一类分段光滑隔振系统的非线性动力学设计方法

分段光滑隔振系统是一类具备分段刚度或阻尼的非线性动力学系统,在振动控制领域中具有广泛代表性,诸如限位隔振系统、分级汽车悬挂等. 分段光滑的刚度或阻尼特性能够实现隔振系统的特定动力学性能及提升隔振性能,如抑制共振响应、提升共振区隔振性能等,但是亦会给隔振系统的动力学行为带来诸多不利影响. 以分段双线性分段光滑隔振系统为理论模型,系统研究了摒除不利于隔振的非线性动力学现象设计方法,包括幅值跳跃、周期运动的倍周期分岔等. 首先,利用平均法与奇异性理论给出了主共振频响曲线拓扑特征的完整拼图. 研究结果表明,参数空间分为4 个区域,其中2 个区域存在幅值跳跃,而其产生跳跃原因分别由鞍结分岔与擦边分岔所导致;基于此提出避免主共振跳跃的设计方法. 其次,建立了隔振有效区内周期运动的庞加莱映射,通过特征值分析给出了避免倍周期分岔发生的条件,证实增大阻尼可以抑制倍周期分岔的发生. 最后通过数值仿真分析了噪声对多稳态运动的影响. 研究结果发现在噪声影响下,分段光滑隔振系统的响应会在不同稳态间跃迁,非常不利于隔振. 因此,在完成跳跃与倍周期分岔的防治设计后,应采用数值仿真校验系统是否存在多稳态运动. 

NONLINEAR DYNAMICS DESIGN FOR PIECEWISE SMOOTH VIBRATION ISOLATION SYSTEM

Piecewise smooth vibration isolation system is a class of nonlinear dynamics system with piecewise sti ness or damping, which can be found widely in vibration control engineering. This nonlinearity can achieve vibration isolation system's specified dynamics behaviour and improve its e ectiveness, but it will also bring some undesired nonlinear dynamics phenomena, such as amplitude sudden jump, period-doubling bifurcation, etc. The object of this paper is to study the design methodology for piecewise bilinear sti ness vibration system in the view of nonlinear dynamics. First, the entire picture of topology characteristic of frequency response for primary resonance is obtained through combining average method and singularity theory. Results show that the entire parameter plane is divided into four parts and the jump can be induced by both saddle-node and grazing bifurcation. Based on the results, the design principle of amplitude jump avoidance is presented. Then, the Poincaré map for periodic response in e ective isolation band is constructed, and the approach to avoid period-doubling bifurcation is given via eigenvalue analysis. It is verified that the stronger linear damping can suppress the period-doubling bifurcation. Last, this paper studies the e ect of noise on multi-steady state motion for piecewise smooth vibration isolation system. We find that the noise induces that the system's response transfer between the di erent steady states and it is adverse for vibration isolation.