Torsional vibration characteristics of an elastic rod structure under arbitrary boundary conditions

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Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (1) : 161-166.

XU Deshui, DU Jingtao, LI Wenda, YANG Tiejun, LI Wanyou

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Abstract

An improved Fourier series method was employed to model torsional vibration of an elastic rod under arbitrary boundary conditions. In order to overcome discontinuities of displacement derivatives of traditional Fourier series at boundary points, an improved method was constructed to improve the convergence and correctness of the series solution. The system characteristic equation was obtained through exactly solving the torsional vibration governing equations and boundary condition equations of the rod. Various numerical examples were presented to validate the feasibility and correctness of the proposed model.

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elastic rod / torsional vibration / boundary condition / Fourier series

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XU Deshui, DU Jingtao, LI Wenda, YANG Tiejun, LI Wanyou. Torsional vibration characteristics of an elastic rod structure under arbitrary boundary conditions[J]. Journal of Vibration and Shock, 2017, 36(1): 161-166

References

[1] W.E. Tefft, S. Spinner. Torsional resonance vibrations of uniform bars of square cross section [J]. Journal of Research of the National Bureau of Standards-A. Physics and Chemistry, 1961, 65(3): 167-171.
[2] H.S. Paul, K. Sridharan. Forced torsional vibration of an elastic circular rod on an elastic half space and on an elastic stratum [J]. Journal of the Acoustical Society of America, 1979, 65(2): 391-398.
[3] C.K. Rao. Torsional frequencies and mode shapes of generally constrained shafts and piping [J]. Journal of Sound and Vibration, 1988, 125(1): 115-121.
[4] 刘清友, 马德坤, 钟青. 钻柱扭转振动模型的建立及求解[J]. 石油学报, 2000, 21(2): 78-82.
Liu Qing-you, Ma De-kun, Zhong Qing. A drilling string torsional vibration model and its solution[J]. ACTA, 2000, 21(2): 78-82.
[5] 刘志先. 推算楔形直杆纵振与扭振自主频率的一个方法[J]. 中国科学, 1977, 7(6): 536-546.
Liu Zhi-xian. A method for calculating the frequency of the longitudinal and torsional vibration of a wedge shaped rod [J]. SCIENCE CHINA , 1977, 7(6): 536-546.
[6] M. Rafiee, S.J. Mehrabadi, N. Rasekh-Saleh. Analytical solutions for the torsional vibrations of variable cross-section rods [J]. International Journal of Engineering and Applied Science, 2010, 2(4): 64-71.
[7] 杨立军, 邓志恒, 叶柏龙, 等. 变截面杆轴向和扭转振动分析的摄动法[J]. 中南大学学报, 2014, 45(3): 855-861.
Yang Li-jun, Liu Zhi-heng, Ye Bai-long, et al. Perturbation method for longitudinal and torsional vibration analysis of bar with variable cross-section[J]. Journal of Central South University, 2014, 45(3): 855-861.
[8] T.G. Chondros. Variational formulation of a rod under torsional vibration for crack identification [J]. Theoretical and Applied Fracture Mechanics, 2005, 44: 95-104.
[9] Y.D. Wei, Y.G. Lv, Z.C. Chen. Active control of torsional vibration of flexible bars [J]. International Journal of Information and Systems Sciences, 2005, 1(3): 347-354.
[10] A.D.S. Barr. Torsional waves in uniform rods of non-circular section [J]. Journal of Mechanical Engineering Science, 1962, 4(2): 127-135.
[11] 舒歌群. 基于扭转弹性波理论的船舶柴油机推进轴系扭振研究[J]. 船舶力学, 2005, 9(5): 137-142.
Shu Ge-qun. Calculation of crankshaft torsional vibration response in diesel engine by torsional elastic wave theory[J]. Journal of Ship Mechanics, 2005, 9(5): 137-142.
[12] J.S. Yang. Nonlinear torsional vibration of a circular cylindrical piezoelectric rod with relatively large shear deformation [J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2007, 54(7): 1482-1485.
[13] 李立群, 段静波, 李家文, 等. 基于传递函数法的非局部弹性直杆扭转振动研究[J]. 力学季刊, 2012, 33(2): 181-187.
Li Li-qun, Duan Jing-bo, Li Jia-wen, et al. Research on torsional vibration of nonlocal elastic bar using transfer function method[J]. CHINESE QUARTERLY OF MECHANICS, 2012, 33(2): 181-187.
[14] S. Narendar, S. Ravinder, S. Gopalakrishnan. Strain gradient torsional vibration analysis of micro/nano rods [J]. International Journal of Nano Dimension, 2012, 3(1): 1-17.
[15] R. Ansari, S. Ajori. Molecular dynamics study of the torsional vibration characteristics of boron-nitride nanotubes [J]. Physics Letters A, 2014, 378: 2876-2880.
[16] 郁殿龙, 刘耀宗, 王刚, 等. 一维杆状结构声子晶体扭转振动带隙研究[J]. 振动与冲击, 2006, 25(1): 104-106.
Yu Dian-long, Liu Yao-zong, Wang Gang, et al. Research on torsional vibration band gaps of one dimensional phononic crystals composed of rod structures[J]. Journal of Vibration and Shock, 2006, 25(1): 104-106.
[17] 杨天智，方勃，杨晓东，等. 复杂约束管道固有频率的快速算法[J]. 哈尔滨工业大学学报, 2007, 39(5): 771-773.
Yang T.Z., Fang B., Yang X.D., et al. A fast algorithm for natural frequencies of pipe with complex restrictions[J]. Journal of Harbin Institute of Technology, 2007, 39(5): 771-773.
[18] 刘向尧，聂宏，魏小辉. 复杂边界条件下的多跨梁的振动模型[J]. 北京航空航天大学学报, 2015, 41(5): 841-846.
Liu X.Y., Nie H., Wei X.H., et al. Vibration model for multi-span beam with arbitrary complex boundary conditions[J]. Journal of Beijing University of Aeronautics and Astronautics, 2015, 41(5): 841-846.
[19] J.T. Du, W.L. Li, G.Y. Jin, T.J. Yang, Z.G. Liu. An analytical method for the in-plane vibration analysis of rectangular plates with elastically restrained edges[J]. Journal of Sound and Vibration, 2007, 306: 908-927.
[20] Cyril M. Harris, Allan G. Piersol. HARRIS’ SHOCK AND VIBRATION HANDBOOK 5th Ed[A]. 刘树林等译. 冲击与振动手册(第五版)[M]. 北京：中国石化出版社, 2008：7.1-7.8.