轴向载荷条件下弹性边界约束梁结构振动特性分析

Abstract
Figure/Table
References (28)
Related Citation (15)

Download: PDF (3141 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract In this paper, an improved Fourier series expansion is employed to establish the vibration analysis model of an axially loaded beam with elastic boundary restraints. Through the introduction of translational and rotational restraining springs at both ends, any types of classical boundary condition and their combination can be simulated by setting the stiffness coefficients accordingly. The vibrational displacement of beam structure is expanded as the superposition of Fourier series and boundary smoothed terms. According to the energy principle, the total kinetic energy, total potential energy and external force of the whole system are formulated, and the system characteristic matrix is obtained in combination with Rayleigh-Ritz procedure. Numerical examples are then given to verify the correctness and reliability of the proposed model for the vibration characteristics analysis of beam structure under different boundary conditions and axial loads. Based on this, the influence of system parameters, including boundary restraining stiffness, axial load and force excitation, on the vibration characteristics of beam structure is investigated. The proposed model has the advantages of high efficiency and precision, which can provide an effective analytical tool for studying the vibration behavior of axially loaded beam with complex boundary conditions.

Key words： Axially loaded Beam structural vibration Elastic boundary restraint Fourier series

Received: 10 April 2019 Published: 28 July 2020

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	ZHAO Yuhao
	DU Jingtao
	XU Deshui

Cite this article:

ZHAO Yuhao,DU Jingtao,XU Deshui. Vibration characteristics analysis for an axially loaded beam with elastic boundary restraints[J]. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(15): 109-117.

URL:

http://jvs.sjtu.edu.cn/EN/ OR http://jvs.sjtu.edu.cn/EN/Y2020/V39/I15/109

[1] D. Stancioiu, H.J. Ouyang, Optimal vibration control of beams subjected to a mass moving at constant speed[J]. Journal of Vibration and Control, 2016, 22(14): 3202-3217.
[2] K.H. Kang, K.J. Kim, Modal properties of beams and plates on resilient supports with rotational and translational complex stiffness[J]. Journal of Sound and Vibration, 1996, 190(2): 207-220.
[3] H.H. Dai, X.J. Jing, Y. Wang, X.K. Yue, J.P. Yuan, Post-capture vibration suppression of spacecraft via a bio-inspired isolation system[J]. Mechanical Systems and Signal Processing, 2008, 105(15): 214-240.
[4] C K RAO, S MIRZA. A note on vibrations of generally
restrained beams[J]. Journal of Sound and Vibration, 1989, 130(3): 453-465.
[5] B A H ABBAS. Vibration of Timoshenko beams with elastically restrained ends[J]. Journal of Sound and Vibration,1984, 97(4) :541-548.
[6] W L LI. Free vibrations of beams with general boundary
conditions[J]. Journal of Sound and Vibration, 2000, 237 (4): 709-725.
[7] I. Elishakoff, Y.K. Lin, L.P. Zhu, Random vibration of uniform beams with varying boundary-conditions by the dynamic-edge-effect method[J]. Computer Methods in Applied Mechanics and Engineering, 1995, 121(1-4): 59-76.
[8] J.D. Jin, X.D. Yang, Y.F. Zhang, Stability and natural characteristics of a supported beam[J]. Product Design and Manufacturing, 2011, 338: 467-472
[9] Z.J. Fan, J.H. Lee, K.H. Kang, K.J. Kim, The forced vibration of a beam with viscoelastic boundary supports[J]. Journal of Sound and Vibration, 1998, 210(5): 673-682.
[10] B. L. Lv et al. Vibration Analysis of beams with arbitrary elastic boundary conditions[J]. Applied Mechanics and Materials, 2011, (66-68): 1325-1329.
[11] 肖伟,霍瑞东,李海超,高晟耀,庞福振.改进傅里叶方法在梁结构振动特性分析中的应用[J]. 噪声与振动控制, 2019, 39(01):10-15.
Xiao W, Huo R D, Li H C, Gao S Y, Pang F Z. Application of improved Fourier series method in vibration analysis of beam structures[J]. Noise and Vibration Control, 2019, 39(01):10-15.
[12] Du J, Li W L, Jin G, et al. An analytical method for the in-plane vibration analysis of rectangular plates with elastically restrained edges[J]. Journal of Sound and Vibration, 2007, 306(3–5):908-927.
[13] Li W L, Zhang X, Du J, et al. An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports[J]. Journal of Sound and Vibration, 2009, 321(1–2):254-269.
[14] 李文达,杜敬涛,杨铁军,刘志刚. 基于改进傅里叶级数方法的旋转功能梯度圆柱壳振动特性分析[J]. 哈尔滨工程大学学报, 2016, 03:388-393.
Li W D, Du J T, Yang T J, Liu Z G. Vibration characteristics analysis of the rotating functionally graded cylindrical shell structure[J]. Journal of Harbin Engineering University, 2016, 37(03):388-393.
[15] 刘华, 朱小芹, 杨嘉陵.冲击载荷下受轴向约束的点阵材料夹芯简支梁[J]. 北京航空航天大学学报, 2009, 35(12):1451-1454.
Liu H, Zhu X Q, Yang J L. Impulsive loading of simply supported lattice truss core sandwich beams with axial restraints[J]. Journal of Beijing University of Aeronautics and Astronautics, 2009, 35(12):1451-1454.

