臺灣博碩士論文加值系統

本論文主要探討分析彈性層狀土壤之波傳動力特性，首先利用理論矩陣法及有限元素法進行層狀土壤地表面受簡諧點負載之三維波傳現象進行模擬，以各種不同層數之層狀土壤為例，假設這些土層表面受水平或垂直向簡諧點負載作用，藉此兩種方法求解沿著波傳遞方向之穩態水平及垂直向位移分佈並探討對應之地表振動。然考量運算效率及節省計算機硬碟容量等因素，本文最後採用理論矩陣方法進行進一步之表面波振動特性模擬與分析，惟在分析前，特別先進行了過去鮮少作者曾探討之理論矩陣法及有限元素法精度比較，主要用意在確認兩方法之可靠性。藉由理論矩陣方法進行層狀土壤地表面波之振動特性尤其針對拉夫波運動時產生之不規則隆起行為，將於本文中作進一步說明。
其次，為驗證模擬結果，本文以高速鐵路為對象，針對其行駛時所引發的地表振動進行量測，分別選定鄰近南部科學園區北側邊界之典型層狀土壤以及台中后里之均質性土壤當作試驗工址，架設一系列儀器進行地表振動之現地量測，試驗結果顯示層狀土壤之低頻振波比高頻振波可傳播的更遠，且水平剪力波在層狀土壤傳播時將可能產生不規則隆起現象，此一隆起現象將成為建物或廠房安全之潛在威脅，亦是本文研究地表振動之主要課題，而均質土壤之量測結果相對並沒有產生明顯隆起現象。
延續以上分析，可預期另一個必要的課題是如何有效減低因各種外負載造成的地表振動，本文嘗試利用時間域有限元素法對三個座標軸方向進行裝水槽溝阻隔地表振動之效益分析,分析結果指出Y方向(水平垂直於車行之方向)之減振效能最差，尤其在低頻振動狀況。此外，數值模擬經與裝滿水槽溝之現地試驗結果作比較可發現，兩者結果有良好的一致性。
最後，我們的研究議題將探討地震波從土壤底層傳至地面後，產生地表振動對高速鐵路安全性之影響，由於台灣位於地震高風險區，本文遂針對高速列車行駛於路堤段之結構型態，發展了一套有限元素程式模組，以探討行駛中列車受地震力侵襲時之脫軌風險。從模擬結果可知，高速行駛列車與地震波的共振現象以及軌道不平整性，是影響行進中列車脫軌非常重要的因素。

This thesis investigates the dynamic characteristics of wave propagation in elastic layered soils. Both the theoretical matrix and finite element methods are employed to simulate the three-dimensional (3D) wave propagation in elastic layered soils with a harmonic point load acting on the surface. Using various multi-layer soils in which harmonic point loads act on the ground surface in the horizontal or vertical directions, these two methods are adopted to solve the steady state solutions of both horizontal and vertical displacement distributions along the direction of wave propagation.
In order to confirm the accuracy and reliability of the two assessment methods, it is necessary to compare their results, although few studies have undertaken this task. Moreover, in order to increase efficiency and reduce demands on the computer’s HD capacity, we utilize the theoretical matrix method to further investigate the vibration features of surface wave propagation, especially the irregular hump activity due to Love wave motion.
With regard to validating the simulation results, an experimental approach is carried out by measuring the ground vibration from a high speed train. Two typical locations represented the layered and homogeneous soils respectively are selected to perform the tests. A series of test devices were installed to undertake the in situ measurements and analyses of the vibrations induced by a high speed train. The results reveal that low frequency waves might propagate farther than high frequency ones. Besides, SH propagations in layered soils could possibly generate irregular ground vibrations, which may threaten the safety of buildings. However, such irregular vibration phenomena would not occur in homogeneous soils.
This study thus also considers how to reduce the ground vibration caused by various external loadings. In addition to a parametric study, a 3D time-domain finite element method is used to analyze the isolation efficiency of open trenches filled with different levels of water. The results indicate that the Y direction wave is difficult to reduce in the water trench, especially for low frequency waves. Meanwhile, field experiments with a full water trench are used to validate this finite element model, and the results show an acceptable level of agreement.
