树脂基复合材料板簧结构阻尼性能研究
|
摘要
由于具有比刚度比强度高等优异的力学性能,纤维增强树脂基复合材料结构在航空航天、海洋工程及汽车等各种民用领域具有广泛而重要的应用。而树脂基体的高阻尼特性和复合材料本身的各向异性使得这种先进复合材料同时展现出优良的阻尼特性,比普通金属高1-2个数量级。近年来,对于复合材料结构阻尼的设计与研究已逐渐引起人们的重视。本研究即针对目前对于复合材料结构阻尼性能日益增长的工程需求,采用悬臂梁法和有限元设计相结合的方法对复合材料板簧结构阻尼性能进行了系统的试验研究和理论分析。
制备了不同铺层角度的玻璃纤维/环氧、玻璃纤维/增韧环氧和碳纤维/增韧环氧共九组复合材料单向板与复合材料板簧结构试件,进行了各项力学性能试验与振动阻尼性能试验。对复合材料单向板及其板簧结构阻尼特征进行了试验研究,并根据半功率带宽-Matlab法,对实时设备显示图数据作进一步分析处理,获得准确的半功率带宽值,再通过理论公式计算最终获得复合材料单向板及其板簧结构阻尼性能(损耗因子)。在有限元分析过程中,根据有限元模态应变能量法和复合材料结构力学理论,建立了复合材料板簧结构阻尼分析的极限状态方程。在试验基础上,编制了基于ANSYS软件的有限元设计分析软件,实现了复合材料板簧结构阻尼性能的有限元分析与设计。并将理论结果与试验结果进行对比分析,两者吻合较好。
在有限元分析的基础上,进一步分析了不同铺层和不同材料组成(包括不同纤维和基体)对于复合材料结构阻尼性能的影响。并通过理论分析获得其最优铺层。本文试验和理论分析结果对于力学性能和阻尼性能两者兼顾的复合材料结构设计与分析具有一定的理论和实际应用价值。
Fiber reinforced polymer-matrix composites are widely used in aerospace, marine engineering and various civil applications, such as automobiles and so on, due to their exceptionally high specific stiffness and strength. The composites are known to exhibit material damping one or two orders higher than most common metals as a result of the high damping of polymer matrices and the material heterogeneity. And the significance of the damping to the dynamic performance of composites structures is broadly recognized in the recent years. Under the circumstances of high requirement to the structural damping of the composites in the engineering applications, the systemically experimental and theoretical study on the vibratioanl damping of the composites was accomplished in this paper, based on the cantilever beam method and the Finite Elemental Analysis (FEA).
Nine groups of laminae and leaf springs made of glass-fiber/epoxy resin, glass-fiber/toughened epoxy resin and carbon-fiber/toughened epoxy resin were manufactured, and different mechanical experiments and vibrational damping tests were performed. The experimental tests were conducted to obtain the mechanical parameters and damping parameters of the laminae and leaf springs. And a half-power bandwidth-Matlab method was used to get the exact values of half-power bandwidth, according to the actural curves from the detectors. And the loss factors of the composite laminae and leaf springs were finally obtained through the calculation by equations. In the finite elemental analysis, the limit state equation for damping analysis of the composite leaf spring structure was set up according to the mode strain energy method and composite structural mechanics. On the basis of experimental results, numerical simulation procedure for the finite elemental analysis based on ANSYS software was complied, which realize the finite elemental design and analysis for the structural damping of the fiber reinforced polymer-matrix composite leaf springs. Good agreement was shown in the comparison between the analytical and experimental results.
The study on the effect of the different layout and different constituents (including fiber and matrix) on the structural damping of the composites were further performed. Finally, the optimal layout was obtained as a result of the theoretical analysis. The experimental and theoretical results in the paper will be valuable to the composite structural design with high requirements both to the mechanical and damping performance.
