Analyzing the Wave Scattering in Timoshenko Beam Based on the Symplectic Theory

WU Feng; XU Xiao-ming; GAO Qiang; ZHONG Wan-xie

doi:10.3879/j.issn.1000-0887.2013.12.001

Volume 34 Issue 12

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WU Feng, XU Xiao-ming, GAO Qiang, ZHONG Wan-xie. Analyzing the Wave Scattering in Timoshenko Beam Based on the Symplectic Theory[J]. Applied Mathematics and Mechanics, 2013, 34(12): 1225-1235. doi: 10.3879/j.issn.1000-0887.2013.12.001

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Analyzing the Wave Scattering in Timoshenko Beam Based on the Symplectic Theory

doi: 10.3879/j.issn.1000-0887.2013.12.001

State Key Laboratory of Structural Analysis of Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R. China

Funds: The National Basic Research Program of China (973 Program)(2009CB918501)

Received Date: 2013-08-11
Rev Recd Date: 2013-10-11
Publish Date: 2013-12-16

Abstract

Abstract

Based on the symplectic theory in applied mechanics, some characteristic theories, such as the symplectic Gramme-Schmidt orthogonal algorithm, the independence between symplectic eigensolutions, precise integration method for the problem with two end boundary conditions, etc. were employed to analyze the energy band structure of Timoshenko beam and the wave scattering in the beam which was connected with a rigid scatterer.
- Timoshenko beam,
- wave scattering,
- energy band,
- symplectic

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References(17)