Finally, this thesis also considers the safety of high speed trains affected by the ground vibration due to seismic wave propagating in layered soils. Since Taiwan in located in a high risk earthquake zone, we developed a finite element model to simulate the derailment of trains moving on embankments under seismic loading. The results show that the rail irregularities and the resonance between the train and earthquake play an important role in train derailment.

摘 要(CHINESE ABSTRACT) I
ABSTRACT III
ACKNOWLEDGEMENTS V
CONTENTS VII
LIST OF TABLES XIII
LIST OF FIGURES XV
NOTATIONS XXI
Chapter 1 INTRODUCTION 1
1.1 Background 1
1.2 Objectives and scope of research 2
1.3 Organization of dissertation 5
Chapter 2 LITERATURE REVIEW 7
2.1 Introduction 7
2.2 Theoretical and numerical studies of wave propagation in layered mediums 8
2.3 Vibration measurements and effects analysis 10
2.4 The various isolation techniques for reducing vibrations 11
2.5 Approaches to estimate seismic hazard and related dynamic behavior for high speed train 12
Chapter 3 FINITE ELEMENT METHOD FOR WAVE PROPAGATION IN SOIL 15
3.1 Introduction 15
3.2 Three-dimensional isoparametric solid element 16
3.2.1 Isoparametric formulation 17
3.2.2 Illustration of element modeling and degenerating 24
3.2.2.1 The interpolation functions of a 3-9-node element 24
3.2.2.2 The interpolation functions of an 8-20-node element 26
3.3 Newmark’s method 31
3.4 Absorbing boundary conditions 34
3.5 The one third (1/3) octave band method and related criteria 39
Chapter 4 FUNDAMENTALS AND CHARACTERISTICS OF WAVE PROPAGATION IN LAYERED SOIL 45
4.1 Introduction 45
4.2 Modeling and derivation of simulation methods 45
4.2.1 Theoretical matrix method 46
4.2.2 Finite element method 49
4.3 Comparisons of simulations 50
4.4 Characteristics of uneven SH wave propagation in layered soil
56
4.4.1 Effects of homogeneous and layered soils 57
4.4.2 Effects of the layered soil thicknesses 59
4.5 Chapter summary 63
Chapter 5 EXPERIMENTAL INVESTIGATIONS OF TRAIN INDUCED WAVES IN LAYERED AND HOMOGENEOUS SOILS 65
5.1 Introduction 65
5.2 Description of geological conditions of test site 66
5.3 Interpretations of measuring instruments 70
5.4 Test procedures and equipment installation 74
5.5 Result of the vibration measurements 79
5.6 Analysis and Discussion of the measurement results 86
5.7 Chapter summary 93
Chapter 6 VIBRATION ISOLATION ANALYSES OF OPEN TRENCH BARRIERS FILLED WITH WATER 95
6.1 Introduction 95
6.2 Fluid-structure interaction finite element analysis 96
6.3 Validation using field experiments 97
6.3.1 Illustration of experiments 97
6.3.2 Finite element model and comparison 100
6.4 Parametric studies of open trenches filled with water 102
6.4.1 Changes in the efficiency of the water trenches with load frequencies 104
6.4.2 Efficiency of the water trenches filled with different water
levels 108
6.4.3 Changes in the efficiency of the water trenches with the trench width 111
6.5 Chapter summary 113
Chapter 7 DYNAMIC INTERACTION ANALYSIS OF TRAINS MOVING ON EMBANKMENTS DURING EARTHQUAKES
115
7.1 Introduction 115
7.2 Models of train, rail irregularities and derailment 116
7.2.1 Train model 116
7.2.2 Rail irregularities 118
7.2.3 Train derailment 119
7.3 Illustration of seismic loading and embankment dimensions 120
7.3.1 Illustration of earthquakes used in this study 120
7.3.2 Absorbing boundary conditions 123
7.3.3 Embankment dimensions and soil properties 123
7.4 Time-domain finite element model with the seismic loading 126
7.5 Investigation of train derailment 129
7.5.1 Train speed and rail irregularity effects 129
7.5.2 Earthquake effects 130
7.5.2.1 Derailment due to earthquake types and PGA 131
7.5.2.2 Derailment due to different train speeds under earthquake loading 136
7.5.3 Discussion of soil effects 137
7.6 Chapter summary 140
