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
王剑1,2,袁秀峰1,胡永彪2. 振动波在质量偏心Timoshenko梁非连续处的传播特性研究[J]. 振动与冲击, 2022, 41(20): 37-45.
WANG Jian1,2,YUAN Xiufeng1,HU Yongbiao2. A study on propagation characteristics of vibration waves in a mass eccentric Timoshenko beam when encounter discontinuities. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(20): 37-45.
[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.