References

[1]	徐志胜, 翟婉明, 王开云. 基于Timoshenko梁模型的车辆-轨道耦合振动分析[J]. 西南交通大学学报, 2003,38(1): 22-27.(XU Zhi-sheng, ZHAI Wan-ming, WANG Kai-yun. Analysis of vehicle-track coupling vibration based on Timoshenko beam model[J]. Journal of Southwest Jiaotong University,2003,38(1): 22-27.(in Chinese))
[2]	孙景江, 江近仁. 高层建筑抗震墙非线性分析的扩展铁木辛哥分层梁单元[J]. 地震工程与工程振动, 2001,21(2): 78-83.(SUN Jing-jiang, JIANG Jin-ren. Extended Timoshenko layered beam element for nonlinear analysis of RC high-rise buildings with structural walls[J]. Earthquake Engineering and Engineering Vibration,2001,21(2): 78-83.(in Chinese))
[3]	陈勇, 刘盼. 等截面铁摩辛柯梁-抗转阻尼器系统的复模态特性[J]. 振动与冲击, 2012,31(23): 174-179.(CHEN Yong, LIU Pan. Complex modal characteristic of a uniform Timoshenko beam with rotational dampers[J].Journal of Vibration and Shock,2012,31(23): 174-179.(in Chinese))
[4]	杨小姜, 施伟辰. 基于欧拉-伯努利梁和铁木辛柯梁理论的功能梯度材料模量测定[J]. 计算机辅助工程, 2012,21(5): 25-29.(YANG Xiao-jiang, SHI Wei-chen. Modulus determination of functionally graded materials based on theories of Euler-Bernoulli beam and Timoshenko beam[J]. Computer Aided Engineering,2012,21(5): 25-29.(in Chinese))
[5]	赵莉, 陈伟球. 功能梯度材料铁木辛柯梁的波传播分析[C]//第二届全国压电和声波理论及器件技术研讨会. 杭州, 2006: 89-91.(ZHAO Li, CHEN Wei-qiu. The wave propagation in Timoshenko beam made of functionally graded materials[C]// The secondsymposium on Piezoelectricity, Acoustic Waves, and Device Applications . Hangzhou, 2006: 89-91.(in Chinese))
[6]	管德清, 蒋欣. 基于小波分析的Timoshenko梁裂缝识别研究[J]. 振动与冲击, 2007,26(5): 67-70.(GUAN De-qing, JIANG Xin. Crack detect of Timoshenko beam based on the wave-let method[J]. Journal of Vibration and Shock,2007,26(5): 67-70(in Chinese))
[7]	侯涛, 张孝卫, 刘洪涛, 袁玉杰. 铁木辛柯弹性稳定理论在深水桩自由站立分析中的应用[J]. 中国海洋平台, 2010,25(2): 34-38.(HOU Tao, ZHANG Xiao-wei, LIU Hong-tao, YUAN Yu-jie. Pile stick up analysis with Timoshenko theory of elastic stability[J]. China Offshore Platform,2010,25(2): 34-38.(in Chinese))
[8]	金磊. 铁木辛柯梁的Winkler边界对偶求解辛方法[J]. 山西建筑, 2012,38(26): 56-57.(JIN Lei. Symplectic algorithm for Timoshenko beam with Winkler boundary[J]. Shanxi Architecture,2012,38(26): 56-57.(in Chinese))
[9]	楼梦麟, 任志刚. Timoshenko简支梁的振动模态特性精确解[J]. 同济大学学报(自然科学版), 2002,30(8): 911-915.(LOU Meng-lin, REN Zhi-gang. Precise solution to modal characteristics of Timoshenko pin-ended beams[J]. Journal of Tongji University(Natural Science),2002,30(8): 911-915.(in Chinese))
[10]	金晶, 邢誉峰. 铁木辛柯梁固有振动频率的边界元解法[J]. 北京航空航天大学学报, 2012,38(7): 976-980.(JIN Jing, XIN Yu-feng. Boundary element solution method of free vibration of Timoshenko beam[J]. Journal of Beijing University of Aeronautics and Astronautics,2012,38(7): 976-980.(in Chinese))
[11]	崔灿, 李映辉. 变截面铁木辛柯梁振动特性快速计算方法[J]. 动力学与控制学报, 2012,10(3): 258-262.(CUI Can, LI Yin-hui. A solution for vibration characteristic of Timoshenko beam with variable cross-section[J]. Journal of Dynamics and Control,2012,10(3): 258-262.(in Chinese))
[12]	陈镕, 万春风, 薛松涛, 唐和生. Timoshenko梁运动方程的修正及其影响[J]. 同济大学学报（自然科学版）, 2005,33(6): 711-715.(CHEN Rong, WAN Chun-feng, XUE Song-tao, TANG He-sheng. Modification of motion equation of Timoshenko beam and its effect[J]. Journal of Tongji University(Natural Science),2005,33(6): 711-715.(in Chinese))
[13]	邓军, 陈国平, 张方. 旋转铁木辛柯梁分布动态载荷的时域识别研究[J]. 机械科学与技术, 2011,30(6): 947-950, 956.(DENG Jun, CHEN Guo-ping, ZHANG Fang. Identification of distributed dynamic load on a rotating Timoshenko beam in time domain[J]. Mechanical Science and Technology for Aerospace Engineering,2011,30(6): 947-950, 956.(in Chinese))
[14]	王振, 孙秦. 几何非线性分析的二维共旋铁摩辛柯梁单元[J]. 机械科学与技术, 2013,32(5): 665-669.(WANG Zhen, SUN Qin. Geometrically nonlinear analisys of 2-D corotational Timoshenko beam element[J]. Mechanical Sciene and Technology for Aerospace Engineering,2013,32(5): 665-669.(in Chinese))
[15]	方剑宇, 韩小云, 蔡力, 郁殿龙. 考虑翘曲的周期铁摩辛柯梁的弯扭耦合振动带隙[J]. 振动与冲击, 2009,28(5): 146-149.(FANG Jian-yu, HAN Xiao-yun, CAI Li, YU Dian-long. Coupled flexural-torsional vibration band gap in periodic Timoshenko beam including warping effect[J]. Journal of Vibration and Shock,2009,28(5): 146-149.(in Chinese))
[16]	方剑宇, 韩小云. 轴向受载的周期铁摩辛柯梁的弯扭耦合振动带隙研究[C]//第二十一届全国振动与噪声高技术及应用学术会议. 合肥, 2008: 97-103.(FANG Jian-yu, HAN Xiao-yun. The coupled flexural-torsional vibration and band structure of the axially loaded periodic Timoshenko beam[C]// The 21th National Conference on the High Technique and Application in Vibration and Noise . Heifei, 2008: 97-103.(in Chinese))
[17]	钟万勰. 应用力学的辛数学方法[M]. 北京: 高等教育出版社, 2006.(ZHOGN Wan-xie. Symplectic Method in Applied Mechanics [M]. Beijing: Higher Education Press, 2006.(in Chinese))