在工程实际中或研究船舶、潜艇等的低频振动时，相应的梁模型有时存在质量中心与形心不重合的情况，此质量偏心会引起弯-纵耦合。本文以弯曲传播波、弯曲衰减波和纵向波为对象，推导了振动波在Timoshenko偏心梁的弹性支撑、变截面、边界和直角转角处的透射和反射矩阵，重点讨论了振动波的耦合及相互转变效应。分析结果表明：质量偏心率越大，弯曲衰减波越容易转变为弯曲传播波；频率提高或者偏心率增大时，弯曲波对纵向波的贡献也变大；三种振动波在边界处不会产生耦合效应；波入射位置存在截面尺寸变化时，弯曲衰减波在新尺寸对应的截止频率处转变为了弯曲传播波。
关键词：波形转换；质量偏心；Timoshenko梁；弯-纵耦合
Abstract
In engineering practice or considering low-frequency vibrations of ships, submarines, etc., sometimes the center of mass and the centroid do not coincide in the corresponding beam model, whereas this mass eccentricity will cause bending-longitudinal coupling effects. Concentrating on flexural propagation waves, flexural attenuation waves and longitudinal waves, the transmission and reflection matrices of these waves at the elastic support, change in cross-section, boundary and right-angle corners of the Timoshenko eccentric beam were derived, and the coupling and transition of waves were discussed in this paper. The results show that enhancement of eccentricity facilitates the transition from flexural attenuation waves to propagation ones. If the frequency or eccentricity is increased, or both, the contribution to longitudinal waves attributes to flexural waves will become greater. The coupling effects will not arise between the three types of waves at boundary. When there exists an abrupt variation of cross-section at the location where waves emit, the transition of flexural attenuation waves to propagation ones occurs at the cut-off frequency corresponding to the geometric size of this new cross-section.
Key words: wave transition; mass eccentricity; Timoshenko beam; bending-longitudinal coupling
关键词
波形转换 /
质量偏心 /
Timoshenko梁 /
弯-纵耦合
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Key words
wave transition /
mass eccentricity /
Timoshenko beam /
bending-longitudinal coupling
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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] Senjanovic I, Vladimir N, Tomic M, et al. Global hydroelastic analysis of ultra large container ships by improved beam structural model[J]. International Journal of Naval Architecture and Ocean Engineering, 2014, 6(4): 1041-1063.
[3] 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 Jirong, Xu Ligang, Shen Shungen. Calculational method for radiating sound excited by vibration of ship propeller[J]. Journal of Ship Mechanics, 2011, 15(5): 563-569.
[4] Valvano S, Alaimo A, Orlando C. Sound transmission analysis of viscoelastic composite multilayered shells structures. Aerospace, 2019, 6(6): 69-78.
[5] 周凤玺, 蒲育. 功能梯度压电材料梁的热-机-电耦合振动及屈曲特性分析[J]. 机械工程学报, 2021, 57(08): 166-174.
Zhou Fengxi, Pu Yu. Vibration and buckling behaviors of functionally graded piezoelectric material beams subjected to thermal-mechanical-electrical loads[J]. Journal of Mechanical Engineering, 2021, 57(08): 166-174.
[6] 赵晔, 叶伟, 俞国新, 等. 非对称船体梁弯扭耦合振动试验及分析[J]. 振动与冲击, 1997, (03): 12-17.
Zhao Ye, Ye Wei, Yu Guoxin, et al. Test and analysis of coupled bending and torsional vibration of asymmetric ship girder[J]. Journal of Vibration and Shock, 1997, (03): 12-17.
[7] 虞爱民, 杨昌锦, 郝颖. 自然弯扭梁的耦合振动分析[J]. 振动与冲击, 2009, 28(08): 175-179.
Yu Aimin, Yang Changjin, Hao Yin. Analysis of coupled vibrational behavior of naturally curved and twisted beams[J]. Journal of Vibration and Shock, 2009, 28(08): 175-179.
[8] Fahy F J. Sound and Structural Vibration: Radiation, Transmission and Response[M]. Amsterdam: Elsevier, 2012. 63-70.
[9] Ji H, Liang Y, Qiu J, et al. Enhancement of vibration based energy harvesting using compound acoustic black holes[J]. Mechanical Systems and Signal Processing, 2019, 132: 441-456.
[10] Mead D J. Vibration response and wave propagation in periodic structures[J], Journal of Engineering for Industry, 1971, 93: 783–792.
[11] Cheng Z, Shi Z, Mo Y-L. Complex dispersion relations and evanescent waves in periodic beams via the extended differential quadrature method[J]. Composite Structures, 2018, 187: 122-136.
[12] Mace B R, Duhamel D, Brennan M J, et al. Finite element prediction of wave motion in structural waveguides[J]. Acoustical Society of America Journal, 2005, 117(5): 2835-2843.
[13] Brun M, Movchan A B, Slepyan L I. Transition wave in a supported heavy beam[J]. Journal of the Mechanics and Physics of Solids, 2013, 61(10): 2067-2085.
[14] Nieves M, Mishuris G, Slepyan L. Analysis of dynamic damage propagation in discrete beam structures[J]. International journal of Solids and Structures, 2016, 97: 699-713.
[15] Kalkowski M K, Muggleton J M, Rustighi E. An experimental approach for the determination of axial and flexural wavenumbers in circular exponentially tapered bars. Journal of Sound and Vibration, 2017, 390: 67-85.
[16] Mace B. Wave reflection and transmission in beams[J]. Journal of Sound and Vibration, 1984, 97(2): 237-246.
[17] Mei C, Mace B R. Wave reflection and transmission in Timoshenko beams and wave analysis of Timoshenko beam structures[J]. Journal of vibration and acoustics, 2005, 127(4): 382-394.
[18] 王剑, 张振果, 华宏星. 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 Jian, Zhang Zhenguo, Hua Hongxing. Coupled flexural and longitudinal natural vibration characteristics of Timoshenko beam consider eccentricity[J]. Journal of Vibration and Shock, 2015, 34(19): 8-12.
[19] 《数学手册》编写组编. 数学手册[M]. 北京: 高等教育出版社, 1979.88-89.
"Mathematics Handbook" compilation group. Mathematics Handbook[M]. Beijing: Higher Education Press, 1979.88-89.
[20] Singiresu S R. Mechanical vibrations[M]. Boston, MA: Addison Wesley, 1995.
[21] Cowper G R. The shear coefficient in Timoshenko’s beam theory[J]. Journal of applied mechanics, 1966, 33(2): 335-340.
[22] El Masri E, Ferguson N, Waters T. Wave propagation and scattering in reinforced concrete beams[J]. Journal of the Acoustical Society of America, 2019, 146(5): 3283-3294.
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