温度变化对悬索主共振响应影响分析

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摘要本文基于增量热场理论，推导考虑均匀温度变化影响下受谐波激励的悬索非线性运动微分方程，利用Galerkin法将方程离散，并对离散后的方程进行线性分析。以悬索主共振响应为例，利用多尺度法求解其高阶近似解及幅频响应方程，通过算例研究温度变化对不同Irvine参数的悬索前四阶模态频率以及幅频响应曲线的影响。研究结果表明：悬索模态振型、频率和主共振响应受温度变化影响明显，且与其Irvine参数密切相关；温度变化有可能定性和定量地改变悬索非线性振动特性，其取决于线性项、平方和立方非线性项系数受温度变化的影响程度；相同程度的升温和降温对悬索振动特性的影响不对称。

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关键词 ：悬索, 温度变化, 多尺度法, 主共振

Abstract：Based on the incremental thermal field theory, the nonlinear vibration equations of the suspended cable under the harmonic excitation where the temperature effects were taken into consideration were derived. The Galerkin method was introduced to discretized the nonlinear partial differential equations and the relative linear analysis were given. The higher order approximate solution and frequency response equation were obtained by the multiple scales method, and the effects of temperature changes on mode shapes, frequencies and frequency response curve of the primary resonance of the suspended cable with different Irvine parameter were illustrated by the numerical calculations. The numerical results show that the effects of different temperature variations on the mode frequencies and primary resonance of the suspended cable are obvious, and they are close related with the Irvine parameter of the suspended cable; the nonlinear vibration characteristics would be changed by the temperature effects quantitatively and qualitatively, and they are depended on the variations of coefficients of the linear, quadratic and cubic nonlinearities; the effects of warming and cooling on the vibration characteristics of the suspended cable are not symmetric.

Key words： suspended cable temperature variations multiple scales method primary resonance

收稿日期: 2015-12-30 出版日期: 2017-07-28

引用本文:

赵珧冰1,彭剑2 3. 温度变化对悬索主共振响应影响分析[J]. 振动与冲击, 2017, 36(15): 240-244.
ZHAO Yaobing 1 PENG Jian 2 3 . Effects of temperature changes on primary resonances of suspended cables. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(15): 240-244.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2017/V36/I15/240

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