Zhao Xin, Qin Honglei, Lang Ronglinget al. GPS position solution algorithm based on the optimization theory[J]. Journal of Beijing University of Aeronautics and Astronautics, 2012, (9): 1219-1223. (in Chinese)
Citation: Jin Jing, Xing Yufeng. Boundary element solution method of free vibration of Timoshenko beam[J]. Journal of Beijing University of Aeronautics and Astronautics, 2012, (7): 976-980. (in Chinese)

Boundary element solution method of free vibration of Timoshenko beam

  • Received Date: 09 Jun 2011
  • Publish Date: 30 Jul 2012
  • The fundamental solution for free vibration of Timoshenko beam was derived using the Fourier transform. Weighted residual method was adapted to deduce the boundary integral formulation from the control differential equations, from which and using boundary conditions one could find the frequency equation which could be solved through algebraic eigenvalue method and influence coefficient method. For any boundary condition, natural frequencies via boundary element method (BEM) for uniform 1D structure are exact, which is validated via the case of rod. The frequencies by BEM of Timoshenko beam were compared with those of finite element method(FEM) and the exact ones.

     

  • [1]
    Brebbia C A,Walker S.Boundary element techniques in engineering [M].London:Newnes-Butterworths,1980
    [2]
    Brebbia C A,Telles J C F,Wrobel L C.Boundary element techniques-theory and applications in engineering [M].New York:Springer-Verlag,1984
    [3]
    杨德全,赵忠生.边界元理论及应用[M].北京:北京理工大学出版社,2002
    Yang Dequan,Zhao Zhongsheng.The theory and application of boundary element method [M].Beijing:Beijing Institute of Technology Press,2002(in Chinese)
    [4]
    Wei X,Leu L J,Chandra A.Shape optimization in elasticity and elasto-viscoplasticity by the boundary element method [J].International Journal of Solids and Structures,1994,31(4):533-550
    [5]
    Chen Chao-shi,Pan ernian,Amadei Bernard.Fracture mechanics analysis of cracked discs of anisotropic rock using the boundary element method [J].International Journal of Rock Mechanics and Mining Sciences,1998,35(2):195-218
    [6]
    Bialecki R A.Solving heat radiation problems using the boundary element method [M].Boston:Computational Mechanics Publications,1993
    [7]
    陈剑,高煜,张永斌,等.基于有限元-边界元的声学构形灵敏度分析[J].振动工程学报,2009,22(2):213-217
    Chen Jian,Gao Yu,Zhang Yongbin,et al.Acoustic configuration sensitivity analysis based on FEM and BEM [J].Journal of Vibration Engineering,2009,22(2):213-217(in Chinese)
    [8]
    林庆华,栗保明.有限元/边界元耦合法计算电磁轨道炮三维瞬态涡流场[J].南京理工大学学报:自然科学版,2010,34(2):218-221
    Lin Qinghua,Li Baoming.Finite-element /boundary-element coupling method for 3D transient eddy current field calculation in electrom agnetic railgun [J].Journal of Nanjing University of Science and Technology:Natural Science,2010,34(2):218-221(in Chinese)
    [9]
    彭红梅,杨德全.双分叉动脉血流动力学特性的边界元分析[J].医用生物力学,2010,25(4):283-287
    Peng Hongmei,Yang Dequan.Boundary element analysis on characteristics of double bifurcation arterial hemo-dynamics [J].Journal of Medical Biomechanics,2010,25(4):283-287(in Chinese)
    [10]
    黄玉美,张广鹏,高峰.虚拟样机整机结构特性边界元法仿真[M].北京:机械工业出版社,2004
    Huang Yumei,Zhang Guangpeng,Gao Feng.The simulation with boundary element method of the whole structural characteristics for the virtual prototype [M].Beijing:China Machine Press,2004(in Chinese)
    [11]
    Jesus A,Costa J.Plate vibrations using BEM [J].Application Mathematics Modelling,1988,12:78-85
    [12]
    Tanaka M,Matsumoto T,Shiozaki A.Application of boundary-domain element method to the free vibration problem of plate structures [J].Computers & Structures,1998,66(6):725-735
    [13]
    Providakis C P,Beskos D E.Free and forced vibrations of plates by boundary elements [J].Computer Methods in Applied Mechanics and Engineering,1989,74(3):231:250
    [14]
    邢誉峰,李敏.计算固体力学原理与方法[M].北京:北京航空航天大学出版社,2011 Xing Yufeng,Li Min.The theory and method of computational solid mechanics [M].Beijing:Beijing University of Aeronautics and Astronautics Press,2011(in Chinese)
    [15]
    邢誉峰,李敏.工程振动基础[M].北京:北京航空航天大学出版社,2011
    Xing Yufeng,Li Min.The foundation of engineering vibration [M].Beijing:Beijing University of Aeronautics and Astronautics Press,2011(in Chinese)
  • Relative Articles

