基于分数导数粘弹性理论的车辆—路面作用研究
|
摘要
公路交通车辆正在向大型、重型化发展,在路面力学分析中继续沿用静载受力模式已不能反映路面的实际受力状况,也无法解释随机动态荷载作用下路面结构产生的各种现象。因此,必须对车辆—路面耦合系统相互动力作用机理进行深入研究。本文在国内外相关研究成果的基础上,以沥青路面为研究对象,基于分数阶导数粘弹性理论,分析了车辆—路面耦合系统相互动力作用。完成的主要工作和取得成果如下:
(1)利用沥青混合料基本性能试验仪(SPT)对AC-13、AC-20、AC-25三种沥青混合料进行动态模量试验研究,基于分数阶导数粘弹性理论,建立了沥青混合料的分数阶导数型粘弹性模型。结果表明,沥青混合料分数阶导数三元件模型能够精确地描述宽温、宽频率范围内的沥青混合料粘弹性动态力学行为,且确定模型的实验参数少,得到的拟合参数具有一定的物理意义,模型的导数阶次α一般在0.40～0.50之间。
(2)针对分数阶导数型粘弹性结构的动力响应问题,本文基于精细时程积分法,提出了一种基于分数阶导数型本构关系的粘弹性结构动力响应的数值计算方法。按该方法计算的结果与解析法及Zhang-Shimizu算法的结果相吻合,并具有很好的收敛性,且计算步长越小计算结果的精度越好。
(3)针对本文所建立的沥青混合料分数阶导数三元件模型的有限元格式化问题,通过分析分数阶导数三元件模型理论,将分数阶导数三元件模型引入到有限元模型中,推导出了基于分数阶导数三元件本构关系的粘弹性结构动力学的有限元方程。
(4)根据柔性路面多层粘弹性体系假设,建立了路基路面结构的二维有限元模型,并引入车辆-路面接触处的几何耦合关系和力学耦合关系,推导出车辆-路面耦合系统的分数阶动力学方程,并转化为状态方程。
(5)本文利用所提出的数值算法,编制了车辆-路面耦合系统响应分析的程序,引入B级路面随机激励,对在随机路面激励下的车辆和路基路面的动态响应进行计算,并分析了车辆载重、车速和路面不平整度等因素对路基路面的的动态粘弹性响应的影响。分析表明,随机动载荷的大小随车速、载重和路面不平整度的变化而变化。其中,路面不平整度起决定性作用。随机动载对路基路面结构的影响较大,故需要严格限制超载和超速现象,同时应重视路面质量和加强路面的养护。
As the traffic vehicles on the highway become larger and heavier, the static load model can not represent the actual state of pressure on the road surface any more. The static load model is unable to explain various phenomena in the road surface structure under the random dynamic load as well. Therefore, it is essential to study the dynamic interaction mechanism in the vehicle and road surface coupling system. Based on the relevant research results in China and abroad, this dissertation is to study the asphalt road surface and to analyze the dynamic interaction of vehicle-road coupling system by applying the viscoelastic property theory with the fractional order derivative. The following research works have been accomplished and the relevant results achieved.
(1)An asphalt mixture testing instrument SPT is used to test the dynamic modulus of three types of asphalt mixtures named AC-13, AC-20 and AC-25. A viscoelastic property model of fractional order derivative for the asphalt mixtures is established based on the viscoelastic property theory of fractional order derivative. The result shows that the three-element model of fractional order derivative can precisely describe the dynamic behavior of viscoelastic asphalt mixtures at a wide range of temperature and frequency. Only a few experiment parameters are required to confirm the model and the fitting parameters obtained have some physical meanings. Generally the derivative orderαof the model is between 0.4 and 0.5.
(2)As the dynamic response of viscoelastic structure of fractional order derivative is concerned, a numerical calculating method for the constitutive relation of fractional order derivative is proposed on the basis of precise time integral method. The calculated result coincides with the results by analytic method and Zhang-Shimizu algorithm. The calculating method is of good convergence and the smaller the counting step, the more precise is the result.
(3)As for FE format of the three-element-model of fractional order derivative for the asphalt mixture, the three-element-model of fractional order derivative is applied to the FE model. The finite element equation of viscoelastic structure dynamics is derived based on the three-element constitutive relation of fractional order derivative.
(4)A two-dimension FEM of road base and road surface is established with the hypothesis of multi-level viscoelastic system of flexible pavement. The geometry and dynamics coupling relations are introduced to the joint of vehicle and road surface. The fractional dynamics equation of vehicle-road surface coupling system is drawn out and then transformed into status equation.
(5)A response analysis program for the vehicle and road surface coupling system is developed by applying the numerical algorithm proposed above. The random excitation of class B pavement is used to calculate the dynamic response of the vehicle, the road base and the road surface. Furthermore, the effects of vehicle load, speed and road roughness on the dynamic viscoelastic response of road are analyzed. Analysis shows that the random dynamic load varies with the speed, the load and the road roughness and the road roughness plays a crucial role. Since the random dynamic load has a great effect on the structure of road base and road surface, it is necessary to limit strictly the overloading and overspeeding on the road, to pay attention to the quality of the pavement and to strengthen the maintenance.
(1)利用沥青混合料基本性能试验仪(SPT)对AC-13、AC-20、AC-25三种沥青混合料进行动态模量试验研究,基于分数阶导数粘弹性理论,建立了沥青混合料的分数阶导数型粘弹性模型。结果表明,沥青混合料分数阶导数三元件模型能够精确地描述宽温、宽频率范围内的沥青混合料粘弹性动态力学行为,且确定模型的实验参数少,得到的拟合参数具有一定的物理意义,模型的导数阶次α一般在0.40～0.50之间。
(2)针对分数阶导数型粘弹性结构的动力响应问题,本文基于精细时程积分法,提出了一种基于分数阶导数型本构关系的粘弹性结构动力响应的数值计算方法。按该方法计算的结果与解析法及Zhang-Shimizu算法的结果相吻合,并具有很好的收敛性,且计算步长越小计算结果的精度越好。
(3)针对本文所建立的沥青混合料分数阶导数三元件模型的有限元格式化问题,通过分析分数阶导数三元件模型理论,将分数阶导数三元件模型引入到有限元模型中,推导出了基于分数阶导数三元件本构关系的粘弹性结构动力学的有限元方程。
(4)根据柔性路面多层粘弹性体系假设,建立了路基路面结构的二维有限元模型,并引入车辆-路面接触处的几何耦合关系和力学耦合关系,推导出车辆-路面耦合系统的分数阶动力学方程,并转化为状态方程。
(5)本文利用所提出的数值算法,编制了车辆-路面耦合系统响应分析的程序,引入B级路面随机激励,对在随机路面激励下的车辆和路基路面的动态响应进行计算,并分析了车辆载重、车速和路面不平整度等因素对路基路面的的动态粘弹性响应的影响。分析表明,随机动载荷的大小随车速、载重和路面不平整度的变化而变化。其中,路面不平整度起决定性作用。随机动载对路基路面结构的影响较大,故需要严格限制超载和超速现象,同时应重视路面质量和加强路面的养护。
As the traffic vehicles on the highway become larger and heavier, the static load model can not represent the actual state of pressure on the road surface any more. The static load model is unable to explain various phenomena in the road surface structure under the random dynamic load as well. Therefore, it is essential to study the dynamic interaction mechanism in the vehicle and road surface coupling system. Based on the relevant research results in China and abroad, this dissertation is to study the asphalt road surface and to analyze the dynamic interaction of vehicle-road coupling system by applying the viscoelastic property theory with the fractional order derivative. The following research works have been accomplished and the relevant results achieved.
(1)An asphalt mixture testing instrument SPT is used to test the dynamic modulus of three types of asphalt mixtures named AC-13, AC-20 and AC-25. A viscoelastic property model of fractional order derivative for the asphalt mixtures is established based on the viscoelastic property theory of fractional order derivative. The result shows that the three-element model of fractional order derivative can precisely describe the dynamic behavior of viscoelastic asphalt mixtures at a wide range of temperature and frequency. Only a few experiment parameters are required to confirm the model and the fitting parameters obtained have some physical meanings. Generally the derivative orderαof the model is between 0.4 and 0.5.
