Design of a nonlinear energy sink with flexible hinges and local bifurcation analysis of the system
LI Shuang1,LOU Jingjun2,CHAI Kai2,LIU Shuyong1,YANG Lihua3
1.College of Power Engineering, Naval University of Engineering, Wuhan 430033, China;
2.College of Naval Architecture and Ocean, Naval University of Engineering, Wuhan 430033, China;
3.Power Control Department, Navy Submarine Academy, Qingdao 266199, China
Abstract：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.
李爽1，楼京俊2，柴凯2，刘树勇1，杨理华3. 柔性铰链型非线性能量阱设计与系统局部分岔特性分析[J]. 振动与冲击, 2020, 39(24): 156-163.
LI Shuang1,LOU Jingjun2,CHAI Kai2,LIU Shuyong1,YANG Lihua3. Design of a nonlinear energy sink with flexible hinges and local bifurcation analysis of the system. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(24): 156-163.
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