    [1]YU Xiaohai, QU Yaobin, SHI Peng. A Task Planning Method for Space-Based Observation of Large-Scale LEO Target Set[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2024.0649
    [2]YE Yi-qiao, SHEN Hai-dong, LIU Yan-bin, GAO Ze-peng, KONG Xiang, CHEN Jin-bao. Integrated design of hypersonic aircraft wing layout and mission trajectory[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2023.0650
    [3]KONG Lingwei, LI Weiqi. Optimization of aircraft speed vector control based on Hp adaptive Pseudo-spectral method[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2024.0405
    [4]ZHOU D P,LI H Q,WANG Y G,et al. Aircraft system identification algorithm based on generalized equivalent model[J]. Journal of Beijing University of Aeronautics and Astronautics,2024,50(5):1454-1462 (in Chinese). doi: 10.13700/j.bh.1001-5965.2022.0507.
    [5]WEI Zhiqiang, XIAO Xinlong. Vertiport operational task planning model and capacity estimation method[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2024.0249
    [6]ZHANG C Y,WANG G,CHE H L,et al. Motion analysis and gait planning of a novel revolving wheel-legged robot[J]. Journal of Beijing University of Aeronautics and Astronautics,2024,50(5):1675-1684 (in Chinese). doi: 10.13700/j.bh.1001-5965.2022.0491.
    [7]WANG R,LI J M,SHI Y L,et al. Vision-based path planning algorithm of unmanned bird-repelling vehicles in airports[J]. Journal of Beijing University of Aeronautics and Astronautics,2024,50(5):1446-1453 (in Chinese). doi: 10.13700/j.bh.1001-5965.2022.0717.
    [8]WEI Ming, SUN Ya-ru, SUN Bo, WANG Sheng-jie. Cooperative planning for safe transportation routes and flight paths of UAVs with multiple dispatching centers and soft time windows[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2023.0509
    [9]WEI Kun-yu, LI Chen-di, LI Bo-wen, YUAN Yuan, HE Xiao-fan. Research on Developing Design Gust Load Spectrum for Bomber-Mounted Air-to-Ground Missiles[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2024.0126
    [10]DENG J X,CHEN L,LU S T,et al. Damage distribution of composite structures of a certain type aircraft[J]. Journal of Beijing University of Aeronautics and Astronautics,2024,50(3):920-930 (in Chinese). doi: 10.13700/j.bh.1001-5965.2022.0379.
    [11]REN Si-yuan, WANG Song, CHEN Gong, DENG Chen, PAN Zheng-xiao. Research on task planning of multiple UAVs with simultaneous arrival constraints[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2023.0783
    [12]FAN B X,CHEN G M,CAO Y Q. Multi-objective optimization of aerodynamic layout for hypersonic reentry vehicle[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(7):1639-1650 (in Chinese). doi: 10.13700/j.bh.1001-5965.2021.0566.
    [13]ZHANG K Q,ZHOU X F,MEN X H,et al. Three-dimensional integrated guidance and control design with fixed-time convergence[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(4):842-852 (in Chinese). doi: 10.13700/j.bh.1001-5965.2021.0360.
