周期结构在屏障隔振中的应用
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摘要
研究发现,经过特别设计的周期结构具有带隙特性,带隙频率范围内的弹性波不能通过。近年来,周期结构在带隙理论和带隙算法方面均取得了重要的进展。具有带隙的周期结构可以抑制振动传播的特性为结构振动控制提供了新的思路和技术途径。相似地,作为一种有效的隔振措施,隔振屏障包括空沟、填充沟及排桩也是通过抑制波的传播来达到隔振的目的。结合两者的特点,本文将周期结构的计算方法应用于带有周期特性的隔振屏障中去,把带隙的理论引入到隔振屏障计算中,不但可以预测屏障隔振的频率范围,还能通过改变周期结构布置获得更好的隔振效果。本文对带有周期性的隔振屏障进行了数值分析,主要内容为：
1.用改进平面波展开法对有周期结构特性的非连续屏障的带隙特性进行计算,讨论了不同空间排布、不同形状桩截面、不同排桩的布置形式对屏障带隙的影响。分析了不同物理参数(如桩材料密度、弹性模量)和几何参数(如填充系数)对第一带隙的影响。
2.用有限差分法计算二维三组元周期结构带隙,对传统平面波展开法、改进平面波展开法和有限差分法在二维三组元周期结构带隙的收敛性进行了比较。
3.利用有限元软件ANSYS,研究了二维具有周期性连续屏障的隔振特性。验证了二维三组元组成的连续屏障隔振的可行性。
Periodic structures specially designed were found to enjoy the frequency gap within which the propagation of vibration is forbidden. Many important progresses in formation mechanism and calculation methods have been achieved in last decade. The characteristics of vibration propagation in periodic structures provide a new way to control the vibration in engineering field. As one of effective countermeasures to isolate vibration, wave barriers such as open and in-filled trenches or screens of piles are also intended to impede the transmission of vibrations in the soil. Combining the characteristics of vibration propagation of two, the calculation methods and theory of band gap in periodic structures are introduced to wave barriers with peroidity in this thesis. It can not only predict the frequency gap of wave barriers, but also design the band gap in order to gain a better vibration-isolation result. This thesis carries out a numerical analysis on wave barriers with peroidity. The contents include:
1. The vibration band gaps of wave barriers with peroidity consisting of different pattern and piles of various shapes are studied numerically by using improved plane wave expansion method (IPWE). Different physical and geometrical parameters such as density, elastic modulus, filling fraction also have been investigated.
2. The vibration band gaps of the two-dimensional three-component periodic structure are calculated by using the finite difference method (FDTD).At the same time, compare and contrast the convergence of the conventional plane expansion method (CPWE), IPWE method and FDTD method.
3. Using ANSYS, the screening effectiveness of the two-dimensional continuous barrier with periodity is numerically studied and prove the feasibility of vibration reduction due to the two-dimensional continuous barrier with periodity.
1.用改进平面波展开法对有周期结构特性的非连续屏障的带隙特性进行计算,讨论了不同空间排布、不同形状桩截面、不同排桩的布置形式对屏障带隙的影响。分析了不同物理参数(如桩材料密度、弹性模量)和几何参数(如填充系数)对第一带隙的影响。
2.用有限差分法计算二维三组元周期结构带隙,对传统平面波展开法、改进平面波展开法和有限差分法在二维三组元周期结构带隙的收敛性进行了比较。
3.利用有限元软件ANSYS,研究了二维具有周期性连续屏障的隔振特性。验证了二维三组元组成的连续屏障隔振的可行性。
Periodic structures specially designed were found to enjoy the frequency gap within which the propagation of vibration is forbidden. Many important progresses in formation mechanism and calculation methods have been achieved in last decade. The characteristics of vibration propagation in periodic structures provide a new way to control the vibration in engineering field. As one of effective countermeasures to isolate vibration, wave barriers such as open and in-filled trenches or screens of piles are also intended to impede the transmission of vibrations in the soil. Combining the characteristics of vibration propagation of two, the calculation methods and theory of band gap in periodic structures are introduced to wave barriers with peroidity in this thesis. It can not only predict the frequency gap of wave barriers, but also design the band gap in order to gain a better vibration-isolation result. This thesis carries out a numerical analysis on wave barriers with peroidity. The contents include:
1. The vibration band gaps of wave barriers with peroidity consisting of different pattern and piles of various shapes are studied numerically by using improved plane wave expansion method (IPWE). Different physical and geometrical parameters such as density, elastic modulus, filling fraction also have been investigated.
