基于余量谐波平衡的两质点动力学系统振动频率与响应分析  

ANALYSIS ON VIBRATION FREQUENCY AND RESPONSE OF TWO-MASS DYNAMIC SYSTEMS BASED ON RESIDUE HARMONIC BALANCE

作　　者：国忠金 夏丽莉[1] 张伟[1,3] Guo Zhongjin;Xia Lili;Zhang Wei(College of Mechanical Engineering,Beijing University of Technology,Beijing 100124,China;School of Mathematics and Statistics,Taishan University,Taian 271000,China;Beijing Key Laboratory on Nonlinear Vibrations and Strength of Mechanical Structures,Beijing 100124,China)

机构地区：[1]北京工业大学机电学院,北京100124 [2]泰山学院数学与统计学院,泰安271000 [3]机械结构非线性振动与强度北京市重点实验室,北京100124

出　　处：《动力学与控制学报》2018年第4期324-331,共8页Journal of Dynamics and Control

基　　金：国家自然科学基金(11290152;11427801;11502160);山东省自然科学基金(ZR2014JL002;ZR2014AQ028);山东省高等学校科研计划项目(J15LI13);北京市博士后资助计划项目(2015zz-18)~~

摘　　要：为全面了解和准确预测两质点动力学系统运动特性.本文以具有固定边界的两质点动力学系统为例,构建了用于研究双自由度质点运动系统的余量谐波平衡解程序.解程序融合了谐波平衡与同伦方法优势,其高阶近似仅依赖于初始谐波近似,不需要根据前一阶近似进行调整.研究结果表明:本文给出的2-阶近似频率比已有的方法结果更加精确,相对误差不同程度减小,相应的近似响应与数值解更加吻合.因此,余量谐波平衡方法可广泛应用于其它质点动力学问题研究中.To fully understand and accurately predict the motion characteristics of two mass dynamic systems,this paper constructs a solution procedure of residue harmonic balance for the study of two-degree-of-freedom motion systems,taking two-mass dynamic system connected with fixed boundaries as an example. This solution procedure combines the advantages of harmonic balance and homotopy method,and the higher-order approximations only depend on the initial harmonic approximation,and they don＇t need to be adjusted according to the previous approximations. The results show that the frequencies based on the presented second-order residue harmonic balance are more accurate than the results obtained by other existing methods,and the relative errors are reduced in different degrees. Moreover,the presented steady responses are in good agreement with the numerical ones. It is shown this method can be applied widely to other nonlinear oscillation problems.

关 键 词：双自由度振动系统 余量谐波平衡 高阶近似 频率响应 

分 类 号：TH113[机械工程—机械设计及理论]