摘要
建立了含铰柔性结构的非线性动力学模型,利用打靶法和伪弧长法计算该结构的非线性模态和频率-能量关系图,研究含铰柔性结构的非线性特性。其次,考虑非线性铰链刚度对结构动态特性的影响,讨论了不同线性/非线性刚度与结构的非线性模态及频率-能量曲线的关系。利用非线性三自由度保守系统的模态分析,阐释频率-能量曲线能够直观反映结构的非线性特性:固有频率变化及分叉、模态转换及内共振。对含铰柔性结构的非线性模态分析及参数影响研究表明:1)含铰柔性结构的固有频率与输入能量存在明显非线性特性;2)铰链非线性刚度的增加,使得含铰柔性结构的固有频率和模态在较低的振动能量下即可发生较大变化;其次,随着线性刚度的增加,非线性特性减弱,各阶固有频率的相对变化降低,频率-能量关系图由曲线变为直线;3)较高的振动能量在结构模态之间发生转换,使得结构出现明显的内共振非线性特性。
Based on the nonlinear dynamic model of the flexible assembled structure with a nonlinear hinge,shooting method and pseudo-arc length continuation approach were applied to nonlinear normal mode construction and frequency-energy plot calculation.In order to further understand the effect of the stiffness of nonlinear hinge on the dynamic characteristic,the nonlinear normal modes and frequency-energy plots(FEP)with different linear and nonlinear stiffness were implemented.The modal analysis for the nonlinear conservative three degrees of freedom system illustrated that the frequency-energy plot could represent the dynamic characteristic clearly:bifurcation and change of natural frequencies,internal resonance and transition of modes.Results from nonlinear hinge flexible structure examples were:1)Obvious nonlinear relationship exists between natural frequencies and input vibrating energies for the flexible structure with hinges.2)With the increase of nonlinear stiffness,the natural frequencies and modes will change quickly under low vibrating energy level;On the other hand,with the linear stiffness increasing,the nonlinear characteristics and the relative change of resonance frequencies decreased and the FEP will be straight instead of curvilinear.3)The higher vibrating energy will transform between structural modes,and the structure will show the internal resonance obviously.
作者
曹芝腑
费庆国
姜东
吴邵庆
刘璟泽
CAO Zhi-fu;FEI Qing-guo;JIANG Dong;WU Shao-qing;LIU Jing-ze(Institute of Aerospace Machinery and Dynamics,Southeast University,Nanjing 211189,China;College of Mechanical and Electronic Engineering,Nanjing Forestry University,Nanjing 210037,China;Department of Engineering Mechanics,Southeast University,Nanjing 210096,China)
出处
《振动工程学报》
EI
CSCD
北大核心
2018年第4期573-581,共9页
Journal of Vibration Engineering
基金
国家自然科学基金资助项目(11602112
11572086)
关键词
柔性结构
非线性铰链
非线性模态
频能图
内共振
flexible structure
nonlinear hinge
nonlinear normal modes
frequency-energy plot
internal resonance