(2)As the dynamic response of viscoelastic structure of fractional order derivative is concerned, a numerical calculating method for the constitutive relation of fractional order derivative is proposed on the basis of precise time integral method. The calculated result coincides with the results by analytic method and Zhang-Shimizu algorithm. The calculating method is of good convergence and the smaller the counting step, the more precise is the result.
(3)As for FE format of the three-element-model of fractional order derivative for the asphalt mixture, the three-element-model of fractional order derivative is applied to the FE model. The finite element equation of viscoelastic structure dynamics is derived based on the three-element constitutive relation of fractional order derivative.
(4)A two-dimension FEM of road base and road surface is established with the hypothesis of multi-level viscoelastic system of flexible pavement. The geometry and dynamics coupling relations are introduced to the joint of vehicle and road surface. The fractional dynamics equation of vehicle-road surface coupling system is drawn out and then transformed into status equation.
(5)A response analysis program for the vehicle and road surface coupling system is developed by applying the numerical algorithm proposed above. The random excitation of class B pavement is used to calculate the dynamic response of the vehicle, the road base and the road surface. Furthermore, the effects of vehicle load, speed and road roughness on the dynamic viscoelastic response of road are analyzed. Analysis shows that the random dynamic load varies with the speed, the load and the road roughness and the road roughness plays a crucial role. Since the random dynamic load has a great effect on the structure of road base and road surface, it is necessary to limit strictly the overloading and overspeeding on the road, to pay attention to the quality of the pavement and to strengthen the maintenance.
引文
[1]沈金安,李福普,陈景.高速公路沥青路面早期损坏分析与防治对策[M].北京:人民交通出版社,2004.
[2]邓学钧,孙璐.车辆-地面结构系统动力学[M].北京:人民交通出版社,2000.
[3]龙晋闽.车辆对路面作用的动载荷研究[D].西安:长安大学,2006.
[4] D.Cebon. Vehicle-Generated Road Damage:A Review. Vehicle System Dynamics.1989,18:107-150
[5] D.J.Cole. Assessing the Road-damaging Potential of Heavy Vehicles. Proc Instn Mech Engrs.1991,205(D):223-232.
[6] T.E .C .Potter,D .Cebon and D .J .Cole. Assessing 'Road-friendliness':a Review . Proc Instn Mech Engrs.1997,211(D):455-473.
[7] T.E .C .Potter,D .Cebon and D .J .Cole.An Investigation of Road Damage Due to Measured Dynamic Tyre Forces. Proc Instn Mech Engrs.1995,209(D):9-24.
[8] T.E .C .Potter,D .Cebon,A .C .Collop and D .J .Cole. Road-Damaging Potential of Measured Dynamic Tyre Forces in Mixed Traffic. Proc Instn Mech Engrs.1996,210(D):215-225.
[9] G.K .Misoi,R .M .Carson.Corrugation of Unmetalled Roads,Part1:Vehicle Dynamics. Proc Instn Mech Engrs.1989,203(D):205-214.
[10] D.J.Cole,A .C .Collop and T.E .C .Potter.Spatial Repeatability of Measured Dynamic Tyre Forces.Proc Instn Mech Engrs.1996,210(D): 185-197.
[11] D .Cebon .Interaction between heavy vehicles and roads.SAE SP-951,1993.
[12]国家自然科学基金委员会编.力学[R].北京:科学出版社,1997.
[13]朱孔源.车辆与柔性路面力学相互作用系统的研究[D].北京:中国农业大学,2001.
[14]华南理工大学道路研究所.沥青混合料动态模量参数研究[R].广州:华南理工大学.2007.
[15]田晓霞.基于SPT的沥青混合料高温性能的试验研究[D].南京:东南大学,2007.
[16] ASTM D3497-79. Standard Test method for Dynamic Modulus of Asphalt Mixtures. 1995.
[17] AASHTO Designation:TP62-03. Standard Method of Test For Determining Dynamic Modulus of Hot-Mix Asphalt Concrete Mixtures. 2003.
[18] NCHRP 9-19. Superpave Support and Performance models Management. Field Validation of the Simple Performance Test. 2001 .
[19] NCHRP 9-29. Simple Performance Tester for Superpave Mix Design. Equipment Specification for the Simple Performance Test System. Advanced Asphalt Technologies,LLC,2004.
[20] Harold L. Von Qunitus, J. Brent Rauhut, and Thomas W. Kennedy, Comparisons of Asphalt concrete Stiffness as Measured by Various Testing Techniques. Proceedings of the Association of Asphalt Paving Technologists,Vol 51,1982.
[21] Herbert F. Southgate. Effects of Construction Variations upon Dynamic Modulus of Asphalt Concrete. AAPT,Vol 51,1982 .
[22] J. F. Shook and B. F. Kallas. Factors Influencing Dynamic Modulus of Asphalt Concrete. AAPT, Vol 38, 1969.
[23] W. Heukelom and A. J. G. Klomp. Road Design and Dynamic Loading. AAPT,Vol 33,1964 .
[24] W. Heukelom and A. J. G. Klomp. Dynamic Testing as a Means of Controlling Paving During and After Construction. Proceeding of the First International Conference on Structural Design of Asphalt Pavement, University of Michigen,1962.
[25] National Cooperative Highway Research Program 1-37A. Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures. ARA,Inc,2004.
[26]高英.基于动态参数的沥青路面设计方法研究[D].上海:同济大学,1999.
[27]许志鸿等.沥青混合料动态性能参数标准研究报告[R].交通部部级科技项目.同济大学,2000.
[28]丰晓.沥青混合料动态性能及疲劳特性分析[D].上海:同济大学,1997.
[29]黎霞,田小革.用动蠕变试验确定沥青混凝土动态粘弹性参数[J].国外公路,2002,20(1):46-48.
[30]许志鸿,李淑明,高英等.沥青混合料动态性能研究[J].同济大学学报,2001,29(8): 893-897.
[31]许志鸿,丰晓,高英等.沥青混合料动态性能影响因素的研究[J].建筑材料学报,2001,4(3):238-243.
[32]杨屹东.沥青路面结构动态模里试验研究[J].公路,2002,2:25-27.
[33]曾梦澜,黄欣哲.沥青结合料与混合料动力性质的关系[J].中南公路工程,2003,28(4):11-14.
[34]孙略伦.聚酷纤维沥青混凝土动态模量的试验研究[D].大连:大连海事大学,2006 .
[35]羊明.沥青混合料动态模量研究[D].长沙:长沙理工大学,2007 .
[36]方萍(译),汪宏(校).沥青混合料的线性粘弹性特性模型[J].国外公路,1998,18(4):46-50.
[37]郑健龙,田小革,应荣华.沥青混合料热粘弹性本构模型的实验研究[J].长沙理工大学学报(自然科学版),2004,1(1):1-7.
[38] Monismith C.L,Secor K. E. Viscoelastic behavior of asphalt concrete Pavements[C]Proceedings of International Conference on Structure Design of Asphalt Pavements, 1962,10:476-498
[39] Krishnan J. M, Rajagopal K. R. on the mechanic behavior of asphalt[J].Mechanics of Materials, 2005,37(11):1085-1100.
[40]徐世法.表征沥青及沥青混合料高低温性能的流变模型[J].北京建筑工程学院学报,1991,14(1):57-65.
[41] Szydlo A,Maekiewicz P. AsPhalt mixes deformation sensitivity to change in rheological Parameters[J].Journal of Materials in Civil Engineering,2005,(2):l-9.
[42] Abbas A.R,Papagiannakis,Masad E. A. Linear and nonlinear viscoelastic analysis of The Microstructure of asphalt Concretes[J].Journal of Materials in Civil Engineering,2004,133-139.
[43] Vlachovicova Z,et al. CreeP characteristies of asphalt modified by radial styrene-butadiene-styrene coPolymer[J].Construetion and BuildingMaterials,2007,21(3):567-577.
[44] W. Zhang,A. Dreseher,D. E. Neweomb. Viseoelastic Analysis of Diametral Compression of Asphalt Conerete.Journal of Engineering Mechanies,1997,123(6):596-603.
[45] W.Zhang,A.Dreseher,D.E.Neweomb.Viseoelastic Behavior of Asphalt Conerete in DiametralCompression. Journal of Transportation Engineering,1997,123(6):495-502.
[46] Lee H J,Kim Y R. Viscoelastic constitutive model for asphalt conerete under cyclic loading[J].Journal of Engineering Mechanics,1998,(1):32-40.
