横向补给系统高架索在一重和双重内共振下的面内振动

张良欣;何学军;任爱娣

振动与冲击 ›› 2011, Vol. 30 ›› Issue (8) : 157-160,.

PDF(1530 KB)
PDF(1530 KB)
振动与冲击 ›› 2011, Vol. 30 ›› Issue (8) : 157-160,.
论文

横向补给系统高架索在一重和双重内共振下的面内振动

  • 张良欣; 何学军; 任爱娣
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IN-PLANE OSCILLATION OF HIGHLINE CABLE FOR ALONGSIDE REPLENISHMENT SYSTEM WITH SINGLE AND DUAL INTERNAL RESONANCES

  • Zhang Liang-xin; He Xue-jun; Ren Ai-di
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摘要

考虑集中质量在高架索上的位置的影响,建立了横向补给高架索系统的面内振动的非线性动力学方程。利用Galerkin方法对高架索偏微分模型进行离散,得到了系统面内振动的直至3阶的标准动力学控制方程。分析了补给过程中,集中质量位置的变化对高架索系统的面内振动的前3阶模态频率的影响,系统的模态频率呈现类似滞回非线性的特征。同时还利用数值方法对1:1:2双重内共振及1:2内共振情况下系统的参数激励振动的非线性动力学行为进行了分析,得到了系统的前3阶模态振动的时间历程曲线和运动相图。研究结果表明,在高架索系统发生内共振时,系统面内振动以前2阶模态振动为主,且存在复杂的倍周期运动现象;而对于1:2内共振情况,只有第1阶模态振动的幅值较大。

Abstract

A nonlinear dynamic model of in-plane motion for highline cable system of alongside replenishment was formulated, which considered the influence of the lumped mass on highline cable. The partial differential equation was discretized into ordinary differential equations by Galerkin approach and the standard dynamic equations of highline cable were acquired. The influence of the position of lumped mass on the first three modal frequencies was analyzed during the course of alongside replenishment and the modal frequencies had nonlinear hysteretic characteristic. The dynamics for parametrically excited highline cable system with 1:1:2 internal resonance and 1:2 internal resonance were analyzed numerically, and time history curves, phase trajectories of which were obtained up to the third model. The results show that there exist complex dynamic behaviors such as multiple period motion in internal resonant cases, and the first two models were dominant in the in-plane oscillation of highline cable system. Whereas only the first model was dominant in the in-plane oscillation of highline cable system with 1:2 internal resonant, and the first modal oscillation was periodical.

关键词

内共振 / 模态频率 / 倍周期 / Galerkin方法 / 高架索

Key words

internal resonance / modal frequency / multiple period / Galerkin approach / highline cable

引用本文

导出引用
张良欣;何学军;任爱娣. 横向补给系统高架索在一重和双重内共振下的面内振动[J]. 振动与冲击, 2011, 30(8): 157-160,
Zhang Liang-xin; He Xue-jun;Ren Ai-di. IN-PLANE OSCILLATION OF HIGHLINE CABLE FOR ALONGSIDE REPLENISHMENT SYSTEM WITH SINGLE AND DUAL INTERNAL RESONANCES[J]. Journal of Vibration and Shock, 2011, 30(8): 157-160,

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