有砟轨道结构弹性波传播特性研究
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摘要
铁路轨道结构沿线路纵向具有明显的周期特征,固体物理领域研究表明弹性波在周期结构中的传播具有带隙特性。以有砟轨道结构为研究对象,从轨道结构周期特征出发,开展弹性波在轨道结构中传播特性的研究。建立周期性轨道结构模型并将钢轨考虑为Timoshenko梁,基于Bloch定理和传递矩阵法求解周期性轨道结构中弹性波的频散曲线,得到轨道结构带隙范围;利用弹性波叠加原理,计算简谐荷载作用下无限长轨道结构的动力响应;采用功率流方法分析弯曲波能量在周期性轨道结构中的传播特性。研究结果表明:周期性轨道结构具有明显的带隙特征,在带隙范围内弹性波在轨道结构中无法自由传播,且外界激励也无法向系统输入能量;通带范围内可进行能量的输入与传播。
Railway track structure has obvious periodic characteristics along the longitudinal direction of the track. The study of solid state physics shows that the propagation of elastic wave in periodic structures has significant band gap properties. Based on the analysis of ballasted track structure and the periodic characteristics of the track structure, the elastic wave propagation properties in the track structure were studied. Firstly, the dynamic model for the periodic track structure was established with the rail being considered as a Timoshenko beam, while the Bloch theorem and the transfer matrix method were applied to solve the dispersion curves of elastic wave in periodic track structure in order to obtain the band gaps. Secondly, based on the principle of superposition, the dynamic response of infinite track structure under harmonic loads was solved. Finally, the power flow method was used to analyse the propagation characteristics of the bending wave energy. The results show that the periodic track structure possesses the band gap properties. The elastic wave propagation in the band gaps is suppressed. No energy can be input into the system by external excitation while the input and propagation of the energy are allowed in the pass band.
Railway track structure has obvious periodic characteristics along the longitudinal direction of the track. The study of solid state physics shows that the propagation of elastic wave in periodic structures has significant band gap properties. Based on the analysis of ballasted track structure and the periodic characteristics of the track structure, the elastic wave propagation properties in the track structure were studied. Firstly, the dynamic model for the periodic track structure was established with the rail being considered as a Timoshenko beam, while the Bloch theorem and the transfer matrix method were applied to solve the dispersion curves of elastic wave in periodic track structure in order to obtain the band gaps. Secondly, based on the principle of superposition, the dynamic response of infinite track structure under harmonic loads was solved. Finally, the power flow method was used to analyse the propagation characteristics of the bending wave energy. The results show that the periodic track structure possesses the band gap properties. The elastic wave propagation in the band gaps is suppressed. No energy can be input into the system by external excitation while the input and propagation of the energy are allowed in the pass band.
引文
[1] MOUSAVI S H,KHANIKAEV A B,WANG Z.Topologically Protected Elastic Waves in Phononic Metamaterials[J].Nature Communications,2015(6):8682.
[2] NORTON M P,KARCZUB D G.Fundamentals of Noise and Vibration Analysis for Engineers:Ⅱ[M].Cambridge:Cambridge University Press,2003.
[3] DEYMIER P A.Acoustic Metamaterials and Phononic Crystals[M].Berlin Heidelberg:Springer,2013:201- 215.
[4] MEAD D M.Wave Propagation in Continuous Periodic Structures:Research Contributions from Southampton,1964-1995[J].Journal of Sound and Vibration,1996,190(3):495-524.
[5] HECKL M A.Coupled Waves on a Periodically Supported Timoshenko Beam[J].Journal of Sound and Vibration,2002,252(5):849-882.
[6] KUSHWAHA M S,HALEI P,DOBRZYNSKI L,et al.Acoustic Band Structure of Periodic Elastic Composites[J].Physical Review Letters,1993,71(13):2022-2025.
[7] XIAO Y,WEN J H,YU D L,et al.Flexural Wave Propagation in Beams with Periodically Attached Vibration Absorbers:Band-gap Behavior and Band Formation Mechanisms[J].Journal of Sound and Vibration,2013,332(4):867-893.
