双频激励下微弯液压管道的非线性振动研究  

A study on nonlinear vibration of slightly curved hydraulic pipes under dual frequency excitation

作　　者：范鑫 舒送 张俊宁 肖璐 毛晓晔 丁虎[3] FAN Xin;SHU Song;ZHANG Junning;XIAO Lu;MAO Xiaoye;DING Hu(The 5720th Factory of PLA,Wuhu 241007,China;Department of Precision Machinery and Precision Instruments,University of Science and Technology of China,Hefei 230026,China;Shanghai Institute of Applied Mathematics and Mechanics,School of Mechanics and Engineering Science,Shanghai University,Shanghai 200444,China)

机构地区：[1]中国人民解放军第5720工厂,安徽芜湖241007 [2]中国科学技术大学精密机械与精密仪器系,合肥230026 [3]上海大学力学与工程科学学院上海市应用数学和力学研究所,上海200444

出　　处：《振动与冲击》2023年第20期181-187,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金青年基金项目(12002195,12025204);上海市教育委员会科研创新计划项目(2019-01-07-00-09-E00018)。

摘　　要：首次研究了双频激励下两端固支微弯液压管道的非线性振动,分析了拍振现象发生时管路非线性受迫振动特性。利用广义哈密顿原理建立微曲管道控制方程,使用Galerkin法将非线性偏微分积分方程离散为非线性耦合常微分方程组,采用龙格库塔法数值求解,并用微分求积单元法进行数值验证,得到了微曲管道受迫振动响应。在此基础上,讨论了两个激励频率差值对管道中点受迫振动响应的影响,并分析了系统横向振动在一阶固有频率附近的分岔现象,考察了液压管道的混沌特性。分析结果表明,当两个激励频率相差较小时会出现混沌现象,随着频率差值的减小,管道的混沌区域先增大后减小。这些结论为多频激励下液压管道系统复杂振动的研究提供了理论依据和研究方法。The nonlinear combined vibration of a slightly curved hydraulic pipe with two fixed supports under dual frequency excitation was studied.The nonlinear forced vibration characteristics were analyzed when the beat vibration phenomenon occurs.The Generalized Hamiltonian principle was used to establish the governing equation of the slightly curved pipe.The nonlinear partial differential integral equation was discretized into a set of nonlinearly coupled ordinary differential equations via the Galerkin method.Numerical solutions of the forced vibration were obtained by the Runge Kutta method based on the discrete ordinary differential equations.The differential quadrature element method verifies its accuracy.On this basis,the influence of the frequency gap between two excitations on the forced vibration of the pipe’s midpoint was discussed.The bifurcation and chaos of the transverse vibration near the first order natural frequency was analyzed.The analysis results show that when the frequency gap is small,chaos will appear.With the decrease of frequency gap,the chaotic frequency band increases and then decreases.These conclusions provide theoretical basis and methods for the study of complex vibration of hydraulic pipe systems under multi-frequency excitation.

关 键 词：双频激励 微弯管道 液压管道 拍振 混沌 

分 类 号：O322[理学—一般力学与力学基础] O326[理学—力学]