制备了不同铺层角度的玻璃纤维/环氧、玻璃纤维/增韧环氧和碳纤维/增韧环氧共九组复合材料单向板与复合材料板簧结构试件,进行了各项力学性能试验与振动阻尼性能试验。对复合材料单向板及其板簧结构阻尼特征进行了试验研究,并根据半功率带宽-Matlab法,对实时设备显示图数据作进一步分析处理,获得准确的半功率带宽值,再通过理论公式计算最终获得复合材料单向板及其板簧结构阻尼性能(损耗因子)。在有限元分析过程中,根据有限元模态应变能量法和复合材料结构力学理论,建立了复合材料板簧结构阻尼分析的极限状态方程。在试验基础上,编制了基于ANSYS软件的有限元设计分析软件,实现了复合材料板簧结构阻尼性能的有限元分析与设计。并将理论结果与试验结果进行对比分析,两者吻合较好。
在有限元分析的基础上,进一步分析了不同铺层和不同材料组成(包括不同纤维和基体)对于复合材料结构阻尼性能的影响。并通过理论分析获得其最优铺层。本文试验和理论分析结果对于力学性能和阻尼性能两者兼顾的复合材料结构设计与分析具有一定的理论和实际应用价值。
Fiber reinforced polymer-matrix composites are widely used in aerospace, marine engineering and various civil applications, such as automobiles and so on, due to their exceptionally high specific stiffness and strength. The composites are known to exhibit material damping one or two orders higher than most common metals as a result of the high damping of polymer matrices and the material heterogeneity. And the significance of the damping to the dynamic performance of composites structures is broadly recognized in the recent years. Under the circumstances of high requirement to the structural damping of the composites in the engineering applications, the systemically experimental and theoretical study on the vibratioanl damping of the composites was accomplished in this paper, based on the cantilever beam method and the Finite Elemental Analysis (FEA).
Nine groups of laminae and leaf springs made of glass-fiber/epoxy resin, glass-fiber/toughened epoxy resin and carbon-fiber/toughened epoxy resin were manufactured, and different mechanical experiments and vibrational damping tests were performed. The experimental tests were conducted to obtain the mechanical parameters and damping parameters of the laminae and leaf springs. And a half-power bandwidth-Matlab method was used to get the exact values of half-power bandwidth, according to the actural curves from the detectors. And the loss factors of the composite laminae and leaf springs were finally obtained through the calculation by equations. In the finite elemental analysis, the limit state equation for damping analysis of the composite leaf spring structure was set up according to the mode strain energy method and composite structural mechanics. On the basis of experimental results, numerical simulation procedure for the finite elemental analysis based on ANSYS software was complied, which realize the finite elemental design and analysis for the structural damping of the fiber reinforced polymer-matrix composite leaf springs. Good agreement was shown in the comparison between the analytical and experimental results.
The study on the effect of the different layout and different constituents (including fiber and matrix) on the structural damping of the composites were further performed. Finally, the optimal layout was obtained as a result of the theoretical analysis. The experimental and theoretical results in the paper will be valuable to the composite structural design with high requirements both to the mechanical and damping performance.
引文
[1]杜善义.先进复合材料与航空航天[J].复合材料学报.2007,24(1)：1-12页
[2]沈军,谢怀勤.航空用复合材料的研究与应用进展[J].玻璃钢/复合材料.2006,(5)：48-54页
[3]伍必兴.聚合物基复合材料[M].北京：航空工业部教材编审室,1986,5-16页
[4]宋焕成,张佐光.混杂纤维复合材料[M].北京：北京航空航天大学,1988,7-22页
[5]刘隶华.粘弹阻尼减振降噪应用技术[M].北京：宇航出版社,1990,1-9页
[6]田农,薛忠民,陈淳等.纤维增强聚合物基复合材料阻尼性能的研究进展[J].玻璃钢/复合材料.2009,(1)：85-88页
[7]Schultz A B, Tsai S W. Dynamic moduli and damping ratio in fiber-reinforced composites [J]. Composite Materials.1968,(2):368-379P
[8]Hashin Z. Complex moduli of viscoelastic composites:Ⅰ.General theory and application to particulate composites [J]. Solid and Structure.1970,(6): 539-552P