2. The vibration band gaps of the two-dimensional three-component periodic structure are calculated by using the finite difference method (FDTD).At the same time, compare and contrast the convergence of the conventional plane expansion method (CPWE), IPWE method and FDTD method.
3. Using ANSYS, the screening effectiveness of the two-dimensional continuous barrier with periodity is numerically studied and prove the feasibility of vibration reduction due to the two-dimensional continuous barrier with periodity.
引文
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[2]Liu ZY, Zhang XX, Mao Y, Zhu YY, Yang Z, Chan CT, et al. Locally resonant sonic materials[J]. Science.2000.289:1734-6.
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[5]Mead DJ, Parthan S. Free wave propagation in two-dimensional periodic plates[J].1979. 64(3):325-346
[6]Heckl MA. Coupled Waves on a periodically supported Timoshenko beam[J]. Journal of Sound and Vibration.2002.252(5):849-882
[7]Mangaraju V, Sonti VR. Wave attenuation in periodic three-layered beams:analytical and FEM study[J]. Journal of Sound and Vibration.2004.276:541-570.
[8]C Mei. Vibration suppression through tunable periodic structures[C]. Twelfth International Congress on Sound and Vibration.2005.
[9]Langley RS and Smith JRD. Statistical energy analysis of periodically stiffened damped plate structures[J]. Journal of Sound and Vibration.1997,208(3):407-526
[10]Richard D, Pines DJ. Passive reduction of gear mesh vibration using a periodic drive shaft[J]. Journal of Sound and Vibration.2003,264:317-342
[11]Diaz-de-Anda A, Pimentel A, Flores J, Morales A, Gutierrez L, and Mendez-sanchez RA. Locally periodic Timoshenko rod:experiment and theory.[J]. Journal of the Acoustical Society of America.2005,117(5):2814-2819
[12]Alakebanga TNT. Finite element and experimental analysis of wave propagation in periodic structures[D].The Catholic University of America,2003
[13]Jeong SM. Analysis of vibration of 2-D periodic cellular structures[D]. Georgia Institute of Technology,2005
[14]Yong Y and Lin YK. Propagation of decaying waves in periodic and piecewise periodic structures of finite length[J]. Journal of Sound and Vibration.1989,129(2):99-118
[15]Bondaryk JE. Vibration of truss structures [J]. Journal of the Acoustical Society of America.1997,102(4):2167-2175
[16]Langley RS. The response of two-dimensional periodic structures to point harmonic forcing[J].Journal of Sound and Vibration.1996,197(4):447-469
[17]温激鸿.声子晶体振动带隙及减振特性研究[D].长沙.国防科学技术大学.2005.
[18]郁殿龙.基于声子晶体理论的梁板类周期结构振动带隙特性研究[D].长沙.国防科学技术大学.2006.
[19]王刚.声子晶体局域共振带隙机理及减振特性研究[D].长沙.国防科学技术大学.2005
[20]李凤明,胡超,黄文虎.周期波导中弹性波局部化问题的研究[J].应用力学学报.2002.19(4)：47-51.
[21]Richart FE, Hall JR, Woods RD著,徐攸在等译.土与基础的振动[M].中国建筑工业出版社.1976
[22]Woods RD. Screening of surface waves in soil[J]. J Soil MechFoundation Eng (ASCE) 1968;94(SM4):951-79.