Chapter 8 CONCLUSIONS AND RECOMMENDATIONS 143
8.1 Conclusions 143
8.2 Recommendations for further research 147
REFERENCES 151
APPENDICES 163
ABOUT THE AUTHOR 167

REFERENCES
[1]H. Lamb, On the propagation of tremors over the surface of elastic solid, Philosophical Transactions of the Royal Society of London. Series A, 203 1-42 (1904)
[2]W.T. Thomson, Transmission of elastic waves through a stratified solid medium, J. Appl. Phys., 21 89-94 (1950)
[3]N.A. Haskell, The dispersion of surface waves on multilayered media, Bull. Seismol. Soc. Am., 43 17–34 (1953)
[4]N.M. Newmark, A Method of Computation for Structural Dynamics, Journal of the Engineering Mechanics Division ASCE, 85 (3) 67-94 (1959)
[5]J. Lysmer, R.L. Kuhlemeyer, Finite dynamic model for infinite media, Journal of the Engineering Mechanics Division, Proc. ASCE, 95 (EM4) 859-877 (1969)
[6]S.P. Timoshenko, J.N. Goodier, Theory of elasticity, McGraw-Hill, Inc., NY, 1970
[7]K.F. Graff, Wave motion in elastic solids, Oxford University Press, London, 1975
[8]D.A. Gasparini, E.H. Vanmarcke, Simulated earthquake motions compatible with prescribed response spectra. MIT civil engineering research report R76-4 (1976), Massachusetts Institute of Technology, Cambridge, MA.
[9]R.R. Kunar, L. Rodriguez-Ovejero, A model with non-reflecting boundaries for use in explicit soil—structure interaction analyses, Earthquake Engineering ＆ Structural Dynamics, 8 (4) 361–374 (1980)
[10]E. Kausel, J.M. Roësset, Stiffness matrices for layered soils, Bulletin of the Seismological Society of America, 71 1743–1761 (1981)
[11]K.J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Inc., NJ, 1982.
[12]R.G. Keys, Absorbing boundary conditions for acoustic media, Geophysics, 50 892–902 (1985)
[13]L.G. Olson, K.J. Bathe, Analysis of fluid-structure interactions. a direct symmetric coupled formulation based on the fluid velocity potential, Computers ＆ Structures, 21(1-2) 21-32 (1985)
[14]H. Schmidt and F.B. Jensen, Efficient numerical solution technique for wave propagation in horizontally stratified environments, Comp. ＆ Maths. with Appls. , 11 (7-8) 699-715 (1985)
[15]P.K. Banerjee, S. Ahmad, K. Chen, Advanced application of BEM to wave barriers in multi-layered three-dimensional soil media, Earthquake Engineering and Structural Dynamics, 16 1041-1060 (1988)
[16]B. Dasgupta, D.E. Beskos, I.G. Vardoulakis, Vibration isolation using open or infilled trenches part 2: 3-D homogeneous soil, Computational Mechanics, 6 129-142 (1990)
[17]C.G. Gordon, Generic Criteria for Vibration-Sensitive Equipment, Proceedings of International Society for Optical Engineering, 1619 ( 4-6) 71-85 (1991)
[18]R.L. Higdon, Absorbing boundary conditions for acoustic and elastic waves in stratified media, Journal of Computational Physics, 101 386–418 (1992)
[19]N. Gucunski, R. Peek, Vertical vibrations of circular flexible foundations on layered media, Soil Dynamics and Earthquake Engineering, 12 183-192 (1993)
[20]D.V. Jones, M. Petpt, Ground vibration in the vicinity of a rectangular load on a half-space, Journal of Sound and Vibration, 166 141-159 (1993)
[21]L. Auersch, Wave propagation in layered soil: theoretical solution in wavenumber domain and experimental results of hammer and railway traffic excitation, Journal of Sound and Vibration, 173 233-264 (1994)
[22]J. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, Journal of Computational Physics, 114 (2) 185–200 (1994)
[23]S. Ahmad, T.M. Al-Hussaini, K.L. Fishman, Investigation on active isolation of machine foundations by open trenches, Journal of Geotechnical Engineering, 122 454-461 (1996)
[24]T.M. Al-Hussaini, S. Ahmad, Active isolation of machine foundations by infilled trench barriers, Journal of Geotechnical Engineering, 122 288-294. (1996)
[25]S.L. Kramer, Geotechnical Earthquake Engineering, Prentice-Hall Publications, NJ , 1996.