[9]Adams R D, Fox MAO, Flood R J, et al. The dynamic properties of unidirectional carbon and glass fiber-reinforced plastics in torsion and flexure [J]. Comp Mater.1969,(3):594-603P
[10]Adams R D, Bacon D G C. Measurement of flexural dynamic capacity and dynamic young's modulus of metals and reinforced plastics [J]. Phys D: Appl Phy.1973,(6):27-41P
[11]Adams R D, Bacon D G C. Effect of fiber orientation and laminate geometry on the dynamic properties of CFRP [J]. Compos Mater.1973, (7):402-428P
[12]Ni R G, Adams R D. The damping and dynamic moduli of symmetric laminated composite beams:Theoretical and experimental results [J]. Compos Sci Technol.1984,(18):104-121P
[13]Lin D X, Ni R, Adams R D. Prediction and measurement of the vibrational parameters of carbon and glass-fiber reinforced plastic plates [J]. Compos Mater.1984,(18):132-152P
[14]Maheri M R, Adams R D. Finite element prediction of modal response of damped layered composite panels [J]. Compos Sci Technol.1995,(55): 13-23P
[15]Saravanos D A, Pereira J M. Effects of interply damping layers on the dynamic characteristics of composite plates [J]. AIAA.1992,30(12): 2906-2913P
[16]Cupial P, Niziol J. Vibration and damping analysis of a three-layered composite plate with a viscoelastic mid-layer [J]. Sound Vib.1995,183(1): 99-114P
[17]Berthelot J M, Sefrani Y. Damping analysis of unidirectional glass and Kevlar fiber composites [J]. Compos Sci Technol.2004, (64):1261-1278P
[18]Liao F S, Su A C, Hsu T C. Vibration damping of interleaved carbon fiber-epoxy composite beams [J]. Compos Mater.1994,28(8):1840-1854P
[19]Yim J H. A damping analysis of composite laminates using the closed form expression for the basic damping of Poisson's ratio [J]. Compos Struct.1999, (46):405-411P
[20]Yim J H, Jang B Z. An analytical method for prediction of the damping in symmetric balanced laminates composites [J]. Polym Compos.1999,20(2): 192-199P
[21]Yim J H, Gillespie Jr J W. Damping characteristics of 0° and 90° AS4/3501-6 unidirectional laminates including the transverse shear effect [J]. Compos Struct.2000,(50):217-225P
[22]Yihua C, Li M, Su Y, et al. Studies on damping characteristics and parameter optimization of anisotropic laminated damped structure [J]. Aircr Eng Aerosp Technol.2002,74(4):332-327P
[23]Berthelot J M. Damping analysis of laminated beams and plates using the Ritz method [J]. Compos Struct.2006,(74):186-201P
[24]Suzuki K, Kazuro K, Isao K, et al. Vibration and damping prediction of laminates with constrained viscoelastic layers-numerical analysis by a multilayer higher-order-deformable finite element and experimental observations [J]. Mech Adv Mater Struct.2003,10(1):43-75P
[25]Finegan I C, Ioana C, Gibson R F, et al. Analytical modeling of damping at micromechanical level in polmyer comopsites reinforced with coating fibers [J]. Comp Sci and Tech.2000,60(7):1077-1084P
[26]Hajime K, Manabu K, Satoshi M, et al. Damping properties of thermo plastic-elastomer interleaved carbon fiber-reinforced epoxy composites [J]. Comp Sci and Tech.2004,(64):2517-2526P
[27]Fujimoto J, Tamura T. Optical coherence tomography of glass reinforced polymer composites [J]. Comp Mater.1999,(4):365-371P
[28]Meunier M, Shenoi R A. Dynamic analysis of composite plates with damping modelled using high-order shear deformation theory [J]. Compos Struct.2001,(54):243-254P
[29]Plagianakos T S, Saravanos D A. High-order layerwise mechanics and finite element for the damped dynamic characteristics of sandwich composite beams [J]. Solids Struct.2004,(41):6853-6871P
[30]Assarar M, El Mahi A, Berthelot J M. Damping analysis of sandwich materials [J]. Compos Mater, submitted for publication.
