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。
Abstract
This paper studied the vibration performance of a single degree of freedom systems with piecewise linear terms and discontinuous damper, aiming to clarify the influence of some parameters of the system on the system. Firstly, the mathematic model of the piecewise linear system was given. By employing an averaging method it was possible to obtain the magnitude-frequency characteristic and phase-frequency characteristic of the system under primary resonance excitation. The transition boundary could be calculated from this function on the basis of constraint bifurcation theory as well as all the type of the amplitude-frequency response. The function could be also used for stability analysis. Critical parameter boundary to avoid jumping was calculated by qualitatively analyzing the Amplitude-Frequency response in the sub-regions of the transition sets. Numerical calculation verified the feasibility of theoretical study. In addition, the influence of damping and stiffness coefficients on the global force transmissibility was discussed, and the transmissibility curve also produced multi-solution problem.
关键词
幅频响应 /
奇异性 /
稳定性 /
跳跃 /
减振
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Key words
Amplitude-frequency response /
strangeness /
stability /
jump /
vibration reduction
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参考文献
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