温度变化对悬索主共振响应影响分析

PDF(712 KB)

振动与冲击 ›› 2017, Vol. 36 ›› Issue (15) : 240-244.

论文

温度变化对悬索主共振响应影响分析

赵珧冰1 ，彭剑2 3

作者信息 +

Effects of temperature changes on primary resonances of suspended cables

ZHAO Yaobing 1 PENG Jian 2 3

Author information +

文章历史 +

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。

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.

导出引用

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[J]. Journal of Vibration and Shock, 2017, 36(15): 240-244

参考文献

[1]. 李兆霞, 王滢, 吴佰建, 等. 桥梁结构劣化与损伤过程的多尺度分析方法及其应用[J]. 固体力学学报, 2010, 21(6): 731-756.
LI Zhao-xia, WANG Ying, WU Bai-jian, et al. Multi-scale modeling and analyses on structural deterioration and damage in long-span bridges and its application [J]. Chinese Journal of Solid Mechanics, 2010, 21(6): 731-756.
[2]. 李爱群, 丁幼亮, 王浩, 等. 桥梁健康监测海量数据分析与评估—“结构健康监测”研究进展[J]. 中国科学: 科学技术, 2012, 42(8): 972-984.
LI Ai-qun, DING You-liang , WANG Hao, et al. Analysis and assessment of bridge health monitoring mass data—progress in research/development of Structural Health Monitoring”. Sci China Tech Sci, 2012, 42(8): 972-984.
[3]. 陈波, 郑瑾, 王建平. 桥梁结构温度效应研究进展[J]. 武汉理工大学学报, 2010, 32(24): 79-83.
CHEN Bo, ZHENG Jin, WANG Jian-ping. State-of-the-art of the temperature effects of bridges [J]. Journal of Wuhan University of Technology, 2010, 32(24): 79-83.
[4]. Treyssede F. Free vibrations of cables under thermal stress [J]. Journal of Sound and Vibration, 2009, 327(1): 1-8.
[5]. Lepidi M, Gattulli V. Static and dynamic response of elastic suspended cables with thermal effects [J]. International Journal of Solids and Structures, 2012, 49(9): 1103-1116.
[6]. 赵珧冰, 孙测世, 彭剑, 王连华. 温度变化对拉索频率与索力的影响 [J]. 应用力学学报, 2013, 30(6): 904-908.
ZHAO Yao-bing, SUN Ce-shi, PENG Jian, WANG Lian-hua. The effects of temperature changes on the frequencies and tension forces of cable [J]. Chinese Journal of Applied Mechanics, 2013, 30(6): 904-908.
[7]. 汪峰, 陈福青, 文晓旭, 等. 考虑温度影响的斜拉索参数振动模型及响应分析[J] 重庆交通大学学报(自然科学版), 2016, 35(2): 1-5.
WANG Feng, CHEN Fu-qing, WEN Xiao-xu, et al. Analysis of cable parametric vibration model and response with consideration of temperature effect [J]. Jounral of Chongqing Jiaotong University (Natural Science), 2016, 35(2): 1-5.
[8]. Lepidi M, Gattulli V, Vestroni F. Static and dynamic response of elastic suspended cables with damage [J]. International Journal of Solids and Structures, 2007, 44: 8194–8212.
[9]. 王立彬, 王达, 吴勇. 损伤拉索的等效弹性模量及其参数分析[J]. 计算力学学报, 2015, 32(3): 339-345.
WANG Li-bin, WANG Da, WU Yong. The equivalent elastic modulus of damaged cables and parameter analysis [J]. Chinese Journal of Computational Mechanics, 2015, 32(3): 339-345.
[10]. Zhu J, Ye G R, Xiang Y Q, et al. Dynamic behavior of cable-stayed beam with localized damage [J]. Journal of Vibration and Control, 2011, 17(7): 1080-1089.
[11]. 樊可清, 倪一清, 高赞明. 大跨度桥梁模态频率识别中的温度影响研究[J]. 中国公路学报, 2006, 19(2): 67-73.
FAN Ke-qing, NI Yi-qing, GAO Zan-ming. Research on temperature Influences in long-span bridge [J]. China Journal of Highway and Transport, 2006, 19(2): 67-73.
[12]. 李顺龙, 李惠, 欧进萍, 等. 考虑温度和风速影响下的桥梁结构模态参数分析[J]. 土木工程学报, 2009, 42(4): 100-106.
LI Shun-long, LI Hui, OU Jin-ping et al. Identification of modal parameters of bridges considering temperature and wind effects [J]. China Civil Engineering Journal, 2009, 42(04): 100-106.
[13]. Rega G, Alaggio R. Experimental unfolding of the nonlinear dynamics of a cable-mass suspended system around a divergence-hopf bifurcation[J]. Journal of Sound and Vibration, 2009, 322(3): 581-611.
[14]. Zhao Y B, Sun C S, Wang Z Q, et al. Analytical solutions for resonant response of suspended cables subjected to external excitation. Nonlinear Dynamics, 2014, 78: 1017-1032.
[15]. 赵珧冰, 孙测世, 彭剑, 等. 不同初拉力拉索对温度变化的敏感性分析[J]. 中南大学学报(自然科学版), 2014, 45(5): 1680-1685.
ZHAO Yao-bing, SUN Ce-shi, PENG Jian, et al. Sensitivity analysis of different initial tension forces of supended cable to temperature changes [J]. Journal of Central Soth University(Science and Technology), 2014, 45(5): 1680-1685.