[31]王晏研,陈喜荣,黄光速.复合阻尼材料最新研究进展[J].材料导报.2004,18(10)：54-56页
[32]李开明.复合高阻尼材料减振效能的研究[J].空间电子技术.2004,1(1)：42-54页
[33]赵新国,左梦春.采用粘弹阻尼结构降低车内噪声[J].汽车工艺与材料.1995,(8)：22-24页
[34]顾健,武高辉.新型阻尼材料的研究进展[J].材料导报.2006,20(12)：53-61页
[35]任润桃,郭万涛,马玉璞.结构型树脂基阻尼复合材料基体胶液阻尼性能研究[J].噪声与振动控制.2003,(2)：20-24页
[36]廖英强,杜楠等.复合材料的阻尼分析[J].玻璃纤维.2007,(1)：15-18页
[37]秦东奇,王静媛等.PU/PMMA IPN的阻尼行为研究[J].高分子材料科学与工程.2000,16(5)：95-98页
[38]钱军民,李旭祥.聚合物—无机纤维复合泡沫材料吸声性能的研究[J].高分子材料科学与工程.2001,17(4)：145-148页
[39]晏雄,张慧萍,住田雅夫.新型减振高分子复合材料研究[J].高分子材料科学与工程.2001,17(5)：86-89页
[40]李明俊,刘桂武等.粘接层对各向异性层合阻尼结构内耗特性的影响[J].复合材料学报.2005,22(4)：96-95页
[41]孙大刚,诸文农.阻尼减振结构的动态优化[J].工程机械.1997,28(11)：22-25页
[42]杨雪,王源升等.多层阻尼复合结构阻尼性能[J].复合材料学报.2005,22(3)：175-181页
[43]戴德沛.阻尼减振降噪技术[M].西安：西安交通大学出版社,1986,62-80页
[44]胡卫强,王敏庆,刘志宏.悬臂梁弯曲共振法自由阻尼结构试件设计研究[J].实验力学.2008,23(3)：241-247页
[45]Chanadra R, Singh S P, Gupta K. Damping studies in fiber-reinforced composites-a review [J]. Composite Structures.1999,(46):41-51P
[46]Adams R D, Maheri M R. Dynamic flexural properties of anisotropic fibrous composite beams [J]. Comp Sci Tech.1994,50(4):497-514P
[47]McIntyre M E, Woodhouse J. On measuring the elastic and damping constants of orthotropic sheet materials [J]. Acta Met.1988,36(6): 1397-1416P
[48]Talbot J P, Woodhouse J. The vibration damping of laminated plates [J]. Composites Part A.1997,28(A):1007-1012P
[49]Crane R M, Gillespe Jr. Analytical model for prediction of the damping loss factor of composite materials [J]. Polym Compos.1992,13(3):179-190P
[50]Barakanov R G, Gassan J. Frequency response analysis of laminated composite beams [J]. Mech Comp Mater.1994,30(5):664-674P
[51]范永忠,孙康等.环氧树脂混杂复合材料的阻尼性能研究[J].材料工程.2000,(3)：29-35页
[52]李明俊,苏媛等.层合阻尼结构各向异性设计之阻尼特性分析[J].复合材料学报.2002,19(3)：94-97P
[53]Cox H L. The elasticity and strength of paper and other fibrous materials [J]. British J Appl Phys.1952,(3):72-79P
[54]White R G, Abdin E M Y. Dynamic properties of aligned short carbon fiber-reinforced plastics in flexure and torsion [J]. Composites.1985,16(4): 293-306P
[55]Willway T A, White R G. The effect of matrix complex modulus on damping properties of CFRP laminate [J]. Comp Sci Tech.1989,(36):77-94P
[56]Chang S, Bert C W. Analysis of damping for filamentary composite materials [C]. In:Proceedings of the Sixth St. Louis Symposium, American Society of Metals,11-12 May 1973:51-62P
[57]Aboudi J. Micromechanical analysis of composites by method of cells[J]. Appl Mech Rev.1989,(42):193-221P
[58]Kaliske M, Rother H. Damping characterization of unidirectional fiber- reinforced composites [J]. Comp Engrg.1995,5(5):551-567P
[59]Hwang S J, Gibson R F. Prediction of fiber-matrix interphase effects on damping of composites using a micromechanical strain energy/finite element approach [J]. Composite Engineering.1993,3(10):975-984P
[60]Saravanos D A, Chamis C C. Unified micromechanics of damping for unidirectional and off-axis fiber composites [J]. Comp Tech Res.1990, 12(1):31-40P
[61]张少辉,陈花玲等.纤维增强树脂基复合材料阻尼特性的数值模拟[J].航空材料学报.2004,24(3)：10-14页
[62]任勇生,张晓梅等.含SMA约束层的复合材料矩形板的阻尼能力分析[J].机械强度.2002,24(3)：339-344页
