On the response of a harmonically excited two degree-of-freedom system consisting of a linear and a nonlinear quasi-zero stiffness oscillator
On the response of a harmonically excited two degree-of-freedom system consisting of a linear and a nonlinear quasi-zero stiffness oscillator
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DOI：
10.1016/j.jsv.2009.11.019
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发表时间：
2010-05
影响因子：
4.7
通讯作者：
G. Gatti;I. Kovacic;M. Brennan
中科院分区：
文献类型：
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作者：
G. Gatti;I. Kovacic;M. Brennan
有许多系统是由附加在线性系统上的非线性振荡器组成的，例如非线性吸振器，或用恒力谐波激励振动筛的非线性测试系统。本文研究了一类特殊的二自由度系统的动力学行为，其中非线性系统不影响强制线性系统的振动。该机构的非线性是由悬挂在两个弹簧上的质量组成的几何构型推导出来的，这两个弹簧被调整为具有纯三次非线性的准零刚度特征。应用平均法分析了系统在激励频率处的响应。研究了系统参数对相对运动频幅响应的影响。研究发现，在主共振曲线的连续路径之外或内部的封闭分离共振曲线都可以作为整体幅频响应的一部分出现。讨论了主共振曲线内部产生分离共振曲线的两种典型情况，这两种情况依赖于非线性振荡器的阻尼。
There are many systems which consist of a nonlinear oscillator attached to a linear system, examples of which are nonlinear vibration absorbers, or nonlinear systems under test using shakers excited harmonically with a constant force. This paper presents a study of the dynamic behaviour of a specific two degree-of-freedom system representing such a system, in which the nonlinear system does not affect the vibration of the forced linear system. The nonlinearity of the attachment is derived from a geometric configuration consisting of a mass suspended on two springs which are adjusted to achieve a quasi-zero stiffness characteristic with pure cubic nonlinearity. The response of the system at the frequency of excitation is found analytically by applying the method of averaging. The effects of the system parameters on the frequency-amplitude response of the relative motion are examined. It is found that closed detached resonance curves lying outside or inside the continuous path of the main resonance curve can appear as a part of the overall amplitude-frequency response. Two typical situations for the creation of the detached resonance curve inside the main resonance curve, which are dependent on the damping in the nonlinear oscillator, are discussed.