[47] Antoni Szydlo,Piotr Mackiewicz. AsPhalt Mixes Deformation Sensitivity to Change in Rheological Parameters,2005,February,1-9.
[48] Tashman L,Masad E,et al. A microstructure-based viscoplastic model for asphalt conerete[J].Intemational Joumal of Plastieity,2005,21:1659-1685.
[49] Lu Y,Wright P J. Numerical approach of viscoelastoPlastic analysis for asphalt mixtures[J].ComP Struct,1998,69:139-147.
[50] Erkens S M J G Liu X,Scarps A.3D finite model for asphalt conerete responsesimulation[J].Int J Geomeeh,2002,2(3):305-330.
[51] Blab R,Harvey J T Modeling measured 3D tire contact stress in a viseoelastoc FE Pavement model[J].Int J Geomeeh,2002,2(3):271-290.
[52] Krishnan J. M and Rajagopal K. R. Thermodynamic Framework for the Constitutive Modeling of Asphalt Concrete:Theory and Applications,J.Mat. Civil Eng,2004,16(2):155-166.
[53]郑建龙.Burgers粘弹性模型在沥青混合料疲劳特性分析中的应用[J].长沙交通学院学报,1995,11(3):32-42.
[54]郑健龙,应荣华,张起森.沥青混合料热粘弹性断裂参数研究[J].中国公路学报,1996,9(3):20-28.
[55]郑健龙,吕松涛,田小革.沥青混合料年弹性参数及其应用[J].郑州大学学报(工学版),2004,25(4):8-12.
[56]郑健龙,周志刚,应荣华.沥青路面温度应力数值分析[J].长沙交通学院学报,2001,17(1):29-32.
[57]钟志海.沥青硅的粘弹性及其参数的确定方法[J].公路与汽车,2005,(4):39-41.
[58]封基良,黄晓明.沥青粘结料粘弹性参数确定方法的研究.2006,23(5):16-22.
[59]钱国平,郭忠印,郑健龙等.环境条件下沥青路面热粘弹性温度应力计算[J].同济大学学报,2003,31(2):150-55.
[60]李一鸣.沥青混合料的松弛劲度模量[J].石油沥青,1995,(1):17-22.
[61]延西利,扈惠敏,张登良.沥青混合料线性流变模型的数值模拟[J1.西安公路交通大学学报,1999,19(1):7-12.
[62]黄卫东,吕伟民.沥青及沥青混合料流变性质与动稳定度的关系[J].同济大学学报2000,28(4):501-504.
[63]邵腊庚,周晓青,李宇峙等.基于直接拉伸试验的沥青混合料粘弹性损伤特性研究[J].土木工程学报,2005,38(4):125-128.
[64]周志刚,钱国平,郑健龙.沥青混合料粘弹性参数测定方法的研究[J].长沙交通学院学报,2001,17(4):23-28.
[65]吕松涛,田小革,郑健龙.沥青混合料粘弹性参数的测定及其在本构模型中的应用[J].长沙交通学院学报,2005,21(1):37-42.
[66]侯金成.纤维沥青混凝土粘弹性能研究[D].大连:大连海事大学,2007.
[67]王随原,周进川. SBS改性氯气混合料蠕变性能试验研究[J].公路交通科技,2006,23(12)10-13.
[68] R.Hilfer Appliacations of Fractional Calculus in Physics[M].World Scientific Press Singapore 2000
[69] K.S. Miller and B. Ross. An Introduction to the Fractional Calculus and Fractional Differential Equations[M].Jphn Wiley&Sons Inc New York,1993.
[70] S.G.Samko,A.A.Kolbas and O.I.Marichev Fractional Integrals and Derivatives:Theory and Applications[M].Gordon and Breach,New York,1993.
[71] H.M.Srivastava and R.K.Saxena,Operators of fractional integration and their applications[J]Appl. Math. Comp,2001,118:15-23.
[72] Nutting. P.G. A new generalized law of deformation. J. Franklin Institute.1921,191:694-685.
[73] Gemant A. on fractional Differences. Phil.Mag.1938,25:92-96.
[74] Rabotnov Y.N. Papernik L.K.H. Zvonov E.N. Tables of the Fractional Exponential Funtion of Negative Parameters and Its Integral,Moscow:Nauka,1969.
[75] Rabotnov Y.N. Element of Hereditary Solids,Mir Publishers,1980.
[76] Bagley R.L. Torvik P.J. A theoretical basis for the application of fractional calculus to viscoelasticity. J.Rheol,1983,27(3):201-210.
[77] Bagley R.L. Power law and fractional calculus model of viscoelasticity.AIAA J,1989,27(10):1412-1417.
[78] Bagley R.L. Torvik P.J. on the fractional calculus model of viscoelasticity Behavior. J.Rheol, 1986,30(1):133-155.
[79] Drozdov A,Kalamkarov A.L. Constituve model for nonlinear viscoelastic behavior of Polymer. Polymer Engrg&Sci,1996:36(14):1907-1919.
[80] Makris N. Three-dimensional constitutive viscoelastic law with fractional order time derivatives. J.Rheol,1997,41(5):1007-1020.
[81] Koeller R.C. Applications of Fractional calculus to the Theory of Viscoelasticity Transacions of the ASME J Applied Mechanics 1984,51:294-298.
[82] Li J,Jiang T.Q. Constitutive Equation for Viscoelastic Fluids via Fractional Derivative in Advances in Structure and Heterogen Continua New York: Allerton Press Inc, 1994: 187-193
[83] Song D. Y,Jiang T.Q.Study on the constitutive equation with fractional derivative for viscoelastic fluids-modified Jeffreys model and its application Rheol Acta,1998,37:512-517.
[84] Wei Zhang,Nobuyuki Shimizu and Hua xu.Thermal effects of the viscoelastic materials described by fractional calculus constitutive lawThe First Asian conference on Multibody dynamics. 2002 July31-August2 2002,I waki,Fukusbima,Japan.
[85] Wei Zhang and Nobuyuki Shimizu ,Damping properties of the viscoelastic material prescribed by fractional Kelvin-voigt model.JSME International Journal.Series C,1999,42(1):1-9.
[86]朱正佑,李根国.具有分数导数本构关系的Timoshenko梁的静动力学行为分析应用数学和力学2002,23(1):
[87]张为民.一种采用分数阶导数的新流变模型理论[J].湘潭大学自然科学学报,2001, 23(1): 30-36.
[88]张为民,张淳源,张平.考虑老化的混凝土粘弹性分数导数模型[J].应用力学学学报,2004, 21(1): 1-4.
[89]孙海忠,张卫.分数算子描述的粘弹性材料的本构关系研究[J].材料科学与工程学报,2006, 24(6): 926-929.
[90]刘林超.分数导数型粘弹性材料的力学行为及在结构减振中的应用研究[D].广州:暨南大学,2005.
[91]夏禾.车辆与结构动力相互作用[M].北京:科学出版社,2002.
[92] Cebon D . Interaction Between Heavy Vehicles and Roads SAE 930001(SEA/SP-93/951)(The T hirty-ninth Ray Buckendale Lecture)
[93] Potter T .E .C,Cebon D and Cole D .J . Assessing‘Road-friendliness’:a review.Proc. Instn Mech.Engrs. 1997,211(D4):455-475.
[94] Mahoney Joe P .The relationship between axle configuration,wheel loads and pavement structure s. SAE 88184.
[95]余卓平,黄锡朋,张洪欣.公路车辆对道路损伤计算方法的研究[J].同济大学学报,1993,21(增刊):115-124.
[96]余卓平,黄锡朋,张洪欣.减轻重型汽车对道路的损伤一汽车悬架优化设计[J].中国公路学报,1994,7(3):83-87.
[97] D.Cebon.Theoretical Road Damage Duo to Dynamic Tyre Forces of Heavy Vehicles Part2:Simulated Damage Caused by a Tandem-Axle Vehiele.Proc Instn Mech Engrs.1988,202(C2): 109-117.
[98]任卫群.公路车辆对道路破坏的数字仿真研究[D].武汉:华中科技大学,2003.
[99] S.Drosner.Beitrag zur.Berechnung der dynamischen Beanspruchung von Brucken unter Verkehrslasten,PhD thesis,Stahlbau RWTH Aachen ,Aachen ,Germany,1989.
[100] H.E.M.Hunt.Modelling of Road Vehieles for Calculation of Traffic-Indueed Ground Vibrations. JOumal of Sound and Vibration,1991,144(1):41-51.
