考虑质量偏心Timoshenko梁的弯-纵耦合固有振动特性研究

王剑1,2,张振果1,2,华宏星1,2

振动与冲击 ›› 2015, Vol. 34 ›› Issue (19) : 8-12.

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (19) : 8-12.
论文

考虑质量偏心Timoshenko梁的弯-纵耦合固有振动特性研究

  • 王剑1,2,张振果1,2,华宏星1,2
作者信息 +

Coupled flexural and longitudinal natural vibration characteristics of Timoshenko beam consider eccentricity#br#

  • WANG Jian1,2, ZHANG Zhen-guo1,2, HUA Hong-xing1,2
Author information +
文章历史 +

摘要

针对有限元法等数值方法较难处理的质量偏心梁问题,考虑质心、形心不重合情形下的弯-纵耦合效应,建立了有偏心Timoshenko梁弯-纵耦合振动的数学模型,推导了相应的特征方程。进而给出了若干偏心工况下Timoshenko梁弯-纵耦合振动的解析表达式,并探讨了偏心率和典型边界条件对纵向和弯曲振动固有频率和模态振型的影响规律。分析结果表明,固有频率随着偏心率的增大而减小,且质量偏心对纵向振动的影响较弯曲振动更为明显。

Abstract

For the vibration of beam with eccentricity is difficult to deal with by numerical methods such as finite element method, the coupling effect caused by centroid(center of mass) do not coincides with center of geometry was considered, the mathematical model of Timoshenko beam’s flexural-longitudinal vibration was established, the corresponding characteristic equation was derived. Then the analytic solutions of Timoshenko beam’s coupled flexural-longitudinal vibration under several eccentric conditions were given, discussions were given on the regular pattern that how eccentricities and boundary conditions influence the natural frequencies and mode shapes of flexural vibration and longitudinal vibration. The results showed that, natural frequencies decrease as eccentricity increases, and the effects on longitudinal vibration caused by eccentricity is more obvious than that on flexural vibration.

关键词

质量偏心 / 弯-纵耦合 / Timoshenko梁 / 振动

Key words

eccentricity / coupled flexural and longitudinal / Timoshenko beam / vibration

引用本文

导出引用
王剑1,2,张振果1,2,华宏星1,2. 考虑质量偏心Timoshenko梁的弯-纵耦合固有振动特性研究[J]. 振动与冲击, 2015, 34(19): 8-12
WANG Jian1,2, ZHANG Zhen-guo1,2, HUA Hong-xing1,2. Coupled flexural and longitudinal natural vibration characteristics of Timoshenko beam consider eccentricity#br#[J]. Journal of Vibration and Shock, 2015, 34(19): 8-12

参考文献

[1]  Daidola J C. Natural vibrations of beams in a fluid with applications to ships and other marine structures[J]. Transactions-Society of Naval Architects and Marine Engineers, 1984, 92: 331-351.
[2]  Klein L. Transverse vibrations of non-uniform beams[J]. Journal of Sound and Vibration, 1974, 37(4): 491-505.
[3]  Auciello N M, Ercolano A. A general solution for dynamic response of axially loaded non-uniform Timoshenko beams[J]. International Journal of Solids and Structures, 2004, 41(18): 4861-4874.
[4]  徐腾飞, 向天宇, 赵人达. 变截面 Euler-Bernoulli 梁在轴力作用下固有振动的级数解[J]. 振动与冲击, 2008, 26(11): 99-101.
    XU Teng-fei, XIANG Tian-yu, ZHAO Ren-da. Series solution of natural vibration of the variable cross-section Euler-Bernoulli beam under axial force[J]. Journal of vibration and shock, 2008, 26(11): 99-101.
[5]  崔灿, 蒋晗, 李映辉. 变截面梁横向振动特性半解析法[J]. 振动与冲击, 2012, 31(14): 85-88.
    CUI Can, JIANG Han, LI Ying-hui. Semi-analytical method for calculating vibration characteristics of variable cross-section beam[J]. Journal of vibration and shock, 2012, 31(14): 85-88.
[6] Chehil D S, Jategaonkar R. Determination of natural frequencies of a beam with varying section properties[J]. Journal of sound and vibration, 1987, 115(3): 423-436.
[7]  Kocatürk T, Şimşek M. Dynamic analysis of eccentrically prestressed viscoelastic Timoshenko beams under a moving harmonic load[J]. Computers & structures, 2006, 84(31): 2113-2127.
[8]  姚熊亮, 计方, 钱德进, 等. 偏心阻振质量阻抑振动波传递特性研究[J]. 振动与冲击, 2010 (1): 48-52.
    YAO Xiong-liang, JI Fang, QIAN De-jin. Characteristics of eccentric blocking masses attenuating vibration wave propagation[J]. Journal of vibration and shock, 2010 (1): 48-52.
[9]  Senjanović I, Ćatipović I, Tomašević S. Coupled flexural and torsional vibrations of ship-like girders[J]. Thin-walled structures, 2007, 45(12): 1002-1021.
[10] 谢基榕, 徐利刚, 沈顺根, 等. 推进器激励船舶振动辐射声计算方法[J]. 船舶力学, 2011, 15(5): 563-569.
    XIE Ji-rong, XU Li-gang, SHEN Shun-gen. Calculational method for radiating sound excited by vibration of ship propeller[J]. Journal of ship mechanics, 2011, 15(5): 563-569.
[11] Cowper G R. The shear coefficient in Timoshenko’s beam theory[J]. Journal of applied mechanics, 1966, 33(2): 335-340.

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