端部激励相位差对悬索亚谐波共振响应的影响
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国家自然科学基金资助项目(51808085)


Influence of end excitation phase difference on subharmonic resonant of suspended cable
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    摘要:

    悬索受多个端部激励后可能产生复杂的非线性动力学现象.为研究端部激励相位差对悬索亚谐波响应的影响,建立两端受激励的悬索模型,得到无限维离散运动方程,采用多尺度法研究面内亚谐波共振,并通过数值积分加以验证.文中给出了多激励系统等效激励幅值和响应相位的一般表达式,定性定量分析了面内两两激励的不同组合对响应幅值和相位的影响.结果表明:端部激励相位差对悬索响应幅值的影响以2π为周期变化,关于π对称.端部激励间的相位差可以使响应相位在一个名义单激励系统的响应相位基础上发生移动,当激励相位差逐渐由0转变为π的同时,相频曲线也非同步地位移了π.激励相位差不改变系统的软硬性质,但会影响响应幅值和共振区宽度,且其共振区宽度关于σ=0对称.

    Abstract:

    Complex nonlinear dynamic phenomena will occur when the suspended cable is subjected to multiple parametric excitations. In order to study the effects of parametric excitation under different phases on the harmonic response of suspended cable, the model of suspended cable with parametric excitation at both ends is established, and the infinitedimensional discrete equations of motion are obtained. The subharmonic resonance in plane is studied by using the multiple scales method verified by numerical integration. The general expressions of equivalent excitation amplitude and response phase of multiexcitation system is given, and the effects of different combinations of inplane two excitations on the response amplitude and phase are qualitatively analyzed. The results show that the effect of multipoint excitations phase difference on the suspended cable response amplitude varies with 2π as a periodic variation and is symmetric about π. These excitations make the response phase of the system shift based on the response phase of the suspended cable. When the phase difference excitation between them gradually changes from 0 to π, the phasefrequency curves also shift by π. The excitation phase difference does not change the soft and hard properties of the system, but affects the response amplitude and the width of the resonance region, and the width of the resonance region is symmetrical about σ=0.

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李聪,孙测世,赵碧航.端部激励相位差对悬索亚谐波共振响应的影响[J].动力学与控制学报,2023,21(4):67~75; Li Cong, Sun Ceshi, Zhao Bihang. Influence of end excitation phase difference on subharmonic resonant of suspended cable[J]. Journal of Dynamics and Control,2023,21(4):67-75.

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  • 收稿日期:2022-11-08
  • 最后修改日期:2023-03-06
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  • 在线发布日期: 2023-04-20
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