线性粘弹性本构方程及其动力学应用研究综述
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摘要
综述了近年来线粘弹性材料本构方程的研究成果,介绍和讨论了复常数模量模型、标准流变学模型、分数阶导数模型、分数指数模型、微振子模型等典型和常用的五种模型,同时简单介绍了这些模型的动力学应用。
The study on linear constitutive equation of viscoelastic materials is summarized. Five typical models in common use are recommend and discussed, they are complex modulus model, standard model, fractional derivative model,fractional exponential model and mini-oscillator model. The dynamics applications of these models are briefly discussed.
The study on linear constitutive equation of viscoelastic materials is summarized. Five typical models in common use are recommend and discussed, they are complex modulus model, standard model, fractional derivative model,fractional exponential model and mini-oscillator model. The dynamics applications of these models are briefly discussed.
引文
1 杨挺青.粘弹性力学.武汉:华中理工大学出版社[M],1990
2 ChristensenRM.Theoryofviscoelasticity[J],NewYork;Aca demicPress,1982
3 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
4 张阿舟,姚起航.振动控制工程[M].北京:航空工业出版社,1989:290—295
5 孙庆鸿,张启军,姚慧珠.振动与噪声的阻尼控制.北京:机械工业出版社,1993,77—81
6 ScanlanRH.Lineardampingmodelsandcausalityinvibra tions[J].SoundandVibration,1970,13(4):499—509
7 BertCW.MaterialDamping.AnIntroductoryReviewofMathematicalModels,MeasuresandExperimentaltechniques,J.Sound&Vib,1973,29:129—135
8 MinleHK.Theimpulseresponsefunctionofasingledegreeoffreedomsystemwithhystereticdamping[J].SoundandVibra tion,1985,100(4):590—593
9 胡海岩.结构阻尼模型及系统时域动响应[J].振动工程学报,1992,5(1):8—15
10丁海平,刘长河.复阻尼理论的一点注记[J].地震工程与工程振动,2001,21(1):61—63
11何钟怡,廖振鹏,王小华.关于复阻尼理论的几点注记[J].地震工程与工程振动,2002,22(1):1—6
12陈 前,朱德懋.弹性-粘弹性复合结构模态理论.固体力学学报,1990,11(1):23—33
13陈 前,朱德懋.复合结构振动分析的数值方法.计算结构力学及应用,1990,7(3):27—35
14任建亭,邱 阳.粘弹复合结构特征问题的迭代算法.计算力学学报,1997,14(3):353—359
15LesieufreGA,BianchiniE.Timedomainmodelingoflinearviscoelasticityusinganelasticdisplacementfields.JournalofVibrationandAcoustics,1995,117(4):424—430
16李军强.粘弹性复合结构动力响应的实用数值算法.机械,2001,28(2):25—26
17GementA.Onfractionaldifferences[J].PhiMag,1938,25(1):92—96
18BagleyRL,TorvikPJ.Fractionalcalculus-adifferentap proachtotheanalysisofviscoelasticallydampedstructures[J].AIAA,J,1983,21(5):741—748
19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,1997,27(1):5—18
20陈 前,朱德懋.关于复合结构振动分析中粘弹性材料本构方程的形式.应用力学学报,1987,4(1):39—51
21JosephP,YuehuaG.Generalresponseofviscoelasticsystemsmodeledbyfractionaloperators[J].FranklinInstitute,1988,325(2):247—275
22李 卓,徐秉业.粘弹性分数阶导数模型的有限元法.工程力学,2002,19(3):40—44
23BagleyRonaldL,TorvikPeterJ.Fractionalcalculusinthetransientanalysisofviscoelasticallydampedstructures[J]AIAA,J,1985,23(6):918—925
24李根国,朱正佑,程昌钧.具有分数导数型本构关系的粘弹性柱的动力稳定性[J].应用数学和力学。2001,22(3):250—258
25EnelundM,MahlerL,RunessonK, etal.Formulationandintegrationofthestandardlinearviscoelasticsolidwithfraction alorderratelaws[J].IntJSolidStrut,1999,36(7):1417—1442
26DrozdorAD.Fractionaldifferentialmodelsinfiniteviscoelas ticity[J].ActaMech,1997,124(1):155—180
27EldredLB,BakerWP.Kelvin-voigtvsfractionalderivativemodelasconstitutiverelationsforviscoelasticmaterials[J].AIAA,1995,33(3):547—550
28BagleyRonaldL.TorvikPeterJ.Onthefractionalcalculusmodelofviscoelasticitybehavior[J].Jofheology,1986,30(1):133—135
29BagleyRL,CalicoRA.Fractionalorderstateequationsforthecontrolofviscoelasticallydampedstructures[J].Guidance,1991,33(2):304—311
30张为民,张淳源.分数指数模型的热力学分析及其应用.工程力学,2002,19(2):95—99
31张为民.一种工程实用的分数指数粘弹性固体模型.力学与实践,2001,23(2):43—47
32张为民.论最佳粘弹性固体流变模型.湘潭大学自然科学学报[J],2001,23(2):31—36