[8] XIAO Y,WEN J H,HUANG L Z,et al.Analysis and Experimental Realization of Locally Resonant Phononic Plates Carrying a Periodic Array of Beam-like Resonators[J].Journal of Physics D:Applied Physics,2014,47(4):045307.
[9] YU D L,WEN J H,ZHAO H G,et al.Flexural Vibration Band Gap in a Periodic Fluid-conveying Pipe System Based on the Timoshenko Beam Theory[J].Journal of Vibration & Acoustics,2011,133(1):014502.
[10] LI Y F,SHEN H J,ZHANG L K,et al.Control of Low-frequency Noise for Piping Systems via the Design of Coupled Band Gap of Acoustic Metamaterials[J].Physics Letters A,2016,380(29/30):2322-2328.
[11] GRASSIE S L,GREGORY R W,HARRISON D,et al.The Dynamic Response of Railway Track to High Frequency Vertical Excitation[J].Journal of Mechanical Engineering Science,1982,24(2):77-90.
[12] THOMPSON D J,VINCENT N.Track Dynamic Beha-viour at High Frequencies.Part 1:Theoretical Models and Laboratory Measurements[J].Vehicle System Dynamics,1995,24(S1):86-99.
[13] VINCENT N,THOMPSON D J.Track Dynamic Beha-viour at High Frequencies.Part 2:Experimental Results and Comparisons with Theory[J].Vehicle System Dynamics,1995,24(S1):100-114.
[14] NORDBORG A.Vertical Rail Vibrations:Pointforce Excitation[J].Acta Acustica United with Acustica,1998,84(2):280-288.
[15] WU T X,THOMPSON D J.Application of a Multiple-beam Model for Lateral Vibration Analysis of a Discretely Supported Rail at High Frequencies[J].Journal of the Acoustical Society of America,2000,108:1341-1344.
[16] SHENG X,JONES C J C,THOMPSON D J.Responses of Infinite Periodic Structures to Moving or Stationary Harmonic Loads [J].Journal of Sound and Vibration,2005,282(1/2):125-149.
[17] SHENG X,LI M H.Propagation Constants of Railway Tracks as a Periodic Structure [J].Journal of Sound and Vibration,2007,299(4/5):1114-1123.
[18] THOMPSON D J.Railway Noise and Vibration:Mechanisms,Modelling and Means of Control[M].Oxford:Elsevier Science & Technology,2009.
[19] KUSHWAHA M S,HALEVI P,MARTINEZ G,et al.Theory of Acoustic Band Structure of Periodic Elastic Composites[J].Physical Review B:Condensed Matter,1994,49(4):2313-2322.
[20] CREMER L,HECKL M,PETERSSON B A T.Structure-borne Sound [M].Berlin Heidelberg:Springer,2005.
[21] MANDAL N K,BISWAS S.Vibration Power Flow:A Critical Review [J].The Shock and Vibration Digest,2005,37(1):3-11.
[22] MEAD D J,YAMAN Y.The Harmonic Response of Uniform Beams on Multiple Linear Supports:A Flexural Wave Analysis[J].Journal of Sound and Vibration,1990,141(3):465-484.
[23] MEAD D J,YAMAN Y.The Response of Infinite Periodic Beams to Point Harmonic Forces:A Flexural Wave Analysis[J].Journal of Sound and Vibration,1991,144(3):507-529.
[2] NORTON M P,KARCZUB D G.Fundamentals of Noise and Vibration Analysis for Engineers:Ⅱ[M].Cambridge:Cambridge University Press,2003.
[3] DEYMIER P A.Acoustic Metamaterials and Phononic Crystals[M].Berlin Heidelberg:Springer,2013:201- 215.
[4] MEAD D M.Wave Propagation in Continuous Periodic Structures:Research Contributions from Southampton,1964-1995[J].Journal of Sound and Vibration,1996,190(3):495-524.
