考虑滞回效应的螺栓连接组合结构非线性随机振动分析  

Nonlinear random vibration analysis of bolted composite structure considering hysteresis effect

作　　者：吴鹏辉 王纪磊 毛晨洋 赵岩 WU Penghui;WANG Jilei;MAO Chenyang;ZHAO Yan(State Key Lab of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Faculty of Vehicle Engineering and Mechanics,Dalian University of Technology,Dalian 116023,China;Ningbo Research Institute,Dalian University of Technology,Ningbo 315016,China)

机构地区：[1]大连理工大学运载工程与力学学部工业装备结构分析优化与CAE软件全国重点实验室,辽宁大连116023 [2]大连理工大学宁波研究院,浙江宁波315016

出　　处：《振动与冲击》2024年第5期223-230,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(11772084,U1906233);国家重点研发计划项目(2017YFC0307203);山东省重点研发计划项目(2019JZZY010801);中央高校基础研究经费(DUT22ZD209)。

摘　　要：针对具有滞回效应的螺栓连接组合结构,结合虚拟激励法和多谐波平衡法实现了随机振动响应频域功率谱分析。首先,对于随机激励作用下的组合结构,以Jenkins模型进行本构建模。其次,将随机激励表达为复指数级数,将响应谱分析转化虚拟响应的向量运算,提出了扩展虚拟激励法(extended pseudo excitation method, E-PEM)。最后,对虚拟响应求解中频域本构的计算困难,引入时频变换处理;将非线性迭代转换为优化问题并利用信赖域方法求解,有效解决了传统牛顿法的收敛困难。以二自由度和组合梁模型为对象,研究了结构的随机振动响应谱特性,并同蒙特卡罗模拟法对比验证E-PEM的正确性,同时对结构特有的非线性随机振动机制进行了讨论。结果表明:建立的E-PEM为一般非线性结构随机振动频域分析提供了一个可借鉴的求解思路。Here,aiming at bolted composite structure with hysteresis effect,the pseudo excitation method and multi-harmonic balance method were combined to realize frequency domain power spectra analysis for random vibration response.Firstly,for composite structure under action of random excitation,Jenkins model was used for constitutive modeling.Secondly,random excitations were expressed as complex exponential series,and response spectrum analysis was converted into vector operation of virtual responses to propose the extended pseudo excitation method(E-PEM).Finally,due to calculating difficulty of frequency domain constitution in solving virtual response,alternating time-frequency(AFT)was introduced for processing.Converting nonlinear iteration into optimization problems and solving them with the trust region method effectively solved convergence difficulties of the traditional Newton method.Random vibration response spectrum characteristics of structure were studied with a 2-DOF composite beam model.Compared with Monte Carlo simulation(MCS)method,the correctness of E-PEM was verified.Meanwhile,the specific nonlinear random vibration mechanism of structure was discussed.The results showed that the established E-PEM can provide a reference solving idea for frequency domain analysis of random vibration of general nonlinear structures.

关 键 词：滞回效应 随机振动 虚拟激励法(PEM) 多谐波平衡法 

分 类 号：O324[理学—一般力学与力学基础]