33张为民.松弛模量与蠕变柔量的实用表达式.湘潭大学自然科学学报[J],1999,21(3):26—28
34GollaDF,HughesPC.Dynamicsofviscoelasticstructures-atime-domain, finiteelementformulation[J].AppliedMechanics,1985,52:897—907
35MctavishDJ,HughesPC.Modelingoflinearviscoelasticspacestructures[J].JofVibrationandAcoustics,1993,115:103—110
36石银明,华宏星,傅志方.粘弹性材料的微振子模型研究[J].振动工程学报,2001,14(1):100—104
37张希农,陈 灵,张景绘.可控约束层阻尼.西安交通大学学报,1998,32(8):117—121
2 ChristensenRM.Theoryofviscoelasticity[J],NewYork;Aca demicPress,1982
3 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
4 张阿舟,姚起航.振动控制工程[M].北京:航空工业出版社,1989:290—295
5 孙庆鸿,张启军,姚慧珠.振动与噪声的阻尼控制.北京:机械工业出版社,1993,77—81
6 ScanlanRH.Lineardampingmodelsandcausalityinvibra tions[J].SoundandVibration,1970,13(4):499—509
7 BertCW.MaterialDamping.AnIntroductoryReviewofMathematicalModels,MeasuresandExperimentaltechniques,J.Sound&Vib,1973,29:129—135
8 MinleHK.Theimpulseresponsefunctionofasingledegreeoffreedomsystemwithhystereticdamping[J].SoundandVibra tion,1985,100(4):590—593
9 胡海岩.结构阻尼模型及系统时域动响应[J].振动工程学报,1992,5(1):8—15
10丁海平,刘长河.复阻尼理论的一点注记[J].地震工程与工程振动,2001,21(1):61—63
11何钟怡,廖振鹏,王小华.关于复阻尼理论的几点注记[J].地震工程与工程振动,2002,22(1):1—6
12陈 前,朱德懋.弹性-粘弹性复合结构模态理论.固体力学学报,1990,11(1):23—33
13陈 前,朱德懋.复合结构振动分析的数值方法.计算结构力学及应用,1990,7(3):27—35
14任建亭,邱 阳.粘弹复合结构特征问题的迭代算法.计算力学学报,1997,14(3):353—359
15LesieufreGA,BianchiniE.Timedomainmodelingoflinearviscoelasticityusinganelasticdisplacementfields.JournalofVibrationandAcoustics,1995,117(4):424—430
16李军强.粘弹性复合结构动力响应的实用数值算法.机械,2001,28(2):25—26
17GementA.Onfractionaldifferences[J].PhiMag,1938,25(1):92—96
18BagleyRL,TorvikPJ.Fractionalcalculus-adifferentap proachtotheanalysisofviscoelasticallydampedstructures[J].AIAA,J,1983,21(5):741—748
19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,1997,27(1):5—18
20陈 前,朱德懋.关于复合结构振动分析中粘弹性材料本构方程的形式.应用力学学报,1987,4(1):39—51
21JosephP,YuehuaG.Generalresponseofviscoelasticsystemsmodeledbyfractionaloperators[J].FranklinInstitute,1988,325(2):247—275
22李 卓,徐秉业.粘弹性分数阶导数模型的有限元法.工程力学,2002,19(3):40—44
23BagleyRonaldL,TorvikPeterJ.Fractionalcalculusinthetransientanalysisofviscoelasticallydampedstructures[J]AIAA,J,1985,23(6):918—925
24李根国,朱正佑,程昌钧.具有分数导数型本构关系的粘弹性柱的动力稳定性[J].应用数学和力学。2001,22(3):250—258
25EnelundM,MahlerL,RunessonK, etal.Formulationandintegrationofthestandardlinearviscoelasticsolidwithfraction alorderratelaws[J].IntJSolidStrut,1999,36(7):1417—1442
26DrozdorAD.Fractionaldifferentialmodelsinfiniteviscoelas ticity[J].ActaMech,1997,124(1):155—180
27EldredLB,BakerWP.Kelvin-voigtvsfractionalderivativemodelasconstitutiverelationsforviscoelasticmaterials[J].AIAA,1995,33(3):547—550
28BagleyRonaldL.TorvikPeterJ.Onthefractionalcalculusmodelofviscoelasticitybehavior[J].Jofheology,1986,30(1):133—135
29BagleyRL,CalicoRA.Fractionalorderstateequationsforthecontrolofviscoelasticallydampedstructures[J].Guidance,1991,33(2):304—311
30张为民,张淳源.分数指数模型的热力学分析及其应用.工程力学,2002,19(2):95—99
31张为民.一种工程实用的分数指数粘弹性固体模型.力学与实践,2001,23(2):43—47
32张为民.论最佳粘弹性固体流变模型.湘潭大学自然科学学报[J],2001,23(2):31—36
33张为民.松弛模量与蠕变柔量的实用表达式.湘潭大学自然科学学报[J],1999,21(3):26—28
34GollaDF,HughesPC.Dynamicsofviscoelasticstructures-atime-domain, finiteelementformulation[J].AppliedMechanics,1985,52:897—907
35MctavishDJ,HughesPC.Modelingoflinearviscoelasticspacestructures[J].JofVibrationandAcoustics,1993,115:103—110
36石银明,华宏星,傅志方.粘弹性材料的微振子模型研究[J].振动工程学报,2001,14(1):100—104
37张希农,陈 灵,张景绘.可控约束层阻尼.西安交通大学学报,1998,32(8):117—121
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