[101] H.E.M. Hunt. Stochastic Modelling of Traffic-lndueed Ground Vibration.Journal of Sound and Vibration. 1991,144(1):53-70.
[102]成祥生.弹性地基板由运动载荷引起的动力反应[J].应用数学的力学,1987,3(4):347-355.
[103]钟阳,王哲人,张肖宁.不平整路面上行驶的车辆对路面随机动压力的分析[J].中国公路学报,1992,5(2):40-44.
[104]黄晓明.路面动荷载与路面平整度关系的随机分析[J].东南大学学报,1993,23(1):56-61.
[105]杨方廷.路面对车辆载荷的动态响应的研究[D].北京:中国农业大学,1996.
[106]孙璐,邓学钧.速度与车辆动态特性对于车路相互作用的影响[J].土木工程学报,1997,30(6):34-40.
[107]李怀璋.车辆-路面系统中的动载、车辙和合理轴限的研究[D].北京:中国农业大学,1999.
[108]郑泉,杨方廷.车轮随机动载与路面及车速相互关系的研究[J].合肥工业大学学报(自然科学版),2001,24(1):139-142.
[109]邓学钧.车辆一地面结构系统动力学研究[J].东南大学学报,2002,32(3):474-479.
[110]陶向华,黄晓明.车辆动载荷的频域模拟计算与分析[J].华中科技大学学报(城市科学版),2003,20(4):47-50.
[111]张军.重型车辆与刚性路面结构的动力相互作用理论分析和试验研究[D].长沙:湖南大学,2003.
[112]陶向华.路桥过渡段差异沉降控制标准与人车路相互作用[D].南京:东南大学,2006.
[113]王暄.随机荷载作用下柔性路面结构及路基动力响应研究[D].长沙:中南大学,2006.
[114]赵延庆,吴剑,文健.沥青混合料动态模量及主曲线的确定与分析[J].公路,2006,(8):163-167.
[115]李德超.沥青混合料动态模量试验研究[J].公路,2008,(1):134-140.
[116]张义同.热粘弹性理论[M].天津:天津大学出版社,2002.
[117]朱耀庭.半刚性基层沥青路面粘弹性有限元分析[D].南京:南京林业大学,2007.
[118]张肖宁.实验粘弹原理[M] .哈尔滨:哈尔滨船舶工程学院出版社,1990.
[119]张肖宁.沥青与沥青混合料的粘弹力学原理及应用[M] .北京:人民交通出版社,2006.
[120] Witczak,M. W. and R. E. Root. Summary of Complex Modulus Laboratory Test Procedures and Results. STP 561,American Society for Testing and Materials,1974:67-94.
[121]交通部公路科学研究所.沥青路面动力参数试验方法的研究[R].北京:交通部公路科学院.1999.
[122]中华人民共和国行业标准《.公路沥青路面设计规范》JTGD50-2006.北京:人民交通出版社,2006.
[123]中华人民共和国行业标准.《公路沥青路面施工技术规范》JTGF40-2004.北京:人民交通出版社,2004.
[124]中华人民共和国行业标准.《公路工程集料试验规程》JTJ058-2004.北京:人民交通出版社,2004.
[125]郑健龙.Burgers粘弹性模型在沥青混合料疲劳特性分析中的应用[J].长沙交通学院学报,1995,11(3):32-36.
[126]吕松涛,马健,郑健龙,等.沥青混合料热粘弹性疲劳本构模型[J].长沙交通学院学报,2006,22(4):33-37.
[127]钱国平,郑健龙,周志刚,等.沥青混合料增量型热粘弹性本构关系研究[J].应用力学学报,2006,23(3):338-343.
[128]叶群山.纤维改性沥青胶浆与混合料流变特性研究[D].武汉:武汉理工大学,2007.
[129]杨挺青.粘弹性力学[M].武汉:华中理工大学出版社,1990.
[130] Christensen R M.Theory of viscoelasticity[M]. New York: Academic Press,1982.
[131]陈前,朱德懋.粘弹结构动力学分析[J].振动工程学报,1989,2 (3):42-51.
[132]周光泉,刘孝敏.粘弹性理论[M].合肥:中国科学技术大学出版社,1996.
[133]陈前,朱德慰.关于复合结构振动分析中粘弹性材料本构方程的形式[J].应用力学学报,1987,(1):39-51.
[134] Bagley R L,Torvik P J. Fractional calculus-a different approach to the analysis of viscoelastically damped structures[J].AIAAJ,1983,21(5):741-748.
[135]张为民,张涥源.分数指数模型的热力学分析及应用[J].工程力学,2002,36(7):95-99.
[136]张为民.一种工程实用的分数指数粘弹性固体模型[J].力学与实践,2001,23(2):43-47.
[137] K.S.Miller and B.Ross.An Introduction to the Fractional calculus and Fractional differential Equations,Wiley,New York,1993.
[138] Lokenath Debnath. Fractional calculus Fundamentals.41st Ieee Conference on Decision and Control.Las Vegas,December 9,2002,1-5.
[139] Rabotonv Y.N,Papernik L.K.H,Zvonov E.N. Tables of the Fractional Exponential Function of Negative Parameters and Its Integral,,Moscow: Nauka,1969.
[140]张为民.聚合物基纳米复合材料的等效粘弹性连续介质微观力学研究[D].湘潭:湘潭大学,2006.
[141] Song D Y,Jiang T Q.Study on the constitutive equation with fractional derivative for viscoelastic fluids-modified Jeffreys model and its application[J].Rhelologica Acta,1998,37:512-517.
[142] hi Miiu Nobuyuki,Zhang Wei.Fractional calculus approach to dynamic problem of Viscoelastic material[J]. JSME,1999,1(42):827-830.
[143]陈艳,陈宏善,康永刚.分数Maxwell模型应用于PTFE松弛模量的研究[J].高等学校化学学报,2006,27(11):2160-2163.
[144]王启宏.材料流变学[M].北京:中国建筑工业出版社,1984.
[145]李晓民,张肖宁,王绍怀.基于动态粘弹力学的沥青胶浆高温性能试验研究[J].公路交通科技,2006,24(4):11-15.
[146]李根国.具有分数导数型本构关系的粘弹性结构的静动力学行为分析[D].上海:上海大学,2001.
[147]李录贤,叶天麒,沈亚鹏,等.三维药柱的热粘弹性有限元分析[J].推进技术,1997,18(3): 45-50.
[148]蔡锷.粘弹性力学基础[M].北京:北京航空航天大学出版社,1990.
[149] Padovan, J.,‘Computational algorithms for FE formulations involving fractional operators’,Computational Mechanics 2,1987,271–287.
[150] Koeller,R. C.,‘Applications of fractional calculus to the theory of viscoelasticity’,ASME Journal of Applied Mechanics 51,1984,299–307.
[151] Enelund,M. and Josefson,B. M.,‘Time-domain Finite Element analysis of viscoelastic structures with fractional derivatives constitutive relations’,AIAA Journal 35(10),1997,1630–1637.
[152]李卓,徐秉业.粘弹性分数阶导数模型的有限元法[J].工程力学,2001,18(3):40-44.
[153]刘林超,闫启方,张卫,等.分数导数型粘弹性阻尼器的动力学有限元方程及数值解[J].橡胶工业,2006,53(5):271-275.
[154]黄文虎,王心清,张景绘等.航天柔性结构振动控制的若干进展[J] .力学进展,1997,Vol. 27(1):5-18.
[155] PODLUBNY I.Fractional Differential Equations[M].San Diego:Academic Press,1999:243-260.
[156] ZHANG W,SHIMIZU N.Numerical algorithm for dynamic problems involving fractional operators [J].Int J of the Japan Society of Me-chanical Engineers,SeriesC,1998,41(3):364-370.
[157] OLDHAM K B,SPANIER J.The Fractional Calculus[M].NewYork:Academic,1974.
[158]池田,川田,小口.分数次微分方程式の时间答の数计算法[J].计测自动制御学会论文集,2001,37(8):795-797.
[159]银花,陈宁,赵尘,等.分数阶导数型粘弹性结构动力学方程的数值算法[J].南京林业大学学报:自然科学版,2010,34(2):115-118.
[160] Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, CA, 1999.
[161]王勖成.有限单元法[M].北京:清华大学出版社,2003.
