求解曲线箱梁空间振动特性的Cayley-Hamilton传递矩阵法

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (8) : 138-143.

论文

闫仙丽1 , 李青宁2

作者信息 +

A Cayley-Hamilton transfer matrix method for solving the vibration characteristics of curved box beams

YAN Xianli1,LI Qingning2

Author information +

文章历史 +

摘要

将传递矩阵法与Cayley-Hamilton定理相结合，以微分方程和矩阵分析理论为基础，提出了一种新的Cayley-Hamilton传递矩阵法。应用该方法，考虑曲线箱梁桥的空间弯曲、剪切、扭转、拉压、翘曲及其相互间的耦合作用，推导了曲线箱梁桥离散模型的振动空间传递矩阵。以某单跨简支曲线箱梁桥为例，采用所推导矩阵，对其进行计算机编程运算，得到该桥梁的自振频率与振型，并与有限元法计算结果相比较，二者吻合良好，表明本文方法有效。

Abstract

A new Cayley-Hamilton transfer matrix method was proposed by integrating the Cayley-Hamilton theorem and the transfer matrix method.It was based on the theory of differential equations and matrix analysis.Adopting this method,the space vibration transfer matrix of the discrete curved box girder bridge model was derived taking into account the spatial bending,shear,torsion,tension,compression,warping and their coupling effects.With a simply supported single span curved bridge as an example,a calculation programming was conducted to obtain the vibration frequency and vibration mode of the bridge by using the derived matrix.And compared with the results of the finite element method,the results agree well with each other.It demonstrates that this method is effective.

导出引用

闫仙丽1,李青宁2. 求解曲线箱梁空间振动特性的Cayley-Hamilton传递矩阵法[J]. 振动与冲击, 2017, 36(8): 138-143

YAN Xianli1,LI Qingning2. A Cayley-Hamilton transfer matrix method for solving the vibration characteristics of curved box beams[J]. Journal of Vibration and Shock, 2017, 36(8): 138-143