[26]J.L. Buchanan, R.P. Gilbert, Transmission loss in the far field over a one-layer seabed assuming the Biot sediment model, ZAMM . Z. angew. Math. Mech., 77 (2) 121 – 135 (1997)
[27]R.P. Gilbert, Z. Lin, Acoustic field in a shallow, stratified ocean with a poro-elastic seabed, ZAMM, Z. angew. Math. Mech., 77 (9) 677-688 (1997)
[28]O. Hunaidi, M. Tremblay, Traffic-induced building vibrations in Montreal, Canadian Journal of Civil Engineering, 24 (5) 736-753 (1997)
[29]S.H. Ju, K.S. Kung, Mass types, element orders and solution schemes for the Richards equation, Comput. Geosci., 23 (2) 175-187 (1997)
[30]R. Klein, H. Antes, D. LeHouedec, Efficient 3D modelling of vibration isolation by open trenches, Computers ＆ Structures, 64 809-817 (1997)
[31]E. Pan, Static green’s functions in multilayered half spaces, Appl. Math. Model, 21 509-521 (1997)
[32]J.F. Semblat, Rheological interpretation of Rayleigh damping, Journal of Sound and Vibration, 206 (5) 741-744 (1997)
[33]D.V. Jones, D.Le Houedec, M. Petpt, Ground vibration due to a rectangular harmonic load, Journal of Sound and Vibration, 212 61-74 (1998)
[34]O.A. Obrezanova, V.S. Rabinovich, Acoustic field generated by moving sources in stratified waveguides, Wave Motion, 27 155-167 (1998)
[35]S.E. Kattis, D. Polyzos, D.E. Beskos, Vibration isolation by a row of piles using a 3-d frequency domain BEM, International Journal for Numerical Methods in Engineering, 46 713-728 (1999)
[36]A.T. Peplow, C.J.C. Jones, M. Petyt, Surface vibration propagation over a layered elastic half-space with an inclusion, Appl. Acoustic., 56 283-296 (1999)
[37]R. Chen, S. Xue, Z. Chen, J. Chen, The numerical solutions of green’s functions for transversely isotropic elastic strata, Appl. Math. Mech.-Engl., 21 49-58 (2000)
[38]C. Madshus, A.M. Kaynia. High-speed railway lines on soft ground: Dynamic behavior at critical train speed, Journal Sound Vibration, 231 (3) 689-701 (2000)
[39]J.F. Semblat, J.J. Brioist, Efficiency of higher order finite elements for the analysis of seismic wave propagation, Journal of Sound and Vibration, 231 (2) 460-467 (2000)
[40]A.K. Chopra, Dynamics of structures, Prentice-Hall, Inc., NJ, 2001
[41]H. Hao, T.C. Ang, J. Shen, Building vibration to traffic-induced ground motion, Building and Environment, 36 (3) 321–336 (2001)
[42]H.H. Hung, J. Kuo, Y.B. Yang, Reduction of train-induced vibrations on adjacent buildings, Structural Engineering and Mechanics, 11 503-518 (2001)
[43]S.H. Ju, Y.M. Wang, Time-dependent absorbing boundary conditions for elastic wave propagation, Int. J. Numer. Meth. Eng., 50 (9) 2159–2174 (2001)
[44]R.D. Cook, D.S. Malkus, M.E. Plesha, R.J. Witt, Concepts and applications of finite element analysis, John Wiley ＆Sons, Inc., NJ, 2002
[45]F. T. K. Au, J. J. Wang, Y. K. Cheung , Impact study of cable-stayed railway bridges with random rail irregularities, Engineering Structures, 24 (5) 529-541 (2002)
[46]E. Kausel, D. Assimaki, Seismic simulation of inelastic soils via frequency-dependent moduli and damping, Journal of Engineering Mechanics ASCE, 128 (1) 34-47 (2002)
[47]Adrianus T. de Hoop, The moving-load problem in soil dynamics—the vertical displacement approximation, Wave Motion, 36 335–346 (2002)
[48]R.K. Shrivastava, N.S.V. Kameswara Rao, Response of soil media due to impulse loads and isolation using trenches, Soil Dynamics and Earthquake Engineering, 22(8) 695-702 (2002)