[162] Jorje. Marcondes, Snyder M B. Predicting Vertical Acceleration in Vehicles Trough Road Roughnessm. Journal of Trans. Eng ASCE. 1992,118(1):33-49.
[163] Zia,Zafir. Raj 5iddharthan,Peter E. Sebaaly. Dynamic Pavement-Strain Histories from Moving Traffic Load. Journal of Transportation Engineering, ASCE. 1994,120(5):821-842.
[164]刘献栋,邓志党等.公路路面不平度的数值模拟方法研究[J].北京航空航天大学学报,2003,(9):843-846
[165] G.R.Watts.Case Studies of the e_ects of tra_c-induced vibrations on heritage buildings. Research report 156,Transport and Road Research Laboratory,1988.
[166] G.R.Watts. The e_ects of tra_c-induced vibrations on heritage buildings, further case studies. Research report 207,Transport and Road Research Laboratory,1989.
[167] M.O. Al-Hunaidi and J.H. Rainer. Remedial measures for traffic induced vibrations at a residential site. Part 1:Field tests. Canadian Acoustics/Acoustique Canadiennne,1991,19(1):3-13.
[168] W.Alaerts,G.Lombaert,and G. Degrande. Trillingsmetingen in het gebouw van Orda-B N.V. aan de interleavenlaan te Leuven. Internal report BWM-1999-09,Department of Civil Engineering,Katholieke Universiteit Leuven,October 1999.
[169] G.Degrande,G. Lombaert, and J.Maeck. Trillingsmetingen in een woning Genthof 48 te Brugge. Internal report BWM-1999-02,Department of Civil Engineering, Katholieke Univerwiteit Leuven, March 1999.
[170] G.Lombaert, W. Alaerts, and G. Degrande. Trillingsmetingen in een woning aan de Vilvoordsebaan 59a te Winksele. Internal report BWM-1999-07,Department of Civil Engineering, Katholieke Universiteit Leuven, August 1999. DWTC Research Programme Sustainable Mobility, Research ProjectMD/01/040.
[171]翟婉明著.车辆-轨道耦合动力学(第二版)[M].北京:中国铁道出版社,2002.
[172]练松良编著.轨道动力学[M].上海:同济大学出版社,2003.
[173]李套岭,孙立军,陆辉.对路面平整度概念的粗浅理解.上海市公路学会第五届年会学术论文集.
[174]赵济海,王哲人,关朝雳.路面不平度的测量分析与应用[J].北京:北京理工大学出版社,2000.
[175]蔚晓丹.国际平整度指数IRI作为路面平整度评价指标的研究[J].公路交通科技,1999,16(增1):9-13.
[176]夏乐天,朱永忠.工程随机振动[M].南京:河海大学出版社,2000.
[177] Sayers M W,S M Karamihas. The Little Book of Profiling. University of Michigan Transportation Research Institute,1998.
[178]张景绘,王超.工程随机振动理论[M].西安:西安交通大学出版社,1988.
[179]La Barre R P,For bes R T,Andrews. The measurement and ananlysis of road surface roughness. MIRA Reprt 1970,5.
[180] Healey A J,Nath man E,Smith C C. An analytical and experimentalstudy of auto mobile dynamics with random road way inpats. Transactions. Of the Asme,Journal of Dynamics Systems,Measure ment and Control,Pecember 1977:284~292.
[181]喻凡,林逸.汽车系统动力学[M].北京:机械工业出版社,2005.
[182]盛灿花.路面平整度特性研究[D].长沙:湖南大学,2005.
[183]刘建民.随机过程[M].西北大学出版社,2004.
[184]张永林,钟毅芳.车辆路面不平度输入的随机激励时域模型[J].农业机械学报,2004,35(2):23-27.
[185]任瑞波,谭忆秋,张肖宁.FWD动荷载作用下沥青路面层状粘弹性路表弯沉的求解[J].中国公路学报,2001,2(4):9-17.
[186]任瑞波,钟岱辉等.沥青路面层状粘弹性半空间轴对称问题的求解[J].山东建筑工程学院学报,2002,(4):1-7.
[187]钟阳,陈静云等.求解动荷载作用下多层粘弹性半空间轴对称问题的精度刚度矩阵法[J].计算力学学报,2003,35(12):43-47.
[188]重庆交通科学研究院.沪宁高速公路(江苏段)扩建工程沥青路面结构环道试验研究[R].重庆交通科学研究院,2005.
[189]张洁.公路车辆与桥梁耦合振动分析研究[D].成都:西南交通大学,2005.
[190]吴有松.高速铁路-桥梁系统耦合振动及程序设计[D].成都:西南交通大学,2005.
[191]李永乐.风-车-桥系统非线性空间耦合振动研究[D].成都:西南交通大学,2003.
[192]韩万水.风一汽车一桥梁系统空间耦合振动研究[D].上海:同济大学,2006.
[193]陈华.交通荷载作用下公路路基的动力有限元分析[D].兰州:兰州理工大学,2004.
[2]邓学钧,孙璐.车辆-地面结构系统动力学[M].北京:人民交通出版社,2000.
[3]龙晋闽.车辆对路面作用的动载荷研究[D].西安:长安大学,2006.
[4] D.Cebon. Vehicle-Generated Road Damage:A Review. Vehicle System Dynamics.1989,18:107-150
[5] D.J.Cole. Assessing the Road-damaging Potential of Heavy Vehicles. Proc Instn Mech Engrs.1991,205(D):223-232.
[6] T.E .C .Potter,D .Cebon and D .J .Cole. Assessing 'Road-friendliness':a Review . Proc Instn Mech Engrs.1997,211(D):455-473.
[7] T.E .C .Potter,D .Cebon and D .J .Cole.An Investigation of Road Damage Due to Measured Dynamic Tyre Forces. Proc Instn Mech Engrs.1995,209(D):9-24.
[8] T.E .C .Potter,D .Cebon,A .C .Collop and D .J .Cole. Road-Damaging Potential of Measured Dynamic Tyre Forces in Mixed Traffic. Proc Instn Mech Engrs.1996,210(D):215-225.
[9] G.K .Misoi,R .M .Carson.Corrugation of Unmetalled Roads,Part1:Vehicle Dynamics. Proc Instn Mech Engrs.1989,203(D):205-214.
[10] D.J.Cole,A .C .Collop and T.E .C .Potter.Spatial Repeatability of Measured Dynamic Tyre Forces.Proc Instn Mech Engrs.1996,210(D): 185-197.
[11] D .Cebon .Interaction between heavy vehicles and roads.SAE SP-951,1993.
[12]国家自然科学基金委员会编.力学[R].北京:科学出版社,1997.
[13]朱孔源.车辆与柔性路面力学相互作用系统的研究[D].北京:中国农业大学,2001.
[14]华南理工大学道路研究所.沥青混合料动态模量参数研究[R].广州:华南理工大学.2007.
[15]田晓霞.基于SPT的沥青混合料高温性能的试验研究[D].南京:东南大学,2007.
[16] ASTM D3497-79. Standard Test method for Dynamic Modulus of Asphalt Mixtures. 1995.
[17] AASHTO Designation:TP62-03. Standard Method of Test For Determining Dynamic Modulus of Hot-Mix Asphalt Concrete Mixtures. 2003.
[18] NCHRP 9-19. Superpave Support and Performance models Management. Field Validation of the Simple Performance Test. 2001 .
[19] NCHRP 9-29. Simple Performance Tester for Superpave Mix Design. Equipment Specification for the Simple Performance Test System. Advanced Asphalt Technologies,LLC,2004.
[20] Harold L. Von Qunitus, J. Brent Rauhut, and Thomas W. Kennedy, Comparisons of Asphalt concrete Stiffness as Measured by Various Testing Techniques. Proceedings of the Association of Asphalt Paving Technologists,Vol 51,1982.
[21] Herbert F. Southgate. Effects of Construction Variations upon Dynamic Modulus of Asphalt Concrete. AAPT,Vol 51,1982 .
[22] J. F. Shook and B. F. Kallas. Factors Influencing Dynamic Modulus of Asphalt Concrete. AAPT, Vol 38, 1969.
[23] W. Heukelom and A. J. G. Klomp. Road Design and Dynamic Loading. AAPT,Vol 33,1964 .
[24] W. Heukelom and A. J. G. Klomp. Dynamic Testing as a Means of Controlling Paving During and After Construction. Proceeding of the First International Conference on Structural Design of Asphalt Pavement, University of Michigen,1962.
