多维相关随机激励下梁结构响应求解方法  

Solution of beam response spectrum under multi-dimensional correlated random excitation

作　　者：张毅成 黄港婷 谢石林[1,2] Zhang Yicheng;Huang Gangting;Xie Shilin(State Key Laboratory for Strength and Vibration of Mechanical Structures,Xi'an Jiaotong University,710049,Xi'an,China;School of Aerospace Engineering,Xi’an Jiaotong University,710049,Xi’an,China)

机构地区：[1]西安交通大学机械结构强度与振动国家重点实验室,西安710049 [2]西安交通大学航天航空学院,西安710049

出　　处：《应用力学学报》2021年第2期566-573,共8页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11872290);国家自然科学联合基金(U1430129)。

摘　　要：工程结构常受到多维的相关随机激励,本文利用解析法对多维相关随机激励下结构响应的求解进行了研究。利用相关系数描述多维激励之间的相关性,基于连续体振动理论,建立了梁结构在两端受到随机相关基础激励下的响应谱计算方法。针对某导弹舱段结构,进行了相关随机基础激励下结构的随机响应仿真分析,并与有限元计算结果进行了对比。结果表明:建立的计算方法与有限元方法分析结果具有较好的一致性,两种方法得到的功率谱密度函数峰值误差小于2%;随机激励相关性的增加将减小导弹舱段结构反对称模态的响应谱峰值,当两激励完全相关时,该模态不被激发;与此相反,导弹舱段结构其余模态的响应谱峰值随着激励间相关性的增加而明显增大。最后,进一步给出了随机力激励与随机基础激励同时存在时的多维相关随机激励下结构响应计算方法。Engineering structures are often subjected to multi-dimensional random excitation.In this paper,the analytical method is used to study the structure response under multi-dimensional random excitation.The correlation coefficient is used to describe the correlation between multi-dimensional excitations.Based on the continuum vibration theory,a method for calculating the response spectrum of a beam structure subjected to random correlation at both ends is established.For the structure of a certain missile section,a simulation analysis of the random response of the structure under the correlated random basic excitation is performed,and the results are compared with the finite element calculation results.The results show that the established calculation method is in good agreement with the analysis results of the finite element method,and the peak error of the PSD is less than 2%.The increase in the correlation of random excitation will reduce the peak of the response spectrum of the anti-symmetric mode of the missile cabin structure.When the two excitation are completely correlated,the mode is not excited.On the contrary,the peak value of the response spectrum of the remaining modes of the missile cabin structure increases significantly with the increase in correlation between the excitations.Finally,the structural response calculation method under the multi-dimensional correlated random excitation when the random force excitation and the random basic excitation coexist is further given.

关 键 词：多维随机激励 响应谱 相关激励 随机基础激励 随机力激励 

分 类 号：O324[理学—一般力学与力学基础]