[1]苏潇阳,朱国敬,康厚军.具有弹性转动约束的斜拉桥多索-浅拱模型及其面内自由振动分析[J].地震工程与工程振动,2021,41(03):075-85.[doi:10.13197/j.eeev.2021.03.75.suxy.008]
 SU Xiaoyang,ZHU Guojing,KANG Houjun.Multi-cable-stayed shallow-arch model of cable-stayed bridge with elastic rotation constraints and its in-plane free vibration analysis[J].EARTHQUAKE ENGINEERING AND ENGINEERING DYNAMICS,2021,41(03):075-85.[doi:10.13197/j.eeev.2021.03.75.suxy.008]
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具有弹性转动约束的斜拉桥多索-浅拱模型及其面内自由振动分析
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《地震工程与工程振动》[ISSN:/CN:]

卷:
41
期数:
2021年03
页码:
075-85
栏目:
论文
出版日期:
2021-06-30

文章信息/Info

Title:
Multi-cable-stayed shallow-arch model of cable-stayed bridge with elastic rotation constraints and its in-plane free vibration analysis
作者:
苏潇阳 朱国敬 康厚军
湖南大学 土木工程学院, 湖南 长沙 410082
Author(s):
SU Xiaoyang ZHU Guojing KANG Houjun
College of Civil Engineering, Hunan University, Changsha 410082, China
关键词:
初始构型斜拉桥弹性转动约束自由振动特征值
Keywords:
initial configurationcable-stayed bridgeelastic rotation constraintsfree vibrationeigenvalue
分类号:
U448.27
DOI:
10.13197/j.eeev.2021.03.75.suxy.008
摘要:
考虑斜拉桥的初始构型,建立具有弹性转动约束的多索-浅拱模型。首先,采用Hamilton变分原理得到了索和浅拱的控制微分方程。为了保证浅拱在索-浅拱连接处满足连续条件,将浅拱分段考虑,通过索-浅拱连接处的位移连续条件和力的平衡条件以及两端支座处的边界条件,推导了求解该系统自由振动问题的基本方法。然后,以弹性转动约束双索-浅拱模型为例,对其面内特征值问题进行求解,同时,建立相应的ANSYS模型,得到该模型频率和振型的有限元解。通过与有限元方法计算结果的对比,表明本文方法的正确性和有效性。最后,选取了斜拉索的倾角、垂度,浅拱的抗弯刚度、矢跨比,以及支座的转动刚度等参数,对模型的前5阶频率进行了参数化分析。
Abstract:
Considering the initial configuration of cable-stayed bridges, the dynamic multi-cable-stayed shallow-arch model with elastic rotation constraints is established. Firstly, the differential equations governing vibrations of cables and shallow arch are obtained by Hamilton’s principle. The shallow arch is divided into several segments so that the continuity conditions at connection points of cables and shallow arch can be satisfied. Meanwhile, the boundary conditions at both ends are taken into account and the basic method to solve the free vibration problem of the system is deduced. Then, taking a double-cable-stayed shallow-arch model with elastic rotation constraints as an example, the planar eigenvalue problem is solved, and the corresponding ANSYS model is also established to obtain the finite element solutions. The comparison of the results with those of finite element method shows the correctness and effectiveness of the method in this paper. Finally, considering the factors affecting the natural frequency of the structure, i.e. the acute angle and sag of the cable, flexural stiffness and rise-to-span ratio of the shallow arch, rotational stiffness of the support, the systematical parametrical analysis is carried out aiming to the first five frequencies of the model.

参考文献/References:

