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Nonlinear planar secondary resonance analyses of suspended cables with thermal effects

机译：具有热效应的悬浮电缆的非线性平面二次共振分析

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摘要

This paper deals with a geometrically nonlinear model of suspended cables in thermal environments. In particular, the secondary resonant behaviors with thermal effects are investigated and discussed analytically and numerically. First, considering the influence of temperature changes, a dimensionless coefficient is generated. The nonlinear dynamic equations of motion in thermal environments are established, and the governing PDEs are reduced to a set of ODEs by using the Galerkin procedure. Four super and sub-harmonic resonant cases are studied, and frequency responses equations and steady-state solutions for each case are obtained. Extensive numerical results show that the hardening/softening behaviors, the response amplitudes, the number of nontrivial solutions, the range of resonant responses, the jump points, and the peak values are all closely connected to temperature. In some specific warming/cooling conditions, the nonlinear system just shows linear vibration behaviors or even just opposite spring characteristics. The time?displacement curves and phase portraits are extremely sensitive to temperature changes, but the number of cluster points in Poincar? sections seem to be independent of temperature changes.
机译：本文研究了热环境中悬浮电缆的几何非线性模型。尤其是，对具有热效应的二次共振行为进行了分析和数值研究。首先，考虑温度变化的影响，生成无量纲系数。建立了热环境中运动的非线性动力学方程，并通过使用Galerkin程序将控制PDE简化为一组ODE。研究了四种超谐和次谐谐振情况，并获得了每种情况的频率响应方程和稳态解。大量的数值结果表明，硬化/软化行为，响应幅度，非平凡解的数量，共振响应的范围，跳跃点和峰值都与温度密切相关。在某些特定的加热/冷却条件下，非线性系统仅表现出线性振动行为，甚至表现出相反的弹簧特性。时间位移曲线和相图对温度变化极为敏感，但是庞加莱中的聚类点数断面似乎与温度变化无关。

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  • 来源
    《Journal of thermal stresses》 |2019年第12期|1515-1534|共20页
  • 作者

    Zhao Yaobing; Huang Chaohui; Chen Lincong;

  • 作者单位

    Huaqiao Univ Coll Civil Engn Xiamen 361021 Fujian Peoples R China|Huaqiao Univ Fujian Prov Key Lab Intelligent Infrastruct & Mon Xiamen Fujian Peoples R China|Hunan Univ Sci & Technol Hunan Prov Key Lab Struct Wind Resistance & Vibra Xiangtan Peoples R China;

    Huaqiao Univ Coll Civil Engn Xiamen 361021 Fujian Peoples R China;

    Huaqiao Univ Coll Civil Engn Xiamen 361021 Fujian Peoples R China|Huaqiao Univ Fujian Prov Key Lab Intelligent Infrastruct & Mon Xiamen Fujian Peoples R China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Suspended cable; thermal effect; secondary resonance; perturbation analysis; numerical integration; vibration characteristic;

    机译：悬挂电缆;热效应二次共振扰动分析;数值积分振动特性;

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