参考文献

[1] 张志新. 高墩曲线连续刚构箱梁桥空间行为研究[D].西安：长安大学. 2010.
ZHANG Zhixin. Study on spatial behavior of curved continuous rigid frame box-girder bridge with high-pier [D]. Xi’an: Chang'an University. 2010.
[2] Mohseni I, Rashid A K A, Kang J. A simplified method to estimate the fundamental frequency of skew continuous multicell box-girder bridges[J]. Latin American Journal of Solids & Structures, 2014, 11(4):649-658.
[3] Ye T, Jin G, Ye X, et al. A series solution for the vibrations of composite laminated deep curved beams with general boundaries[J]. Composite Structures, 2015, 127:450-465.
[4] Ziane N, Meftah S A, Belhadj H A, et al. Free vibration analysis of thin and thick-walled FGM box beams[J]. International Journal of Mechanical Sciences, 2013, 66(2):273-282.
[5] Benedettini F, Dilena M, Morassi A. Vibration analysis and structural identification of a curved multi-span viaduct [J]. Mechanical Systems & Signal Processing, 2015, 54-55:84-107.
[6] He X, Noda Y, Hayashikawa T, et al. An analytical approach to coupled vibration of curved rationalized girder bridges and running vehicles[J]. Procedia Engineering, 2011, 14:2906-2915.
[7] 刘铁林, 赵阳, 吴金国. 面内变形曲梁的显式单元刚度矩阵[J]. 沈阳建筑大学学报 (自然科学版), 2013, 6: 005.
LIU Tielin, ZHAO Yang, WU Jinguo. Explicit element stiffness matrix for curved beam with in-plane deformation [J]. Journal of Shenyang Jianzhu University (Natural Science), 2013, 6: 005.
[8] 杨允表. 曲线箱梁考虑曲率及剪力滞影响的力学分析[J]. 土木工程学报, 1999, 32(1): 43-49.
YANG Yunbiao. Mechanical analysis of curved box beam including the effect of curvature and shear- lag [J]. China Civil Engineering Journal, 1999, 32(1): 43-49.
[9] 韦成龙, 曾庆元. 薄壁曲线箱梁考虑翘曲, 畸变和剪滞效应的空间分析[J]. 土木工程学报, 2000, 33(6): 81-87.
WEI Chenglong, ZENG Qingyuan. A new element for thin-walled curved box girder analysis including warping distortion and shear-lag effects [J]. China Civil Engineering Journal, 2000, 33(6): 81-87.
[10] 任茶仙, 竺润祥. 连续曲线箱梁预应力效应分析[J]. 工程力学, 2000, 17(4): 138-144.
REN Chaxian, ZHU Runxiang. Analysis of prestressing effect for curved continuous box girders [J]. Engineering Mechanics, 2000, 17(4): 138-144.
[11] 段海娟, 张其林. 钢筋混凝土曲线箱梁非线性分析的有限元法[J]. 同济大学学报: 自然科学版, 2003,
31(3): 282-286.
DUAN Haijuan, ZHANG Qilin. Finite segment element method for nonlinear analysis of reinforced concrete curved box girder [J]. Journal of Tongji University (Natural Science), 2003, 31(3): 282-286.
[12] 谢旭, 黄剑源. 曲线箱梁桥结构分析的一种有限元计算方法[J]. 土木工程学报, 2005, 38(2): 75-80.
XIE Xu , HUANG Jianyuan. A finite element method for analysis of curved box girder bridge structures [J]. China Civil Engineering Journal, 2005, 38(2): 75-80.
[13] 魏双科. 曲线梁桥的固有振动特性及地震反应分析[D]. 南京: 南京工业大学, 2006.
WEI Shuangke. Inherent vibration characteristics and seismic response analysis of curved girder [D]. Nanjing: Nanjing University of Technology, 2006.
[14] 张翠. 钢-混凝土组合曲线箱梁的动力特性分析[D].中南大学, 2014.
ZHANG Cui. Dynamic characteristics of steel-concrete composite curved box beams [D]. Central South University,
2014.
[15] 徐勋, 卫星, 刘德军, 强士中. 扁平曲线箱梁静动力特性分析[J]. 公路交通科技. 2007(12):60-65,84.
XU Xun, WEI Xing, LIU Dejun, et al. Analysis for static and dynamic characteristics of flat curved box beam [J]. Journal of Highway and Transportation Research and Development. 2007(12):60-65, 84.
[16] 赵青, 肖卓. 行波效应对连续曲线箱梁桥地震反应的影响[J].地震工程与工程振动,2010,30(3):123-128.
ZHAO Qing, XIAO Zhuo. Effects of traveling wave on seismic responses of continuous curved box-girders bridge [J]. Earthquake Engineering And Engineering Vibration, 2010, 30(3):123-128.
[17] 吴亚平, 赖远明, 张学富, 朱元林.曲线箱梁静动力特性的有限段元分析[J]. 铁道学报,2001,05:81-84.
WU Ya ping, LAI Yuan ming , ZHANG Xue fu, et al. Analysis of finite beam element for static and dynamic characteristics of curved box beams [J]. Journal of the China Railway Society. 2001, 05: 81-84.
[18] 严亮亮. 曲线薄壁箱梁的动力分析[D]. 重庆交通大学, 2014.
YAN Liangliang .The dynamic analysis about curved thin-walled box-girder [D]. Chongqing Jiaotong University, 2014.
[19] 芮筱亭, 贠来峰, 陆毓琪, 等. 多体系统传递矩阵法及其应用[M]. 北京:科学出版社, 2008,5:13-14.
Rui Xiaoting, Yun Laifeng, Lu Yuqi, et al. Transfer matrix method of multibody system and its applications [M]. Beijing: Science Press, 2008,5: 13-14.
[20] 琚莉. 利用哈密顿-凯莱定理求解微分方程组的两种方法[J]. 科教导刊, 2011 (24): 146-147.
JU Li. Two ways for Cayley-Hamilton to solve differential equations [J]. Natural Science Discipline Research, 2011 (24): 146-147.
[21] William A. Harris, Jr., Jay P. Fillmore, Donald R. Smith. Matrix exponentials-another approach [J]. SIAM Review, 2001, 43(4): 694-706.
[22] 邵容光,夏淦.混凝土弯梁桥[M].北京:人民交通出版社,1997.
SHAO Rongguang, XIA Gan. Concrete curved girder bridge [M]. Beijing: China Communications Press, 1997.
[23] 姚玲森.曲线梁[M].北京:人民交通出版社,1989.
YAO Lingsen curved beam [M]. Beijing: China Communications Press, 1989.