[63]Tsai J L, Chi Y K. Effect of fiber array on damping behaviors of fiber composites [J]. Composites.2008,(39):1196-1204P
[64]任勇生,刘立厚.纤维增强复合材料结构阻尼研究进展[J].力学与实践.2004,26(1)：9-14页
[65]Trego A,Eastman D. Flexural damping predications of mechanical elements designed using stress coupled, co-cured damping fiber reinforced composites [J]. Advanced Materials.1999,31(1):7-17P
[66]Moser K,Lumassegger M. Increasing the damping of flexural vibration of laminated FPC structures by incorporation of soft intermediate plies with minimum reduction of stiffness [J]. Comp Struct.1988,(10):321-333P
[67]张少辉,陈花玲.共固化复合材料粘弹阻尼结构的损耗因子研究[J].航空材料学报.2005,25(1)：53-57页
[68]Mantena P R, Gibson R F. Dynamic mechanical properties of hybrid polyethylene/graphite composites [C]. In:Proc.22nd International SAMPE Technical Conference. Covina, CA:Society for the Advancement of Materials and Process Engineering.1990:370-382P
[69]杨霜,孙康等.混杂纤维复合材料阻尼性能的研究[J].纤维复合材料.2002,(1)：6-10页
[70]GB/T 18258-2000《阻尼材料-阻尼性能测试方法》[s].国家质量技术监督局,2000,11
[2]沈军,谢怀勤.航空用复合材料的研究与应用进展[J].玻璃钢/复合材料.2006,(5)：48-54页
[3]伍必兴.聚合物基复合材料[M].北京：航空工业部教材编审室,1986,5-16页
[4]宋焕成,张佐光.混杂纤维复合材料[M].北京：北京航空航天大学,1988,7-22页
[5]刘隶华.粘弹阻尼减振降噪应用技术[M].北京：宇航出版社,1990,1-9页
[6]田农,薛忠民,陈淳等.纤维增强聚合物基复合材料阻尼性能的研究进展[J].玻璃钢/复合材料.2009,(1)：85-88页
[7]Schultz A B, Tsai S W. Dynamic moduli and damping ratio in fiber-reinforced composites [J]. Composite Materials.1968,(2):368-379P
[8]Hashin Z. Complex moduli of viscoelastic composites:Ⅰ.General theory and application to particulate composites [J]. Solid and Structure.1970,(6): 539-552P
[9]Adams R D, Fox MAO, Flood R J, et al. The dynamic properties of unidirectional carbon and glass fiber-reinforced plastics in torsion and flexure [J]. Comp Mater.1969,(3):594-603P
[10]Adams R D, Bacon D G C. Measurement of flexural dynamic capacity and dynamic young's modulus of metals and reinforced plastics [J]. Phys D: Appl Phy.1973,(6):27-41P
[11]Adams R D, Bacon D G C. Effect of fiber orientation and laminate geometry on the dynamic properties of CFRP [J]. Compos Mater.1973, (7):402-428P
[12]Ni R G, Adams R D. The damping and dynamic moduli of symmetric laminated composite beams:Theoretical and experimental results [J]. Compos Sci Technol.1984,(18):104-121P
[13]Lin D X, Ni R, Adams R D. Prediction and measurement of the vibrational parameters of carbon and glass-fiber reinforced plastic plates [J]. Compos Mater.1984,(18):132-152P
[14]Maheri M R, Adams R D. Finite element prediction of modal response of damped layered composite panels [J]. Compos Sci Technol.1995,(55): 13-23P
[15]Saravanos D A, Pereira J M. Effects of interply damping layers on the dynamic characteristics of composite plates [J]. AIAA.1992,30(12): 2906-2913P
[16]Cupial P, Niziol J. Vibration and damping analysis of a three-layered composite plate with a viscoelastic mid-layer [J]. Sound Vib.1995,183(1): 99-114P
[17]Berthelot J M, Sefrani Y. Damping analysis of unidirectional glass and Kevlar fiber composites [J]. Compos Sci Technol.2004, (64):1261-1278P
[18]Liao F S, Su A C, Hsu T C. Vibration damping of interleaved carbon fiber-epoxy composite beams [J]. Compos Mater.1994,28(8):1840-1854P