[5] HECKL M A.Coupled Waves on a Periodically Supported Timoshenko Beam[J].Journal of Sound and Vibration,2002,252(5):849-882.
[6] KUSHWAHA M S,HALEI P,DOBRZYNSKI L,et al.Acoustic Band Structure of Periodic Elastic Composites[J].Physical Review Letters,1993,71(13):2022-2025.
[7] XIAO Y,WEN J H,YU D L,et al.Flexural Wave Propagation in Beams with Periodically Attached Vibration Absorbers:Band-gap Behavior and Band Formation Mechanisms[J].Journal of Sound and Vibration,2013,332(4):867-893.
[8] XIAO Y,WEN J H,HUANG L Z,et al.Analysis and Experimental Realization of Locally Resonant Phononic Plates Carrying a Periodic Array of Beam-like Resonators[J].Journal of Physics D:Applied Physics,2014,47(4):045307.
[9] YU D L,WEN J H,ZHAO H G,et al.Flexural Vibration Band Gap in a Periodic Fluid-conveying Pipe System Based on the Timoshenko Beam Theory[J].Journal of Vibration & Acoustics,2011,133(1):014502.
[10] LI Y F,SHEN H J,ZHANG L K,et al.Control of Low-frequency Noise for Piping Systems via the Design of Coupled Band Gap of Acoustic Metamaterials[J].Physics Letters A,2016,380(29/30):2322-2328.
[11] GRASSIE S L,GREGORY R W,HARRISON D,et al.The Dynamic Response of Railway Track to High Frequency Vertical Excitation[J].Journal of Mechanical Engineering Science,1982,24(2):77-90.
[12] THOMPSON D J,VINCENT N.Track Dynamic Beha-viour at High Frequencies.Part 1:Theoretical Models and Laboratory Measurements[J].Vehicle System Dynamics,1995,24(S1):86-99.
[13] VINCENT N,THOMPSON D J.Track Dynamic Beha-viour at High Frequencies.Part 2:Experimental Results and Comparisons with Theory[J].Vehicle System Dynamics,1995,24(S1):100-114.
[14] NORDBORG A.Vertical Rail Vibrations:Pointforce Excitation[J].Acta Acustica United with Acustica,1998,84(2):280-288.
[15] WU T X,THOMPSON D J.Application of a Multiple-beam Model for Lateral Vibration Analysis of a Discretely Supported Rail at High Frequencies[J].Journal of the Acoustical Society of America,2000,108:1341-1344.
[16] SHENG X,JONES C J C,THOMPSON D J.Responses of Infinite Periodic Structures to Moving or Stationary Harmonic Loads [J].Journal of Sound and Vibration,2005,282(1/2):125-149.
[17] SHENG X,LI M H.Propagation Constants of Railway Tracks as a Periodic Structure [J].Journal of Sound and Vibration,2007,299(4/5):1114-1123.
[18] THOMPSON D J.Railway Noise and Vibration:Mechanisms,Modelling and Means of Control[M].Oxford:Elsevier Science & Technology,2009.
[19] KUSHWAHA M S,HALEVI P,MARTINEZ G,et al.Theory of Acoustic Band Structure of Periodic Elastic Composites[J].Physical Review B:Condensed Matter,1994,49(4):2313-2322.
[20] CREMER L,HECKL M,PETERSSON B A T.Structure-borne Sound [M].Berlin Heidelberg:Springer,2005.
[21] MANDAL N K,BISWAS S.Vibration Power Flow:A Critical Review [J].The Shock and Vibration Digest,2005,37(1):3-11.
[22] MEAD D J,YAMAN Y.The Harmonic Response of Uniform Beams on Multiple Linear Supports:A Flexural Wave Analysis[J].Journal of Sound and Vibration,1990,141(3):465-484.
[23] MEAD D J,YAMAN Y.The Response of Infinite Periodic Beams to Point Harmonic Forces:A Flexural Wave Analysis[J].Journal of Sound and Vibration,1991,144(3):507-529.