[25] National Cooperative Highway Research Program 1-37A. Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures. ARA,Inc,2004.
[26]高英.基于动态参数的沥青路面设计方法研究[D].上海:同济大学,1999.
[27]许志鸿等.沥青混合料动态性能参数标准研究报告[R].交通部部级科技项目.同济大学,2000.
[28]丰晓.沥青混合料动态性能及疲劳特性分析[D].上海:同济大学,1997.
[29]黎霞,田小革.用动蠕变试验确定沥青混凝土动态粘弹性参数[J].国外公路,2002,20(1):46-48.
[30]许志鸿,李淑明,高英等.沥青混合料动态性能研究[J].同济大学学报,2001,29(8): 893-897.
[31]许志鸿,丰晓,高英等.沥青混合料动态性能影响因素的研究[J].建筑材料学报,2001,4(3):238-243.
[32]杨屹东.沥青路面结构动态模里试验研究[J].公路,2002,2:25-27.
[33]曾梦澜,黄欣哲.沥青结合料与混合料动力性质的关系[J].中南公路工程,2003,28(4):11-14.
[34]孙略伦.聚酷纤维沥青混凝土动态模量的试验研究[D].大连:大连海事大学,2006 .
[35]羊明.沥青混合料动态模量研究[D].长沙:长沙理工大学,2007 .
[36]方萍(译),汪宏(校).沥青混合料的线性粘弹性特性模型[J].国外公路,1998,18(4):46-50.
[37]郑健龙,田小革,应荣华.沥青混合料热粘弹性本构模型的实验研究[J].长沙理工大学学报(自然科学版),2004,1(1):1-7.
[38] Monismith C.L,Secor K. E. Viscoelastic behavior of asphalt concrete Pavements[C]Proceedings of International Conference on Structure Design of Asphalt Pavements, 1962,10:476-498
[39] Krishnan J. M, Rajagopal K. R. on the mechanic behavior of asphalt[J].Mechanics of Materials, 2005,37(11):1085-1100.
[40]徐世法.表征沥青及沥青混合料高低温性能的流变模型[J].北京建筑工程学院学报,1991,14(1):57-65.
[41] Szydlo A,Maekiewicz P. AsPhalt mixes deformation sensitivity to change in rheological Parameters[J].Journal of Materials in Civil Engineering,2005,(2):l-9.
[42] Abbas A.R,Papagiannakis,Masad E. A. Linear and nonlinear viscoelastic analysis of The Microstructure of asphalt Concretes[J].Journal of Materials in Civil Engineering,2004,133-139.
[43] Vlachovicova Z,et al. CreeP characteristies of asphalt modified by radial styrene-butadiene-styrene coPolymer[J].Construetion and BuildingMaterials,2007,21(3):567-577.
[44] W. Zhang,A. Dreseher,D. E. Neweomb. Viseoelastic Analysis of Diametral Compression of Asphalt Conerete.Journal of Engineering Mechanies,1997,123(6):596-603.
[45] W.Zhang,A.Dreseher,D.E.Neweomb.Viseoelastic Behavior of Asphalt Conerete in DiametralCompression. Journal of Transportation Engineering,1997,123(6):495-502.
[46] Lee H J,Kim Y R. Viscoelastic constitutive model for asphalt conerete under cyclic loading[J].Journal of Engineering Mechanics,1998,(1):32-40.
[47] Antoni Szydlo,Piotr Mackiewicz. AsPhalt Mixes Deformation Sensitivity to Change in Rheological Parameters,2005,February,1-9.
[48] Tashman L,Masad E,et al. A microstructure-based viscoplastic model for asphalt conerete[J].Intemational Joumal of Plastieity,2005,21:1659-1685.
[49] Lu Y,Wright P J. Numerical approach of viscoelastoPlastic analysis for asphalt mixtures[J].ComP Struct,1998,69:139-147.
[50] Erkens S M J G Liu X,Scarps A.3D finite model for asphalt conerete responsesimulation[J].Int J Geomeeh,2002,2(3):305-330.
[51] Blab R,Harvey J T Modeling measured 3D tire contact stress in a viseoelastoc FE Pavement model[J].Int J Geomeeh,2002,2(3):271-290.
[52] Krishnan J. M and Rajagopal K. R. Thermodynamic Framework for the Constitutive Modeling of Asphalt Concrete:Theory and Applications,J.Mat. Civil Eng,2004,16(2):155-166.
[53]郑建龙.Burgers粘弹性模型在沥青混合料疲劳特性分析中的应用[J].长沙交通学院学报,1995,11(3):32-42.
[54]郑健龙,应荣华,张起森.沥青混合料热粘弹性断裂参数研究[J].中国公路学报,1996,9(3):20-28.
[55]郑健龙,吕松涛,田小革.沥青混合料年弹性参数及其应用[J].郑州大学学报(工学版),2004,25(4):8-12.
[56]郑健龙,周志刚,应荣华.沥青路面温度应力数值分析[J].长沙交通学院学报,2001,17(1):29-32.
[57]钟志海.沥青硅的粘弹性及其参数的确定方法[J].公路与汽车,2005,(4):39-41.
[58]封基良,黄晓明.沥青粘结料粘弹性参数确定方法的研究.2006,23(5):16-22.
[59]钱国平,郭忠印,郑健龙等.环境条件下沥青路面热粘弹性温度应力计算[J].同济大学学报,2003,31(2):150-55.
[60]李一鸣.沥青混合料的松弛劲度模量[J].石油沥青,1995,(1):17-22.
[61]延西利,扈惠敏,张登良.沥青混合料线性流变模型的数值模拟[J1.西安公路交通大学学报,1999,19(1):7-12.
[62]黄卫东,吕伟民.沥青及沥青混合料流变性质与动稳定度的关系[J].同济大学学报2000,28(4):501-504.
[63]邵腊庚,周晓青,李宇峙等.基于直接拉伸试验的沥青混合料粘弹性损伤特性研究[J].土木工程学报,2005,38(4):125-128.
[64]周志刚,钱国平,郑健龙.沥青混合料粘弹性参数测定方法的研究[J].长沙交通学院学报,2001,17(4):23-28.
[65]吕松涛,田小革,郑健龙.沥青混合料粘弹性参数的测定及其在本构模型中的应用[J].长沙交通学院学报,2005,21(1):37-42.
[66]侯金成.纤维沥青混凝土粘弹性能研究[D].大连:大连海事大学,2007.
[67]王随原,周进川. SBS改性氯气混合料蠕变性能试验研究[J].公路交通科技,2006,23(12)10-13.
[68] R.Hilfer Appliacations of Fractional Calculus in Physics[M].World Scientific Press Singapore 2000
[69] K.S. Miller and B. Ross. An Introduction to the Fractional Calculus and Fractional Differential Equations[M].Jphn Wiley&Sons Inc New York,1993.
[70] S.G.Samko,A.A.Kolbas and O.I.Marichev Fractional Integrals and Derivatives:Theory and Applications[M].Gordon and Breach,New York,1993.
[71] H.M.Srivastava and R.K.Saxena,Operators of fractional integration and their applications[J]Appl. Math. Comp,2001,118:15-23.
[72] Nutting. P.G. A new generalized law of deformation. J. Franklin Institute.1921,191:694-685.
[73] Gemant A. on fractional Differences. Phil.Mag.1938,25:92-96.
[74] Rabotnov Y.N. Papernik L.K.H. Zvonov E.N. Tables of the Fractional Exponential Funtion of Negative Parameters and Its Integral,Moscow:Nauka,1969.
[75] Rabotnov Y.N. Element of Hereditary Solids,Mir Publishers,1980.
[76] Bagley R.L. Torvik P.J. A theoretical basis for the application of fractional calculus to viscoelasticity. J.Rheol,1983,27(3):201-210.
[77] Bagley R.L. Power law and fractional calculus model of viscoelasticity.AIAA J,1989,27(10):1412-1417.
[78] Bagley R.L. Torvik P.J. on the fractional calculus model of viscoelasticity Behavior. J.Rheol, 1986,30(1):133-155.
[79] Drozdov A,Kalamkarov A.L. Constituve model for nonlinear viscoelastic behavior of Polymer. Polymer Engrg&Sci,1996:36(14):1907-1919.