[19]Yim J H. A damping analysis of composite laminates using the closed form expression for the basic damping of Poisson's ratio [J]. Compos Struct.1999, (46):405-411P
[20]Yim J H, Jang B Z. An analytical method for prediction of the damping in symmetric balanced laminates composites [J]. Polym Compos.1999,20(2): 192-199P
[21]Yim J H, Gillespie Jr J W. Damping characteristics of 0° and 90° AS4/3501-6 unidirectional laminates including the transverse shear effect [J]. Compos Struct.2000,(50):217-225P
[22]Yihua C, Li M, Su Y, et al. Studies on damping characteristics and parameter optimization of anisotropic laminated damped structure [J]. Aircr Eng Aerosp Technol.2002,74(4):332-327P
[23]Berthelot J M. Damping analysis of laminated beams and plates using the Ritz method [J]. Compos Struct.2006,(74):186-201P
[24]Suzuki K, Kazuro K, Isao K, et al. Vibration and damping prediction of laminates with constrained viscoelastic layers-numerical analysis by a multilayer higher-order-deformable finite element and experimental observations [J]. Mech Adv Mater Struct.2003,10(1):43-75P
[25]Finegan I C, Ioana C, Gibson R F, et al. Analytical modeling of damping at micromechanical level in polmyer comopsites reinforced with coating fibers [J]. Comp Sci and Tech.2000,60(7):1077-1084P
[26]Hajime K, Manabu K, Satoshi M, et al. Damping properties of thermo plastic-elastomer interleaved carbon fiber-reinforced epoxy composites [J]. Comp Sci and Tech.2004,(64):2517-2526P
[27]Fujimoto J, Tamura T. Optical coherence tomography of glass reinforced polymer composites [J]. Comp Mater.1999,(4):365-371P
[28]Meunier M, Shenoi R A. Dynamic analysis of composite plates with damping modelled using high-order shear deformation theory [J]. Compos Struct.2001,(54):243-254P
[29]Plagianakos T S, Saravanos D A. High-order layerwise mechanics and finite element for the damped dynamic characteristics of sandwich composite beams [J]. Solids Struct.2004,(41):6853-6871P
[30]Assarar M, El Mahi A, Berthelot J M. Damping analysis of sandwich materials [J]. Compos Mater, submitted for publication.
[31]王晏研,陈喜荣,黄光速.复合阻尼材料最新研究进展[J].材料导报.2004,18(10)：54-56页
[32]李开明.复合高阻尼材料减振效能的研究[J].空间电子技术.2004,1(1)：42-54页
[33]赵新国,左梦春.采用粘弹阻尼结构降低车内噪声[J].汽车工艺与材料.1995,(8)：22-24页
[34]顾健,武高辉.新型阻尼材料的研究进展[J].材料导报.2006,20(12)：53-61页
[35]任润桃,郭万涛,马玉璞.结构型树脂基阻尼复合材料基体胶液阻尼性能研究[J].噪声与振动控制.2003,(2)：20-24页
[36]廖英强,杜楠等.复合材料的阻尼分析[J].玻璃纤维.2007,(1)：15-18页
[37]秦东奇,王静媛等.PU/PMMA IPN的阻尼行为研究[J].高分子材料科学与工程.2000,16(5)：95-98页
[38]钱军民,李旭祥.聚合物—无机纤维复合泡沫材料吸声性能的研究[J].高分子材料科学与工程.2001,17(4)：145-148页
[39]晏雄,张慧萍,住田雅夫.新型减振高分子复合材料研究[J].高分子材料科学与工程.2001,17(5)：86-89页
[40]李明俊,刘桂武等.粘接层对各向异性层合阻尼结构内耗特性的影响[J].复合材料学报.2005,22(4)：96-95页
[41]孙大刚,诸文农.阻尼减振结构的动态优化[J].工程机械.1997,28(11)：22-25页
[42]杨雪,王源升等.多层阻尼复合结构阻尼性能[J].复合材料学报.2005,22(3)：175-181页
[43]戴德沛.阻尼减振降噪技术[M].西安：西安交通大学出版社,1986,62-80页
[44]胡卫强,王敏庆,刘志宏.悬臂梁弯曲共振法自由阻尼结构试件设计研究[J].实验力学.2008,23(3)：241-247页
[45]Chanadra R, Singh S P, Gupta K. Damping studies in fiber-reinforced composites-a review [J]. Composite Structures.1999,(46):41-51P
