的正确性,通过和已存在的统计分析结果的比较,表明了统计分析具有更高的分析精度,能够定性和定量的给出随机结构振动响应的统计变化情况。

The statistical characteristics of vibrational response to uncertain dynamic structures were analyzed in this paper, by applying random process theory, and taking energy as variables. Via the decoupling correlation method of the input excitation, which based on proper orthogonal decomposition, the correlative excitations were translated into statistically independent excitations. The relativity of eigenfrequency in structural response was counted in when analyzing the statistical characteristics of vibrational response to uncertain dynamic structures. The calculative expression of vibrational response to uncertain dynamic structures was proposed in the paper. Experimental sample was designed to validate the correctness of the method. It shows that： compared with the existent result, the proposed statistical analysis method is of more accuracy, and it can qualitatively and quantitatively present the statistical characteristics of vibrational response to uncertain dynamic structures.