铁木辛柯梁固有振动频率的边界元解法

金晶; 邢誉峰

铁木辛柯梁固有振动频率的边界元解法

金晶,
邢誉峰

北京航空航天大学航空科学与工程学院, 北京 100191

基金项目: 国家自然科学基金资助项目(10772014)

详细信息

中图分类号: O343;TB12
计量
- 文章访问数: 3075
- HTML全文浏览量: 300
- PDF下载量: 940
- 被引次数: 0
出版历程
- 收稿日期: 2011-06-09
- 网络出版日期: 2012-07-30

Boundary element solution method of free vibration of Timoshenko beam

School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

摘要

摘要: 根据傅里叶变换推导具有两个广义位移的铁木辛柯梁固有振动的基本解.利用加权残量方法,从控制微分方程出发建立边界积分方程,进而根据边界条件得到频率方程,采用代数特征值方法和影响系数方法求解频率,并分析了两种方法的特点.以杆为例证明了对于一维均匀结构,对不同的边界条件利用边界元方法(BEM,Boundary Element Method)都可以得到精确频率.将铁木辛柯梁的BEM结果与有限元结果和精确解进行了比较.
- 傅里叶变换 /
- 剪切梁 /
- 固有频率 /
- 边界元法
Abstract: 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.
- Fourier transform /
- Timoshenko beam /
- free vibration /
- boundary element method (BEM)

HTML全文

参考文献(15)

[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)