    [14]XING Na, DI Hao-tian, YIN Wen-jie, HAN Ya-jun, ZHOU Yang. Path planning for agents based on adaptive polymorphic ant colony optimization[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2023.0432
    [15]YAN Y,MA X L. Air freight route planning based on transshipment under air alliance[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(1):115-127 (in Chinese). doi: 10.13700/j.bh.1001-5965.2021.0166.
    [16]ZHANG H B,WANG X,XU Y H,et al. Relative entropy method in target recognition with fuzzy features[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(12):3547-3558 (in Chinese). doi: 10.13700/j.bh.1001-5965.2020.0237.
    [17]SONG E B,YAO Y P. Method of improving tracking precision of planning path for impact rollers[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(1):106-114 (in Chinese). doi: 10.13700/j.bh.1001-5965.2021.0495.
    [18]LI J,ZHANG R C,PAN C Y,et al. Micro immune optimization algorithm for single objective probabilistic constrained programming[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(3):525-537 (in Chinese). doi: 10.13700/j.bh.1001-5965.2021.0288.
    [19]SHI Y,WAN Z Q,WU Z G,et al. Aerodynamic order reduction method for elastic aircraft flight dynamics simulation[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(7):1689-1706 (in Chinese). doi: 10.13700/j.bh.1001-5965.2021.0510.
    [20]ZHAO M,LU H,WANG S Q,et al. A multimodal multi-objective path planning algorithm based on multi-swarm cooperative learning[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(3):606-616 (in Chinese). doi: 10.13700/j.bh.1001-5965.2021.0274.
  • Created with Highcharts 5.0.7Amount of accessChart context menuAbstract Views, HTML Views, PDF Downloads StatisticsAbstract ViewsHTML ViewsPDF Downloads2024-072024-082024-092024-102024-112024-122025-012025-022025-032025-042025-052025-06010203040
    Created with Highcharts 5.0.7Chart context menuAccess Class DistributionFULLTEXT: 28.6 %FULLTEXT: 28.6 %META: 70.4 %META: 70.4 %PDF: 1.0 %PDF: 1.0 %FULLTEXTMETAPDF
    Created with Highcharts 5.0.7Chart context menuAccess Area Distribution其他: 2.6 %其他: 2.6 %Kao-sung: 0.1 %Kao-sung: 0.1 %上海: 0.4 %上海: 0.4 %北京: 1.9 %北京: 1.9 %南京: 0.3 %南京: 0.3 %南阳: 0.1 %南阳: 0.1 %哈尔滨: 0.2 %哈尔滨: 0.2 %哥伦布: 0.2 %哥伦布: 0.2 %大连: 0.3 %大连: 0.3 %天津: 0.1 %天津: 0.1 %宣城: 0.1 %宣城: 0.1 %库比蒂诺: 0.1 %库比蒂诺: 0.1 %张家口: 1.6 %张家口: 1.6 %扬州: 0.2 %扬州: 0.2 %无锡: 0.4 %无锡: 0.4 %昆明: 0.3 %昆明: 0.3 %景德镇: 0.1 %景德镇: 0.1 %杭州: 0.5 %杭州: 0.5 %沈阳: 0.1 %沈阳: 0.1 %深圳: 7.8 %深圳: 7.8 %温州: 0.2 %温州: 0.2 %漯河: 0.9 %漯河: 0.9 %盐城: 0.1 %盐城: 0.1 %石家庄: 0.1 %石家庄: 0.1 %芒廷维尤: 6.0 %芒廷维尤: 6.0 %芝加哥: 0.2 %芝加哥: 0.2 %襄阳: 0.1 %襄阳: 0.1 %西宁: 71.7 %西宁: 71.7 %西安: 0.1 %西安: 0.1 %邯郸: 0.1 %邯郸: 0.1 %郑州: 2.6 %郑州: 2.6 %阳泉: 0.2 %阳泉: 0.2 %其他Kao-sung上海北京南京南阳哈尔滨哥伦布大连天津宣城库比蒂诺张家口扬州无锡昆明景德镇杭州沈阳深圳温州漯河盐城石家庄芒廷维尤芝加哥襄阳西宁西安邯郸郑州阳泉

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views(3167) PDF downloads(946) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return