分段线性系统的振动性能分析

Vibration performance analysis of piecewise linear system

分析了一类含非连续阻尼的单自由度分段线性系统的振动性能,以研究某些参数对系统振动性能的影响。首先建立分段线性系统的数学模型,利用平均法求解,获得系统的幅频特性和相频特性;然后利用约束分岔理论,计算转迁集,得到系统可能的幅频响应类型,并利用幅频响应方程进行稳定性分析;最后计算系统的传递率,讨论了阻尼和刚度系数对传递率的影响,同时发现传递率曲线也产生了多解现象。

The vibration performance of a single degree of freedom system with piecewise linear terms and discontinuous damper was investigated, aiming to clarify the influence of some system parameters on the system＇s behaviors. A mathematic model of the piecewise linear system was built. By employing an averaging method, the magnitude-frequency characteristic and phase-frequency characteristic functions of the system under primary resonance excitation were obtained. The transition boundary was calculated in accordance with the functions on the basis of the constraint bifurcation theory as well as all the types of the amplitude-frequency responses. The functions were also used for stability analysis. The critical parameter boundary to avoid jumping phenmenon was calculated by qualitatively analyzing the amplitude-frequency responses in the sub-regions of the transition sets. The feasibility of the theoretical study was verified by numerical calculations. In addition, the influences of damping and stiffness coefficients on the global force transmissibility were discussed, and it is found that on the transmissibility curve, the multi-solution problem also appears.