基于高精度模态综合法的螺栓连接组合结构不确定模型更新  

Stochastic model updating of assembled structures with bolted joints based on the high-precision modal synthesis method

作　　者：张勇 赵岩[1,2] 欧阳华江 ZHANG Yong;ZHAO Yan;OUYANG Huajiang(Department of Engineering Mechanics,Dalian University of Technology,116023 Dalian,China;Ningbo Research Institute,Dalian University of Technology,315000 Ningbo,China;University of Liverpool,L693GH Liverpool,UK)

机构地区：[1]大连理工大学工程力学系,大连116023 [2]大连理工大学宁波研究院,宁波315000 [3]英国利物浦大学,L693GH利物浦

出　　处：《应用力学学报》2024年第2期443-452,共10页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目(No.11772084,U1906233);国家重点研发计划资助项目(No.2017YFC0307203);山东省重点研发计划资助项目(No.2019JZZY010801)。

摘　　要：由于螺栓结构中存在复杂的微观特征,数值模型中无法避免的会引入不确定性。针对螺栓设计中参数不确定性量化问题,一种基于高精度模态综合法的螺栓连接组合结构随机模型更新方法被提出。首先考虑高阶剩余模态的影响,推导了适用于螺栓组合结构弹性交界面的高精度模态综合法;之后,在贝叶斯推理框架下,通过组合结构的自振频率和振型的概率分布,建立螺栓连接参数的后验概率密度函数,并借助DRAM(delayed rejection adaptive metropolis)抽样方法量化参数的不确定性。数值算例表明,针对各子结构之间自振频率差别较大的结构,与模态综合法相比,本研究方法在较少子结构模态参与的情形下,也可以保证良好的模型更新结果。The existence of complex microscopic features in the bolted structure leads to inevitable uncertainty in the numerical model.Aiming at the quantification of parameter uncertainty in bolt design,this paper proposes a stochastic model updating method for assembled structures with bolted joints based on a high-precision modal synthesis method.First,considering the influence of higher-order residual modes,a high-precision modal synthesis method suitable for the elastic interface of bolted joints is derived.Then,under the framework of Bayesian inference,using the natural frequency and mode shape probability distribution of the assembled structure,the posterior probability density function of the bolt parameters is established,and the parameter uncertainty is quantified with delayed rejection adaptive metropolis(DRAM)sampling method.The numerical examples indicate that for structures with large differences in natural frequencies among the substructures,compared with the general modal synthesis methods,the method proposed in this paper can ensure good model updating performance in the case of using a small number of substructure modes.

关 键 词：组合结构 随机模型更新 贝叶斯方法 模态综合法 

分 类 号：O324[理学—一般力学与力学基础]