[46]Adams R D, Maheri M R. Dynamic flexural properties of anisotropic fibrous composite beams [J]. Comp Sci Tech.1994,50(4):497-514P
[47]McIntyre M E, Woodhouse J. On measuring the elastic and damping constants of orthotropic sheet materials [J]. Acta Met.1988,36(6): 1397-1416P
[48]Talbot J P, Woodhouse J. The vibration damping of laminated plates [J]. Composites Part A.1997,28(A):1007-1012P
[49]Crane R M, Gillespe Jr. Analytical model for prediction of the damping loss factor of composite materials [J]. Polym Compos.1992,13(3):179-190P
[50]Barakanov R G, Gassan J. Frequency response analysis of laminated composite beams [J]. Mech Comp Mater.1994,30(5):664-674P
[51]范永忠,孙康等.环氧树脂混杂复合材料的阻尼性能研究[J].材料工程.2000,(3)：29-35页
[52]李明俊,苏媛等.层合阻尼结构各向异性设计之阻尼特性分析[J].复合材料学报.2002,19(3)：94-97P
[53]Cox H L. The elasticity and strength of paper and other fibrous materials [J]. British J Appl Phys.1952,(3):72-79P
[54]White R G, Abdin E M Y. Dynamic properties of aligned short carbon fiber-reinforced plastics in flexure and torsion [J]. Composites.1985,16(4): 293-306P
[55]Willway T A, White R G. The effect of matrix complex modulus on damping properties of CFRP laminate [J]. Comp Sci Tech.1989,(36):77-94P
[56]Chang S, Bert C W. Analysis of damping for filamentary composite materials [C]. In:Proceedings of the Sixth St. Louis Symposium, American Society of Metals,11-12 May 1973:51-62P
[57]Aboudi J. Micromechanical analysis of composites by method of cells[J]. Appl Mech Rev.1989,(42):193-221P
[58]Kaliske M, Rother H. Damping characterization of unidirectional fiber- reinforced composites [J]. Comp Engrg.1995,5(5):551-567P
[59]Hwang S J, Gibson R F. Prediction of fiber-matrix interphase effects on damping of composites using a micromechanical strain energy/finite element approach [J]. Composite Engineering.1993,3(10):975-984P
[60]Saravanos D A, Chamis C C. Unified micromechanics of damping for unidirectional and off-axis fiber composites [J]. Comp Tech Res.1990, 12(1):31-40P
[61]张少辉,陈花玲等.纤维增强树脂基复合材料阻尼特性的数值模拟[J].航空材料学报.2004,24(3)：10-14页
[62]任勇生,张晓梅等.含SMA约束层的复合材料矩形板的阻尼能力分析[J].机械强度.2002,24(3)：339-344页
[63]Tsai J L, Chi Y K. Effect of fiber array on damping behaviors of fiber composites [J]. Composites.2008,(39):1196-1204P
[64]任勇生,刘立厚.纤维增强复合材料结构阻尼研究进展[J].力学与实践.2004,26(1)：9-14页
[65]Trego A,Eastman D. Flexural damping predications of mechanical elements designed using stress coupled, co-cured damping fiber reinforced composites [J]. Advanced Materials.1999,31(1):7-17P
[66]Moser K,Lumassegger M. Increasing the damping of flexural vibration of laminated FPC structures by incorporation of soft intermediate plies with minimum reduction of stiffness [J]. Comp Struct.1988,(10):321-333P
[67]张少辉,陈花玲.共固化复合材料粘弹阻尼结构的损耗因子研究[J].航空材料学报.2005,25(1)：53-57页
[68]Mantena P R, Gibson R F. Dynamic mechanical properties of hybrid polyethylene/graphite composites [C]. In:Proc.22nd International SAMPE Technical Conference. Covina, CA:Society for the Advancement of Materials and Process Engineering.1990:370-382P
[69]杨霜,孙康等.混杂纤维复合材料阻尼性能的研究[J].纤维复合材料.2002,(1)：6-10页
[70]GB/T 18258-2000《阻尼材料-阻尼性能测试方法》[s].国家质量技术监督局,2000,11