[49]Y.B. Yang, Y.S. Wu, Dynamic stability of trains moving over bridges shaken by earthquakes, Journal of Sound and Vibration, 258 (1) 65-94 (2002)
[50]Evergreen Consulting Engineering, inc., Report on the vibration isolation efficiency using water trenches for Tainan industrial park, (In Chinese) (2003)
[51]G. Festa, S. Nielsen, PML absorbing boundaries, Bulletin of the Seismological Society of American, 93 (2) 891-903 (2003)
[52]L. Hall, Simulations and analyses of train-induced ground vibrations in finite models, Soil Dynamics and Earthquake Engineering, 23 403-413 (2003)
[53]X. Sheng, C.J.C. Jones, D.J. Thompson, A comparison of a theoretical model for quasi-statically and dynamically induced environmental vibration from trains with measurements, Journal of Sound and Vibration, 267 621–635 (2003)
[54]Y.B. Yang, H.H. Hung, D.W. Chang, Train-induced wave propagation in layered soils using finite/infinite element simulation, Soil Dynamics and Earthquake Engineering, 23(4) 263-278 (2003)
[55]Q. Gao, W. Zhong, W.P. Howson, A precise method for solving wave propagation problems in layered anisotropic media, Wave Motion, 40 191–207 (2004)
[56]H.H. Hung, Y.B. Yang, D.W. Chang, Wave barriers for reduction of train-induced vibrations in soils, J. Geotech. and Geoenvir. Engrg., 130 1283 (2004)
[57]S.H. Ju, 3D finite element analyses of wave barriers for reduction of train-induced vibrations, J. Geotech. Geoenviron., 130(7) 740-748 (2004)
[58]J. Novak and S. Bonazzola, Absorbing boundary conditions for simulation of gravitational waves with spectral methods in spherical coordinates, Journal of Computational Physics, 197(1) 186-196 (2004)
[59]Y.S. Wu, Y.B. Yang, A semi-analytical approach for analyzing ground vibrations caused by trains moving over elevated bridges, Soil Dynamics and Earthquake Engineering, 24 949-962 (2004)
[60]L. Auersch, The exciting of ground vibration by rail traffic: theory of vehicle-track-soil interaction and measurements on high-speed lines, Journal of Sound and Vibration, 284 103-132 (2005)
[61]D.M. Boore, J.J. Bommer, Processing of strong-motion accelerograms : needs, options and consequences, Soil Dynamics and Earthquake Engineering, 25 93-115 (2005)
[62]F.Q. Hu, A Perfectly Matched Layer absorbing boundary condition for linearized Euler equations with a non-uniform mean flow, Journal of Computational Physics, 208 469–492 (2005)
[63]X. Jun, Z. Qingyuan, A study on mechanical mechanism of train derailment and preventive measures for derailment, Vehicle System Dynamics, 43 (2) 121-147 (2005)
[64]X. Luo, Study on methodology for running safety assessment of trains in seismic design of railway structures, Soil Dynamics and Earthquake Engineering, 25 (2) 79-91 (2005)
[65]B. Picouxa, D. Le Houe´ddecb, Diagnosis and prediction of vibration from railway trains, Soil Dynamics and Earthquake Engineering, 25 905–921 (2005)
[66]H. Xia, N. Zhang, Y.M. Cao, Experimental study of traininduced vibrations of environments and buildings, Journal of Sound and Vibration, 280 (3–5) 1017–1029 (2005)
[67]L. Auersch, Ground vibration due to railway traffic—The calculation of the effects of moving static loads and their experimental verification, Journal of Sound and Vibration, 293 599–610 (2006)
[68]S. Iwnicki, Handbook of Railway Vehicle Dynamics, Taylor ＆ Francis Publications, NW, 2006