[16] 王文浩,苟文选,杨帆,闫五柱.轴向载荷作用下H形悬臂梁稳定性能研究[J]. 重型机械, 2016, 5:36-41.
Wang W H, Gou W X, Yang F, Yan W Z. Research on stability of H-section cantilever beam under axial load[J]. Heavy Machinery, 2016, (05):36-41.
[17] Daniel Y. Abebe, Sijeong Jeong, Jeonghyun Jang, Jaehyouk Choi, Jeong-Ung Park. Study on inelastic buckling and residual strength of H-section steel column member[J]. International Journal of Steel Structures, 2015, 15(2): 365-374.
[18] 陈红永,李上明.轴向运动梁在轴向载荷作用下的动力学特性研究[J]. 振动与冲击, 2016, 35(19):75-80.
Chen H Y, Li S M. Dynamic characteristics of an axially moving Timoshenko beam under axial loads.[J]. Journal of Vibration and Shock, 2016, 35 (19):75-80.
[19] Jer-Rong Chang, Wei-Jr Lin, Chun-Jung Huang, Siu-Tong Choi. Vibration and stability of an axially moving Rayleigh beam[J]. Applied Mathematical Modelling, 2010, 34(6): 1482-1497.
[20] 邢维巍,张硕,樊尚春.动态轴向载荷下谐振梁振动响应分析[J]. 传感技术学报, 2016, 29(09):1372-1375.
Xing W W, Zhang S, Fan S C. Resonant beam vibrating response under dynamic axial load analysis[J]. Chinese Journal of Sensors and Actuators, 2016, 29 (09):1372-1375.
[21] 黄悦. 轴向载荷作用下功能梯度材料梁的动力屈曲分析[D]. 太原理工大学, 2018.
Huang Y. Dynamic buckling of functionally graded material beam[D]. Taiyuan University of Technology, 2018.
[22] 任福深,陈素丽,姚志刚.轴向载荷作用下细长柔性旋转梁横向振动响应分析[J].中国机械工程, 2013, 24(24):3392-3396.
Ren F S, Chen S L, Yao Z G. Vibration response analysis of slender flexible revolving beam under axial load[J]. Chinese Mechanical Engineering, 2013, 24(24):3392-3396.
[23] 龚善初.轴向载荷、转动惯量和剪切变形对简支梁固有频率的影响[J]. 河南科学, 2004, 5:592-596.
Gong S C. The influence of axial load、moment of inertia and shear deformation of the natural frequency of simply supported beam[J]. Henan Science, 2004, (05):592-596.
[24] 李楠,韩志军,路国运.基于里兹法研究复合材料层合板的动力屈曲问题[J].振动与冲击, 2016, 35(10):180-184.
Li N, Han Z J, Lu G Y. Study on dynamic buckling of Composite Laminates based on Ritz method[J]. Journal of Vibration and Shock, 2016, 35(10):180-184.
[25] 马连生, 李靓君. 纵横向载荷作用下经典梁非线性静态响应的精确解[J]. 兰州理工大学学报,2017, 43(05):157-161.
Ma L S, Li L J. Exact solution of nonlinear static response of classical beams under longitudinal and transverse loads[J]. Journal of Lanzhou University of Technology, 2017, 43(05):157-161.
[26] H. Ding, Ze-Qi Lu, L. Q. Chen. Nonlinear isolation of transverse vibration of pre-pressure beams[J]. Journal of Sound and Vibration, 2019, 442(3): 738-751.
[27] 黄开志,陈小亮.两端任意线弹性支承的压杆稳定性研究[J]. 四川理工学院学报, 2014, 27(05):22-24.
Huang K Z, Chen X L. Study on the stability of compression bar supported by arbitrary Linear elastic support at both ends[J]. Journal of Sichuan University of Science Engineering, 2014, 27(05):22-24.
[28] 黄开志,陈小亮. 任意线弹性支承的双跨压杆稳定性计算[J]. 武汉工程大学学报, 2014, 36(09):7-11.
Huang K Z, Chen X L. Stability ca lculation of double span compression bar with arbitrary linear elastic support[J]. Journal of Wuhan Institute of Technology, 2014, 36(09):7-11.