[23]Aboudi J. Elastic waves in half-space with thin barrier[J]. Journal of the Engineering Mechanics Division (ASCE) 1973;99(1):69-73.
[24]Lysmer J, Waas G. Shear wave in plane infinite structures[J]. Journal of the Engineering Mechanics Division (ASCE)1972,Vol 98, No,EMI:85-105
[25]Haupt WA. Surface waves in nonhomogeneous half-space[A]. In:Prange B, editor. Dynamic methods in soil and rock mechanics. Rotterdam:Balkema; 1981:335-67.
[26]Segol GP, Lee CY,Abel JF. Amplitude reduction of surface wave by Trenches[J]. Journal of the Engineering Mechanics Division(ASCE) 1978,104(3):621-41
[27]Banerjee PK, Ahmad S and Chen K. Advanced Application of BEM to Wave Barriers in multi-layered three-dimensional soil media
[28]Haupt WA. Isolation of vibration by concrete core walls[A]. Proceedings of 9th Conference on Soil Mechanics and Foundation Engineering.Tokyo.1977,Vol.2:251-256
[29]Haupt WA. Model Tests on Screening of Surface Waves[A]. Proceedings of 10th Conference on Soil Mechanics and Foundation Engineering.Tokyo.1981,Vol.3:215-222
[30]Leung KL, Vardoutakis IG, Beskos DE(1987). Vibration isolation of structures from surface waves in homogeneous and nonhomogeneous Soil. In:Cakmak AS. Soil-structure Interaction. Southampton:the Netherlands computational mechanics publications,1987:155-169
[31]钱菊生.屏障隔振的边界单元法分析及试验研究[D].杭州：浙江大学,1988.
[32]冯卫,边界元法研究基础振动及屏障隔振问题[D].杭州：浙江大学,1991.
[33]Liao S, Sangrey DA. Use of piles as isolation barriers[J]. Journal of Geotechnical Engineering Division(ASCE),1978.104(9):1139-1152.
[34]Aviles J, Sanchez-Sesma FJ. Piles as barriers for elastic waves[J]. Journal of Geotechnical Engineering Division(ASCE),1983,Vol.104, No GT9:1133-1146.
[35]Aviles J, Sanchez-Sesma FJ. Foundation isolation from vibration using piles as barriers[J]. Journal of Geotechnical Engineering Division(ASCE),1988, Vol.114, No EM11:1854-1870.
[36]Woods RD, Barnett NE, Sagesser R. Holography-a new tool for soil dynamics[J]. Journal of Geotechnical Engineering Division(ASCE),1974,Vol.100,No GT11L1234-1247.
[37]高广运.非连续性屏障隔振的理论分析和试验研究[D].长沙：湖南大学,1991
[38]杨先健,高广运,王贻荪等.排桩隔振的理论与应用[J].建筑结构学报,1997,4：58～69
[39]吴世明,吴建平.利用粉煤灰屏障隔振[A].：见第五届土力学及基础工程学术会议论文集[C].北京：中国土木工程学会,1990
[40]Pei-hsun Tsai, Zheng-yi Feng,Tin-lon Jen.Three-dimensional analysis of the screening e(?)ectiveness of hollow pile barriers for foundation-induced vertical vibration[J]. Computers and Geotechnics 35 (2008) 489-499.
[41]高广运,邱畅.屏障区振动放大一场现象的理论分析[J].岩土工程学报,2002,Vol.24,No3:565-568.
[42]高广运,邱畅.屏障系统失效机理的探讨[J].西北地震学报,2003,Vol.25,No3,198-203.
[43]邱畅,连续屏障和连续屏障远场被动隔振三维分析[D].上海：同济大学,2003
[44]Andrew T, Peplow, Amir M. Kayniab.Prediction and validation of traffic vibration reduction due to cement column stabilization[J]. Soil Dynamics and Earthquake Engineering 27 (2007) 793-802
[45]Dowling JP. Sonic band structure in fluids exhibiting periodic density variations[J].The Journal of the Acoustical Society of America,1992,91(5):2539-2543
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