柔性铰链型非线性能量阱设计与系统局部分岔特性分析  

Design of a nonlinear energy sink with flexible hinges and local bifurcation analysis of the system

作　　者：李爽[1] 楼京俊[2] 柴凯 刘树勇[1] 杨理华 LI Shuang;LOU Jingjun;CHAI Kai;LIU Shuyong;YANG Lihua(College of Power Engineering,Naval University of Engineering,Wuhan 430033,China;College of Naval Architecture and Ocean,Naval University of Engineering,Wuhan 430033,China;Power Control Department,Navy Submarine Academy,Qingdao 266199,China)

机构地区：[1]海军工程大学动力工程学院,武汉430033 [2]海军工程大学舰船与海洋学院,武汉430033 [3]海军潜艇学院动力系,山东青岛266199

出　　处：《振动与冲击》2020年第24期156-163,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金(51509253,51579242,51679245);湖北省自然科学基金(2018CFB182)。

摘　　要：提出了一种预压式柔性铰链结构与螺旋弹簧并联的新型非线性能量阱结构设计方法。分析了单根柔性铰链静力学特性,并对所设计结构的整体力学特性进行了仿真分析;建立了周期激励下单自由度线性主系统耦合柔性铰链型非线性能量阱结构的系统动力学模型,并通过复变量平均法推导了耦合系统慢变流方程,得到了系统鞍结分岔以及Hopf分岔边界条件,进一步研究了系统参数对耦合系统动力学特性的影响规律;通过数值计算探索了初始条件对多解共存区域内耦合系统响应的影响。研究结果表明:在临界预压条件下,所设计的非线性能量阱结构既能提供本质非线性立方刚度特性,又能满足一定承载要求;在特定参数区域内,耦合系统可能出现一个周期解或三个周期解的情形,同时系统参数还会影响周期解的稳定性;特别地,在某些激励频率失调参数下系统存在多解共存的情况,不同初始条件下会呈现出周期响应、弱调制响应以及强调制响应三种响应形式。In this paper,a novel nonlinear energy sink was proposed,which is constituted by the flexible hinges under preloaded state in parallel with linear springs.Firstly,the static characteristics of a single flexible hinge were analyzed in detail,and the overall mechanical properties of the proposed nonlinear energy sink structure were simulated.Then,the dynamical model of a single-degree-of-freedom linear main structure coupled with nonlinear energy sink using flexible hinges under periodic excitation was established,after that the reduced slow flow equations of the coupled system were derived by a complexification-averaging approach.The saddle-node and Hopf bifurcation boundary conditions were obtained,and the influence of the system parameters on the dynamical characteristics of the coupled system was further studied.Finally,the numerical verification was used to investigate the co-existence of response regimes for the same set of parameters but for different initial conditions.The result shows that under a critical preload,the proposed nonlinear energy sink structure can provide essentially nonlinear cubic stiffness characteristics and also meet a certain bearing requirement.Besides,the coupled system may have one or three periodic solutions in the selected parameter region which also affect the stability of the periodic solutions.In particular,under a certain region of excitation frequency detuning parameter,the coupled system will exhibit three forms of response responding to periodic response,weakly modulated response and strongly modulated response.

关 键 词：柔性铰链 非线性能量阱 立方刚度 局部分岔 强调制响应 

分 类 号：O328[理学—一般力学与力学基础]