[80] Makris N. Three-dimensional constitutive viscoelastic law with fractional order time derivatives. J.Rheol,1997,41(5):1007-1020.
[81] Koeller R.C. Applications of Fractional calculus to the Theory of Viscoelasticity Transacions of the ASME J Applied Mechanics 1984,51:294-298.
[82] Li J,Jiang T.Q. Constitutive Equation for Viscoelastic Fluids via Fractional Derivative in Advances in Structure and Heterogen Continua New York: Allerton Press Inc, 1994: 187-193
[83] Song D. Y,Jiang T.Q.Study on the constitutive equation with fractional derivative for viscoelastic fluids-modified Jeffreys model and its application Rheol Acta,1998,37:512-517.
[84] Wei Zhang,Nobuyuki Shimizu and Hua xu.Thermal effects of the viscoelastic materials described by fractional calculus constitutive lawThe First Asian conference on Multibody dynamics. 2002 July31-August2 2002,I waki,Fukusbima,Japan.
[85] Wei Zhang and Nobuyuki Shimizu ,Damping properties of the viscoelastic material prescribed by fractional Kelvin-voigt model.JSME International Journal.Series C,1999,42(1):1-9.
[86]朱正佑,李根国.具有分数导数本构关系的Timoshenko梁的静动力学行为分析应用数学和力学2002,23(1):
[87]张为民.一种采用分数阶导数的新流变模型理论[J].湘潭大学自然科学学报,2001, 23(1): 30-36.
[88]张为民,张淳源,张平.考虑老化的混凝土粘弹性分数导数模型[J].应用力学学学报,2004, 21(1): 1-4.
[89]孙海忠,张卫.分数算子描述的粘弹性材料的本构关系研究[J].材料科学与工程学报,2006, 24(6): 926-929.
[90]刘林超.分数导数型粘弹性材料的力学行为及在结构减振中的应用研究[D].广州:暨南大学,2005.
[91]夏禾.车辆与结构动力相互作用[M].北京:科学出版社,2002.
[92] Cebon D . Interaction Between Heavy Vehicles and Roads SAE 930001(SEA/SP-93/951)(The T hirty-ninth Ray Buckendale Lecture)
[93] Potter T .E .C,Cebon D and Cole D .J . Assessing‘Road-friendliness’:a review.Proc. Instn Mech.Engrs. 1997,211(D4):455-475.
[94] Mahoney Joe P .The relationship between axle configuration,wheel loads and pavement structure s. SAE 88184.
[95]余卓平,黄锡朋,张洪欣.公路车辆对道路损伤计算方法的研究[J].同济大学学报,1993,21(增刊):115-124.
[96]余卓平,黄锡朋,张洪欣.减轻重型汽车对道路的损伤一汽车悬架优化设计[J].中国公路学报,1994,7(3):83-87.
[97] D.Cebon.Theoretical Road Damage Duo to Dynamic Tyre Forces of Heavy Vehicles Part2:Simulated Damage Caused by a Tandem-Axle Vehiele.Proc Instn Mech Engrs.1988,202(C2): 109-117.
[98]任卫群.公路车辆对道路破坏的数字仿真研究[D].武汉:华中科技大学,2003.
[99] S.Drosner.Beitrag zur.Berechnung der dynamischen Beanspruchung von Brucken unter Verkehrslasten,PhD thesis,Stahlbau RWTH Aachen ,Aachen ,Germany,1989.
[100] H.E.M.Hunt.Modelling of Road Vehieles for Calculation of Traffic-Indueed Ground Vibrations. JOumal of Sound and Vibration,1991,144(1):41-51.
[101] H.E.M. Hunt. Stochastic Modelling of Traffic-lndueed Ground Vibration.Journal of Sound and Vibration. 1991,144(1):53-70.
[102]成祥生.弹性地基板由运动载荷引起的动力反应[J].应用数学的力学,1987,3(4):347-355.
[103]钟阳,王哲人,张肖宁.不平整路面上行驶的车辆对路面随机动压力的分析[J].中国公路学报,1992,5(2):40-44.
[104]黄晓明.路面动荷载与路面平整度关系的随机分析[J].东南大学学报,1993,23(1):56-61.
[105]杨方廷.路面对车辆载荷的动态响应的研究[D].北京:中国农业大学,1996.
[106]孙璐,邓学钧.速度与车辆动态特性对于车路相互作用的影响[J].土木工程学报,1997,30(6):34-40.
[107]李怀璋.车辆-路面系统中的动载、车辙和合理轴限的研究[D].北京:中国农业大学,1999.
[108]郑泉,杨方廷.车轮随机动载与路面及车速相互关系的研究[J].合肥工业大学学报(自然科学版),2001,24(1):139-142.
[109]邓学钧.车辆一地面结构系统动力学研究[J].东南大学学报,2002,32(3):474-479.
[110]陶向华,黄晓明.车辆动载荷的频域模拟计算与分析[J].华中科技大学学报(城市科学版),2003,20(4):47-50.
[111]张军.重型车辆与刚性路面结构的动力相互作用理论分析和试验研究[D].长沙:湖南大学,2003.
[112]陶向华.路桥过渡段差异沉降控制标准与人车路相互作用[D].南京:东南大学,2006.
[113]王暄.随机荷载作用下柔性路面结构及路基动力响应研究[D].长沙:中南大学,2006.
[114]赵延庆,吴剑,文健.沥青混合料动态模量及主曲线的确定与分析[J].公路,2006,(8):163-167.
[115]李德超.沥青混合料动态模量试验研究[J].公路,2008,(1):134-140.
[116]张义同.热粘弹性理论[M].天津:天津大学出版社,2002.
[117]朱耀庭.半刚性基层沥青路面粘弹性有限元分析[D].南京:南京林业大学,2007.
[118]张肖宁.实验粘弹原理[M] .哈尔滨:哈尔滨船舶工程学院出版社,1990.
[119]张肖宁.沥青与沥青混合料的粘弹力学原理及应用[M] .北京:人民交通出版社,2006.
[120] Witczak,M. W. and R. E. Root. Summary of Complex Modulus Laboratory Test Procedures and Results. STP 561,American Society for Testing and Materials,1974:67-94.
[121]交通部公路科学研究所.沥青路面动力参数试验方法的研究[R].北京:交通部公路科学院.1999.
[122]中华人民共和国行业标准《.公路沥青路面设计规范》JTGD50-2006.北京:人民交通出版社,2006.
[123]中华人民共和国行业标准.《公路沥青路面施工技术规范》JTGF40-2004.北京:人民交通出版社,2004.
[124]中华人民共和国行业标准.《公路工程集料试验规程》JTJ058-2004.北京:人民交通出版社,2004.
[125]郑健龙.Burgers粘弹性模型在沥青混合料疲劳特性分析中的应用[J].长沙交通学院学报,1995,11(3):32-36.
[126]吕松涛,马健,郑健龙,等.沥青混合料热粘弹性疲劳本构模型[J].长沙交通学院学报,2006,22(4):33-37.
[127]钱国平,郑健龙,周志刚,等.沥青混合料增量型热粘弹性本构关系研究[J].应用力学学报,2006,23(3):338-343.
[128]叶群山.纤维改性沥青胶浆与混合料流变特性研究[D].武汉:武汉理工大学,2007.
[129]杨挺青.粘弹性力学[M].武汉:华中理工大学出版社,1990.
[130] Christensen R M.Theory of viscoelasticity[M]. New York: Academic Press,1982.
[131]陈前,朱德懋.粘弹结构动力学分析[J].振动工程学报,1989,2 (3):42-51.
[132]周光泉,刘孝敏.粘弹性理论[M].合肥:中国科学技术大学出版社,1996.
[133]陈前,朱德慰.关于复合结构振动分析中粘弹性材料本构方程的形式[J].应用力学学报,1987,(1):39-51.
[134] Bagley R L,Torvik P J. Fractional calculus-a different approach to the analysis of viscoelastically damped structures[J].AIAAJ,1983,21(5):741-748.
[135]张为民,张涥源.分数指数模型的热力学分析及应用[J].工程力学,2002,36(7):95-99.
[136]张为民.一种工程实用的分数指数粘弹性固体模型[J].力学与实践,2001,23(2):43-47.
[137] K.S.Miller and B.Ross.An Introduction to the Fractional calculus and Fractional differential Equations,Wiley,New York,1993.
