Abstract：Mode localization can reflect rapid and even violent changes in dynamic modes. It also reflects that the dynamic system is fairly sensitive at a certain parameter. Therefore, the significance of mode localization and mode jumping was paid attention in this work. Firstly, according to the real mode Firstorder Sensitivity Theory, the factors affecting the real mode firstorder sensitivity were analyzed, and the relation between the real frequency curve veering and the real mode firstorder sensitivity was removed. Secondly, through the analysis of the structure of closed frequencies and the structure of multiple frequencies, the mode jumping phenomenon was illustrated and the reasons for mode jumping were explored. Then the concept and determination method of the modewhich is not differentiable at a certain point of design parameterwere proposed. Finally, through computing the steadystate responses of the two structures under simple harmonic excitation, the effects of mode jumping and closely & multiple frequencies on vibration analysis were studied.
[1] Eduard R，Charle C R，Francis A B. On the solution of mode jumping phenomena in thin-walled shell structures[J]. Computer Methods in Applied Mechanics and Engineering,1996,136:59–92.
[2] Everall P R，Hunt G W. Mode jumping in the buckling of struts and plates: a comparative study[J]. International Journal of Non-Linear Mechanics,2000,35:1067–1079.
[3] 于岩磊，高维成，刘 伟，王兆敏，孙 毅. 密集模态结构模态跃迁分析的简化摄动法[J]. 工程力学，2012, 29(3): 33-39.
YU Yan-lei, GAO Wei-cheng, LIU Wei, WANG Zhao-min, SUN Yi. Simplified perturbation mehtod for analyzing the mode jumping of closed mode structure [J]. Engineering Mechanics, 2012, 29(3): 33-39.
[4] 蒋友宝，冯 健，孟少平. 结构损伤识别中模态跃迁的研究[J]. 工程力学，2006, 23 (6):35-40.
JIANG You-bao, FENG Jian, MENG Shao-ping. Mode jumping research in structural damage identification[J]. Engineering Mechanics, 2006, 23 (6):35-40.
[5] 张 淼，于 澜，鞠 伟. 重频结构模态灵敏度分析的高精度截模态算法[J]. 振动工程学报，2014, 27 (4):526-532.
ZHANG Miao, YU Lan, JU Wei. A high accuracy truncated modal algorithm of sensitivity analysis for multiple-frequency structure[J]. Journal of Vibration Engineering, 2014, 27 (4):526-532.
[6] 张 淼，于 澜，鞠 伟. 模态跳跃现象对振动分析的影响研究[J]. 合肥工业大学学报：自然科学版，2015, 38 (11):1524-1529.
ZHANG Miao, YU Lan, JU Wei. Reserch on the effect of modal jumping phenomenon on vibration analysis [J]. Journal of Hefei University of Technology ( Nature Secience), 2015, 38 (11):1524-1529.
[7] 刘潇翔，胡 军. 包含密集模态的空间结构的模糊主动振动控制[J]. 空间控制技术与应用，2010，36(4)：18-24.
LIU Xiao-xiang, HU Jun. Fuzzy vibration control of space structures with close modes [J]. Aerospace Control and Application, 2010，36(4)：18-24.
[8] 刘利军，樊江玲，张志谊，华宏星. 密频系统模态参数辩识及其振动控制的研究进展[J]. 振动与冲击，2007, 26(4):109-115.
LIU Li-jun, FAN Jiang-ling, ZHANG Zhi-yi, HUA Hong-xing. Study progresses in modal parameters identification and vibration control of systems with crowded modes [J]. Journal of Vibration and Shock, 2007, 26(4):109-115.
[9] 谭 平，卜国雄，刘红军，周福霖. 带TMD结构的随机地震响应分析的新方法[J]. 北京理工大学学报，2010，30(4)：390-394.
TAN Ping, Bu Guo-xiong, LIU Hong-jun, ZHOU Fu-lin. A new method for the random earthquake response analysis of the TMD-Structure[J]. Transactions of Beijng Institute of Technology, 2010，30(4)：390-394.
[10] 陈臻林. 大型结构动力响应的状态方程的Krylov精细时程积分法[J]. 力学与实践，2010, 32(2):76-81.
CHEN Zhen-lin. Krylov precise time-step integration algorithm for large-scale structure dynamic equations[J]. Mechanics in Engineering, 2010, 32(2):76-81.
[11] 张 淼，于 澜，鞠 伟. 基于频响函数矩阵计算阻尼系统动力响应的新方法[J]. 振动与冲击，2014，33(4)：161-166.
ZHANG Miao, YU Lan, JU Wei. A new method for computing dynamic response of a damped linear system based on frequency response function matrix[J]. Journal of Vibration and Shock , 2014，33(4)：161-166.