[69]S.H. Ju, H.T. Lin, Reduction of vibration due to foundation slabs, J. Geotech. Geoenviron., 132(4) 511-520 (2006)
[70]A. Karlstrom, A. Bostrom, An analytical model for train-induced ground vibrations from railways, Journal of Sound and Vibration, 292 221–241 (2006)
[71]X. Sheng, C.J.C. Jones, D.J. Thompson, Prediction of ground vibration from trains using the wave number finite and boundary element methods, Journal of Sound and Vibration, 293 575-586 (2006)
[72]H. Xia, Y. Han, N Zhang, W.W. Guo, Dynamic analysis of train-bridge system subjected to non-uniform seismic excitations, Earthquake Engineering ＆ Structure Dynamics, 35 1563-79 (2006)
[73]C. Comina, S. Foti, Surface wave tests for vibration mitigation studies, J. Geotech. and Geoenvir. Engrg., 133 1320 (2007)
[74]S.H. Ju, Finite element analysis of structure-borne vibration from high-speed train, Soil Dynamics and Earthquake Engineering, 27 259-273 (2007)
[75]S.H. Ju, H.T. Lin, Investigating vehicle dynamic response due to braking and acceleration, Journal of Sound and Vibration, 303 (1-2) 46-57 (2007)
[76]S.H. Ju, H.T. Lin, T.K. Chen, Studying characteristics of train-induced Ground Vibrations Adjacent to an elevated railway by field experiments, Journal of Geotechnical and Geoenvironmental Engineering ASCE, 133 (10) 1302–1307 (2007)
[77]S.H. Ju, S.H. Ni, Determining Rayleigh damping parameters of soils for finite element analysis, International Journal for Numerical and Analytical Methods in Geomechanics, 31(10) 1239-1255 (2007)
[78]A. Karlstrom, A. Bostrom, Efficiency of trenches along railways for trains moving at sub- or supersonic speeds, Soil Dynamics and Earthquake Engineering, 27(7) 625-641 (2007)
[79]R. Kumar, B. S. Hundal, Surface wave propagation in a fluid saturated incompressible porous half-space lying under two layers of different liquids, Earth Planets Space, 59 929–936 (2007)
[80]X.G. Wang, Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground, Appl. Math. Mech.-Engl., 28 1383–1396 (2007)
[81]Bin Xu, Jian-Fei Lu, Jian-Hua Wang, Dynamic response of an infinite beam overlying a layered poroelastic half-space to moving loads, Journal of Sound and Vibration, 306 91–110 (2007)
[82]J.D. Yau, L. Fryba, Response of suspended beams due to moving loads and vertical seismic ground excitations, Engineering Structures, 29 (12) 3255-3262 (2007)
[83]M. Eskandari-Ghadi, R.Y.S. Pak, A. Ardeshir-Behrestaghi, Transversely isotropic elastodynamic solution of a finite layer on an infinite subgrade under surface loads, Soil Dynamics and Earthquake Engineering, 28 986-1003 (2008)
[84]S.H. Ju, H.T. Lin, Experimentally investigating finite element accuracy for ground vibrations induced by high-speed trains, Engineering Structures, 30 733–746 (2008)
[85]K.C. Meza-Fajardo, A.S. Papageorgiou, A nonconvolutional, split-field, perfevtly matched layer for wave propagation in isotropic and anisotropic elastic media: stability analysis, Bull. Seismol. Soc. Am., 98 1811-1836 (2008)
[86]M. Tanabe, N. Matsumoto, H. Wakui, M. Sogabe, H. Okuda,Y. Tanabe, A simple and efficient numerical method for dynamic interaction analysis of a high-speed train and railway structure during an earthquake, Journal of Computational and Nonlinear Dynamics, Transactions of the ASME, 3 (4) 041002 (8 pages) (2008)