[138] Lokenath Debnath. Fractional calculus Fundamentals.41st Ieee Conference on Decision and Control.Las Vegas,December 9,2002,1-5.
[139] Rabotonv Y.N,Papernik L.K.H,Zvonov E.N. Tables of the Fractional Exponential Function of Negative Parameters and Its Integral,,Moscow: Nauka,1969.
[140]张为民.聚合物基纳米复合材料的等效粘弹性连续介质微观力学研究[D].湘潭:湘潭大学,2006.
[141] Song D Y,Jiang T Q.Study on the constitutive equation with fractional derivative for viscoelastic fluids-modified Jeffreys model and its application[J].Rhelologica Acta,1998,37:512-517.
[142] hi Miiu Nobuyuki,Zhang Wei.Fractional calculus approach to dynamic problem of Viscoelastic material[J]. JSME,1999,1(42):827-830.
[143]陈艳,陈宏善,康永刚.分数Maxwell模型应用于PTFE松弛模量的研究[J].高等学校化学学报,2006,27(11):2160-2163.
[144]王启宏.材料流变学[M].北京:中国建筑工业出版社,1984.
[145]李晓民,张肖宁,王绍怀.基于动态粘弹力学的沥青胶浆高温性能试验研究[J].公路交通科技,2006,24(4):11-15.
[146]李根国.具有分数导数型本构关系的粘弹性结构的静动力学行为分析[D].上海:上海大学,2001.
[147]李录贤,叶天麒,沈亚鹏,等.三维药柱的热粘弹性有限元分析[J].推进技术,1997,18(3): 45-50.
[148]蔡锷.粘弹性力学基础[M].北京:北京航空航天大学出版社,1990.
[149] Padovan, J.,‘Computational algorithms for FE formulations involving fractional operators’,Computational Mechanics 2,1987,271–287.
[150] Koeller,R. C.,‘Applications of fractional calculus to the theory of viscoelasticity’,ASME Journal of Applied Mechanics 51,1984,299–307.
[151] Enelund,M. and Josefson,B. M.,‘Time-domain Finite Element analysis of viscoelastic structures with fractional derivatives constitutive relations’,AIAA Journal 35(10),1997,1630–1637.
[152]李卓,徐秉业.粘弹性分数阶导数模型的有限元法[J].工程力学,2001,18(3):40-44.
[153]刘林超,闫启方,张卫,等.分数导数型粘弹性阻尼器的动力学有限元方程及数值解[J].橡胶工业,2006,53(5):271-275.
[154]黄文虎,王心清,张景绘等.航天柔性结构振动控制的若干进展[J] .力学进展,1997,Vol. 27(1):5-18.
[155] PODLUBNY I.Fractional Differential Equations[M].San Diego:Academic Press,1999:243-260.
[156] ZHANG W,SHIMIZU N.Numerical algorithm for dynamic problems involving fractional operators [J].Int J of the Japan Society of Me-chanical Engineers,SeriesC,1998,41(3):364-370.
[157] OLDHAM K B,SPANIER J.The Fractional Calculus[M].NewYork:Academic,1974.
[158]池田,川田,小口.分数次微分方程式の时间答の数计算法[J].计测自动制御学会论文集,2001,37(8):795-797.
[159]银花,陈宁,赵尘,等.分数阶导数型粘弹性结构动力学方程的数值算法[J].南京林业大学学报:自然科学版,2010,34(2):115-118.
[160] Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, CA, 1999.
[161]王勖成.有限单元法[M].北京:清华大学出版社,2003.
[162] Jorje. Marcondes, Snyder M B. Predicting Vertical Acceleration in Vehicles Trough Road Roughnessm. Journal of Trans. Eng ASCE. 1992,118(1):33-49.
[163] Zia,Zafir. Raj 5iddharthan,Peter E. Sebaaly. Dynamic Pavement-Strain Histories from Moving Traffic Load. Journal of Transportation Engineering, ASCE. 1994,120(5):821-842.
[164]刘献栋,邓志党等.公路路面不平度的数值模拟方法研究[J].北京航空航天大学学报,2003,(9):843-846
[165] G.R.Watts.Case Studies of the e_ects of tra_c-induced vibrations on heritage buildings. Research report 156,Transport and Road Research Laboratory,1988.
[166] G.R.Watts. The e_ects of tra_c-induced vibrations on heritage buildings, further case studies. Research report 207,Transport and Road Research Laboratory,1989.
[167] M.O. Al-Hunaidi and J.H. Rainer. Remedial measures for traffic induced vibrations at a residential site. Part 1:Field tests. Canadian Acoustics/Acoustique Canadiennne,1991,19(1):3-13.
[168] W.Alaerts,G.Lombaert,and G. Degrande. Trillingsmetingen in het gebouw van Orda-B N.V. aan de interleavenlaan te Leuven. Internal report BWM-1999-09,Department of Civil Engineering,Katholieke Universiteit Leuven,October 1999.
[169] G.Degrande,G. Lombaert, and J.Maeck. Trillingsmetingen in een woning Genthof 48 te Brugge. Internal report BWM-1999-02,Department of Civil Engineering, Katholieke Univerwiteit Leuven, March 1999.
[170] G.Lombaert, W. Alaerts, and G. Degrande. Trillingsmetingen in een woning aan de Vilvoordsebaan 59a te Winksele. Internal report BWM-1999-07,Department of Civil Engineering, Katholieke Universiteit Leuven, August 1999. DWTC Research Programme Sustainable Mobility, Research ProjectMD/01/040.
[171]翟婉明著.车辆-轨道耦合动力学(第二版)[M].北京:中国铁道出版社,2002.
[172]练松良编著.轨道动力学[M].上海:同济大学出版社,2003.
[173]李套岭,孙立军,陆辉.对路面平整度概念的粗浅理解.上海市公路学会第五届年会学术论文集.
[174]赵济海,王哲人,关朝雳.路面不平度的测量分析与应用[J].北京:北京理工大学出版社,2000.
[175]蔚晓丹.国际平整度指数IRI作为路面平整度评价指标的研究[J].公路交通科技,1999,16(增1):9-13.
[176]夏乐天,朱永忠.工程随机振动[M].南京:河海大学出版社,2000.
[177] Sayers M W,S M Karamihas. The Little Book of Profiling. University of Michigan Transportation Research Institute,1998.
[178]张景绘,王超.工程随机振动理论[M].西安:西安交通大学出版社,1988.
[179]La Barre R P,For bes R T,Andrews. The measurement and ananlysis of road surface roughness. MIRA Reprt 1970,5.
[180] Healey A J,Nath man E,Smith C C. An analytical and experimentalstudy of auto mobile dynamics with random road way inpats. Transactions. Of the Asme,Journal of Dynamics Systems,Measure ment and Control,Pecember 1977:284~292.
[181]喻凡,林逸.汽车系统动力学[M].北京:机械工业出版社,2005.
[182]盛灿花.路面平整度特性研究[D].长沙:湖南大学,2005.
[183]刘建民.随机过程[M].西北大学出版社,2004.
[184]张永林,钟毅芳.车辆路面不平度输入的随机激励时域模型[J].农业机械学报,2004,35(2):23-27.
[185]任瑞波,谭忆秋,张肖宁.FWD动荷载作用下沥青路面层状粘弹性路表弯沉的求解[J].中国公路学报,2001,2(4):9-17.
[186]任瑞波,钟岱辉等.沥青路面层状粘弹性半空间轴对称问题的求解[J].山东建筑工程学院学报,2002,(4):1-7.
[187]钟阳,陈静云等.求解动荷载作用下多层粘弹性半空间轴对称问题的精度刚度矩阵法[J].计算力学学报,2003,35(12):43-47.
[188]重庆交通科学研究院.沪宁高速公路(江苏段)扩建工程沥青路面结构环道试验研究[R].重庆交通科学研究院,2005.
[189]张洁.公路车辆与桥梁耦合振动分析研究[D].成都:西南交通大学,2005.
[190]吴有松.高速铁路-桥梁系统耦合振动及程序设计[D].成都:西南交通大学,2005.
[191]李永乐.风-车-桥系统非线性空间耦合振动研究[D].成都:西南交通大学,2003.
[192]韩万水.风一汽车一桥梁系统空间耦合振动研究[D].上海:同济大学,2006.
[193]陈华.交通荷载作用下公路路基的动力有限元分析[D].兰州:兰州理工大学,2004.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |