Analysis of free vibration characteristics of composite L-shaped variable cross-section beam

PDF(1160 KB)

Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (5) : 228-234.

NIU Guohua1,2, WANG Gangfeng1,2, WANG Jian1,2

Author information +

History +

Abstract

The composite beam structure is often used as a sub-organization of a large complex structure and is widely used in machinery, civil engineering and other equipment. Aiming at the problem of the vibration characteristics of composite beams, a structural vibration characteristics calculation method based on the composite L-shaped variable cross-section beam is proposed. Based on Euler-Bernoulli beam theory, the calculation process of natural frequency and mode shape of cantilever L-shaped variable cross-section beam is deduced and a calculation example is given. Convergence analysis is carried out for the calculation results, and the effectiveness of the proposed method is verified by comparison with the FEM. This method can provide a theoretical basis for the dynamic calculation of frame structures in machinery or buildings, especially in the case of variable cross-section.

Key words

composite beam / vibration characteristics / L-shaped beams / variable cross-section

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

WANG Gangfeng1,2, NIU Guohua1,2, WANG Jian1,2. Analysis of free vibration characteristics of composite L-shaped variable cross-section beam[J]. Journal of Vibration and Shock, 2022, 41(5): 228-234

References

[1] 龚善初. 简支矩形截面组合梁横向振动的固有频率[J]. 兰州理工大学学报，2005，(03):146-148.
GONG Shan-chu. Natural frequency of transverse vibration of simply supported compound beams with rectangular cross-ection [J]. Journal of Lanzhou University of Technology, 2005, (03):146-148.
[2] 陶彦鸣，张旭鹏，鲍四元. 变截面欧拉梁自由振动特性的谱方法分析[J]. 低温建筑技术，2019，41(09):24-28.
TAO Yan-ming, ZHNAG Xu-peng, BAO Si-yuan. Free vibration analysis of euler beam with variable cross-section by using the spectral method [J]. Journal of Low temperature building technology, 2019, 41(09):24-28.
[3] 王民，秦鹏，张彦琳，等. 组合阶梯梁振动特性计算方法及应用[J]. 北京工业大学学报，2019，45(01):1-7.
WANG Min, QIN Peng, ZHNAG Yan-lin, et al. Solution and application for vibration characteristics of combined stepped beam [J]. Journal of Beijing University of Technology, 2019, 45(01):1-7.
[4] 张文福，杜娟，刘迎春，等. 索桁架组合体系的固有振动能量变分解[J]. 东北石油大学学报，2013，37(05):103-108+33.
ZHANG Wen-fu, DU Juan, LIU Yang-chun, et al. Energy variational solution for the nature vibration of the cable-trusses combination system [J]. Journal of Northeast Petroleum University, 2013, 37(05):103-108+33.
[5] 罗延忠. 组合梁振动分析的折算系数法[J]. 黑龙江矿业学院学报，2000，10(1):33-35 .
LUO Yan-zhong. Reduced coefficient method for analysis of the vibration of combined beam [J]. Journal of Heilongjiang Mining Institute, 2000, 10(1):33-35.
[6] Wang G. Coupled free vibration of composite beams with asymmetric cross-sections [J]. Composite Structures, 2013, 100: 373-384.
[7] Georgiades F，Warminski J，Cartmell M P. Linear Modal Analysis of L-shaped Beam Structures – Parametric Studies [J]. Journal of Physics: Conference Series, 2012, 382(1): 012006.
[8] Georgiades F，Warminski J，Cartmell M P. Towards linear modal analysis for an L-shaped beam: Equations of motion [J]. Mechanics Research Communications, 2013, 47(3):50-60.
[9] Georgiades F，Warminski J，Cartmell M P. Linear modal analysis of L-shaped beam structures [J]. Mechanical Systems and Signal Processing, 2013, 38(2):312-332.
[10] 鲍四元，周静，陆健炜. 任意弹性边界的多段梁自由振动研究[J]. 应用数学和力学，2020，41(09):985-993.
BAO Si-yuan, ZHOU Jing, LU Jian-wei. Free vibration of multi-segment beams with arbitrary boundary conditions [J]. Journal of Applied Mathematics and Mechanics, 2020, 41(09):985-993.
[11] 葛仁余，张金轮，姜忠宇，等. 轴向功能梯度变截面Timoshenko梁自由振动的研究[J]. 振动与冲击，2017，36(22):158-165+244.
GE Ren-yu, ZHANG Jin-lun, JIANG Zhong-yu, et al. Free vibration analysis of axially functionally Timoshenko beams with a non-uniform cross-section [J]. Journal of Vibration and Shock, 2017, 36(22):158-165+244.
[12] 王剑，张振果，任龙龙，等. 考虑质量偏心的阶梯梁-基础的强迫振动计算[J]. 振动与冲击，2017，36(22):118-124.
WANG Jian, ZHANG Zhen-guo, REN Long-long, et al. Flexural-longitudinal coupled natural vibration characteristics of a Timoshenko beam considering mass eccentricity [J]. Journal of Vibration and Shock, 2017, 36(22):118-124.
[13] 马一江，李园园，陈国平，等. 含多条裂纹变截面简支梁的自由振动[J]. 振动与冲击，2019，38(19):149-154.
MA Yi-jiang, LI Yuan-yuan, CHEN Guo-ping, et al. Free vibration of a variable cross-section simple supported beam with multi-crack [J]. Journal of Vibration and Shock, 2019, 38(19):149-154.
[14] 刘鹏，刘红军，林坤，等. 基于样条有限点法的变截面Euler梁横向自由振动分析[J]. 振动与冲击，2016，35(11):66-73.
LIU Peng, LIU Hong-jun, LIN Kun, et al. Free transverse vibration analysis of tapered bernoulli-euler beams based on spline finite point method [J]. Journal of Vibration and Shock, 2016, 35(11):66-73.
[15] Li Q S. Vibratory characteristics of multi-step beams with an arbitrary number of cracks and concentrated masses [J]. Applied Acoustics, 2001, 62(6):691-706.
[16] Lee J. Application of Chebyshev-tau method to the free vibration analysis of stepped beams [J]. International Journal of Mechanical Sciences, 2015, 101-102: 411-420.
[17] Failla G，Santini A. A solution method for Euler–Bernoulli vibrating discontinuous beams [J]. Mechanics Research Communications, 2008, 35(8): 517-529.
[18] Mao Q. Free vibration analysis of multiple-stepped beams by using Adomian decomposition method [J]. Mathematical and Computer Modelling, 2011, 54(1-2):756-764.
[19] 杜飞平，谭永华，陈建华，等. 航天器子结构模态综合法研究现状及进展[J]. 火箭推进，2010，36(03):39-44+62.
DU Fei-ping, TAN Yong-hua, CHEN Jian-hua, et al. Status and progress on substructural modal synthesis techniques for space vehicles [J]. Journal of Rocket Propulsion, 2010, 36(03):39-44+62.
[20] 缪炳祺，曲广吉. 柔性航天器动力学模型的模态综合—混合坐标法建模研究[J]. 航天器工程，1998，(01):29-35.
MIU Bing-qi, QU Guang-qi. Modal Synthesis of Dynamic Model of Flexible Spacecraft—Modeling Research of Hybrid Coordinate Method [J]. Journal of Spacecraft Engineering, 1998, (01):29-35.