[87]N. Bouaanani, F.Y. Lu, Assessment of potential-based fluid finite elements for seismic analysis of dam–reservoir systems, Computers ＆ Structures, 87(3-4) 206-224 (2009)
[88]N. Delepine, L. Lenti, G. Bonnet, J.F. Semblat, Nonlinear viscoelastic wave propagation : an extension of Nearly Constant Attenuation (NCQ) models, Journal of Engineering Mechanics ASCE, 135 (11) 1305-1314 (2009)
[89]L. Driad-Lebenu, N. Lokmane, J.F. Semblat, G. Bonnet, Local amplification of deep mining induced vibrations Part 1: Experimental evidence for site effects in a coal basin, Soil Dynamics and Earthquake Engineering, 29 (1) 39-50 (2009)
[90]L. Fryba, J.D. Yau, Suspended bridges subjected to moving loads and support motions due to earthquake, Journal of Sound and Vibration, 319 (1-2) 218-227 (2009)
[91]S.H. Ju, H.T. Lin, J.Y. Huang, Dominant frequencies of train-induced vibrations, Journal of Sound and Vibration, 319 247–259 (2009)
[92]L. Sun, W. Gu, F. Luo, Steady-State Wave Propagation in Multilayered Viscoelastic Media Excited by a Moving Dynamic Distributed Load, J. Appl. Mech., 78 041001-15 (2009)
[93]J.G. Wang, W. Sun, S. Anand, Numerical investigation on active isolation of ground shock by soft porous layers, Journal of Sound and Vibration, 321(3-5) 492-509 (2009)
[94]M. Q. Xu, L. H. Jian, J. H. Li, B. Xu, J.F. Lu, Dynamic responses of a layered saturated soil subjected to harmonic horizontal loads, Rock Soil Mech., 30 2633-2642 (2009)
[95]Y.M. Cao, H. Xia, G. Lombaert, Solution of moving-load-induced soil vibrations based on the Betti–Rayleigh Dynamic Reciprocal Theorem, Soil Dynamics and Earthquake Engineering, 30 470–480 (2010)
[96]S. Gupta, A. Chattopadhyay, S. Kundu, A. K. Gupta, Effect of rigid boundary on the propagation of torsional waves in a homogeneous layer over a heterogeneous half-space, Arch Appl. Mech., 80 143–150 (2010)
[97]S.H. Ju, J.R. Liao, Y.L. Ye, Behavior of ground vibrations induced by trains moving on embankments with rail roughness, Soil Dynamics and Earthquake Engineering, 30 (11) 1237–1249 (2010)
[98]N. Lantos, F. Nataf, Perfectly Matched Layers for the heat and advection-diffusion equations, C. R. Math. Acad. Sci. Paris, 348 (13-14) 781-785 (2010)
[99]T.C.T. Ting, Existence of anti-plane shear surface waves in anisotropic elastic half-space with depth-dependent material properties, Wave Motion, 47 350–357 (2010)
[100]R. Chattaraj, S.K. Samal, N.C. Mahanti, Propagation of torsional surface wave in anisotropic poroelastic medium, Wave Motion, 48 184–195 (2011)
[101]S.H. Ju, H.C. Li, 3D Analyses of open trench barriers filled with water, J Geotech. Geoenviron., ASCE, 137 (11) 1114-1120 (2011)
[102]G. Kouroussis, O. Verlinden, C. Conti, Finite-Dynamic Model for Infinite Media: Corrected Solution of Viscous Boundary Efficiency, J. Eng. Mech. ASCE, 137(7) 509-511 (2011)
[103]E.N. Rovithis, H. Parashakis, G. E. Mylonakis , 1D harmonic response of layered inhomogeneous soil: Analytical investigation, Soil Dynamics and Earthquake Engineering, 31 879–890 (2011)
[104]T.C.T. Ting, Surface waves in an exponentially graded, general anisotropic elastic material under the influence of gravity, Wave Motion, 48 335-344 (2011)
[105]F. Wuttke, P.Dineva, T.Schanz, Seismic wave propagation in laterally inhomogeneous geological region via a new hybrid approach, Journal of Sound and Vibration, 330 664–684 (2011)