[1] 梁剑青, 欧进萍. 大跨斜拉桥桥面风致抖振的粘滞阻尼控制分析[J]. 地震工程与工程振动, 2006,26(1):139-144. LIANG Jianqing, OU Jinping. Lateral buffeting control of long-span cable-stayed bridge deck by viscous dampers[J]. Earthquake Engineering and Engineering Dynamics, 2006, 26(1):139-144. (in Chinese)
[2] 王贵春, 潘家英, 陈淮. 考虑约束扭转的斜拉桥车激横向振动分析[J]. 地震工程与工程振动, 2008, 28(5):65-70. WANG Guichun, PAN Jiaying, CHEN Huai. The lateral dynamic analysis of cable-stayed bridge due to vehicle when considering restrained torsion[J]. Earthquake Engineering and Engineering Dynamics, 2008, 28(5):65-70. (in Chinese)
[3] 赵跃宇, 王涛, 康厚军. 斜拉索主参数共振的稳定性分析[J].动力学与控制学报, 2008, 6(2):112-117. ZHAO Yueyu, WANG Tao, KANG Houjun. Analysis of the stability of principle parametric resonance of stayed-cable[J]. Journal of Dynamics and Control, 2008, 6(2):112-117. (in Chinese)
[4] GATTULLI V, MORANDINI M, PAOLONE A. A parametric analytical model for non-linear dynamics in cable-stayed beam[J]. Earthquake Engineering & Structural Dynamics, 2010, 31(6):1281-1300.
[5] 赵跃宇, 蒋丽忠, 王连华, 等. 索-梁组合结构的动力学建模理论及其内共振分析[J]. 土木工程学报, 2004, 37(3):69-72. ZHAO Yueyu, JIANG Lizhong, WANG Lianhua, et al. The dynamical modeling theory and internal resonance of cable-beam composite structure[J]. China Civil Engineering Journal, 2004, 37(3):69-72. (in Chinese)
[6] 赵跃宇. 大跨径斜拉桥非线性动力学的模型与理论研究[D]. 长沙:湖南大学, 2000. ZHAO Yueyu. Study of the Non-linear Dynamical Modeling Theory of Long-span Cable-stayed Bridges[D]. Changsha:Doctoral Dissertation of Hunan University, 2000. (in Chinese)
[7] 赵跃宇, 王连华, 陈得良, 等. 斜拉索面内振动和面外摆振的耦合分析[J]. 土木工程学报, 2003, 36(4):65-69. ZHAO Yueyu, WANG Lianhua, CHEN Deliang,et al. Coupled analysis of out-of-plane oscillation and in-plane vibration for stay cable[J]. China Civil Engineering, 2003, 36(4):65-69. (in Chinese)
[8] 孙测世, 王志搴, 赵珧冰, 等.两端水平激励斜拉索面内非线性振动响应[J]. 地震工程与工程振动, 2014,34(6):122-126. SUN Ceshi, WANG Zhiqian, ZHAO Yaobing, et al. In-plane nonlinear vibrations of stayed cables under horizontal excitations[J]. Earthquake Engineering and Engineering Dynamics, 2014, 34(6) 122-126. (in Chinese)
[9] CAO D Q, SONG M T, ZHU W D, et al. Modeling and analysis of the in-plane vibration of a complex cable-stayed bridge[J]. Journal of Sound and Vibration, 2012, 331(26):5685-5714.
[10] 龚平, 苏潇阳, 蔡向阳, 等. 拉索对斜拉桥竖向频率的影响研究[J]. 振动工程学报, 2018, 31(6):53-61. GONG Ping, SU Xiaoyang, CAI Xiangyang, et al. Study on the influence of cables on the vertical frequency of cable-stayed bridges[J]. Journal of Vibration Engineering, 2018, 31(6):53-61. (in Chinese)
[11] SU X Y, KANG H J, GUO T D, et al. Dynamic analysis of the in-plane free vibration of a multi-cable-stayed beam with transfer matrix method[J]. Archive of Applied Mechanics, 2019, 89(12):2431-2448.
[12] KANG H J, GUO T D, ZHAO Y Y, et al. Dynamic modeling and in-plane 1:1:1 internal resonance analysis of cable-stayed bridge[J]. European Journal of Mechanics-A/Solids, 2017(62):94-109.
[13] CONG Y Y, KANG H J, GUO T D. Planar multimodal 1:2:2 internal resonance analysis of cable-stayed bridge[J]. Mechanical System and Signal Processing, 2019(120):505-523.
[14] 易壮鹏, 张勇, 王连华. 弹性约束浅拱的非线性动力响应与分岔分析[J]. 应用数学和力学, 2013, 34(11):1182-1196. YI Zhuangpeng, ZHANG Yong, WANG Lianhua. Nonlinear dynamic response and bifurcation analysis of the elastically constrained shallow arch[J]. Applied Mathematics and Mechanics, 2013, 34(11):1182-1196. (in Chinese)
[15] 曾有艺, 易壮鹏. 弹性约束浅拱的内共振非线性模态[J].振动与冲击, 2015, 34(23):48-53. ZENG Youyi, YI Zhuangpeng. Nonlinear normal modes associated with internal resonance for an elastically constrained shallow arch[J].Vibration and Impact, 2015, 34(23):48-53. (in Chinese)
[16] 曾有艺, 易壮鹏, 颜东煌, 等. 转动弹性约束浅拱的2:1内共振非线性模态[J]. 中南大学学报(自然科学版), 2015, 46(10):3922-3927. ZENG Youyi, YI Zhuangpeng, YAN Donghuang, et al. Nonlinear normal modes of rotationally elastically constrained shallow arch in case of two-to-one internal resonance[J].Journal of Central South University (Natural Science Edition), 2015, 46(10):3922-3927. (in Chinese)
[17] 易壮鹏, 康厚军, 王连华, 等. 弹性支撑浅拱的非线性动力行为分析[J]. 动力学与控制学报, 2013, 11(2):142-148. YI Zhuangpeng, KANG Houjun, WANG Lianhua, et al. Research on the nonlinear dynamic behaviors of elastic support shallow arch[J]. Journal of Dynamics and Control, 2013, 11(2):142-148. (in Chinese)
[18] LEISSA A W, QATU M S. Vibrations of Continuous Systems[M]. McGraw-Hill, New York, 2011:116.
[19] OZKAYA E, SARIGVL M, BOYACI H. Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass[J]. Acta Mechanica Sinica, 2009, 25(6):871-882.
[20] 苏潇阳, 康厚军, 丛云跃, 等. 不同斜拉索模型对多塔斜拉桥力学性能的影响[J]. 公路工程, 2017, 42(2):42-46. SU Xiaoyang, KANG Houjun, CONG Yunyue, et al. Influence of different cable models on mechanical performance of multi-tower cable-stayed bridge[J]. Highway Engineering, 2017, 42(2):42-46. (in Chinese)

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备注/Memo

备注/Memo:
收稿日期:2020-03-03;改回日期:2020-06-06。
基金项目:国家自然科学基金项目(11972151,11872176)
作者简介:苏潇阳(1994-),男,博士研究生,主要从事桥梁结构动力学研究.E-mail:su_xiaoyang@hnu.edu.cn
通讯作者:康厚军(1977-),男,副教授,博士,主要从事桥梁结构动力学研究.E-mail:khjun@hnu.edu.cn
更新日期/Last Update: 1900-01-01