考虑损伤效应的粘弹性/压电智能层合结构的非线性静动力学研究
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摘要
本论文以纤维增强复合材料层合板结构以及压电膜片与纤维增强复合材料层合板所构成的压电智能层合板结构为研究对象,系统地研究了考虑损伤效应的粘弹性层合板的非线性动力响应、非线性振动、蠕变后屈曲、分岔与混沌行为,以及具损伤压电智能层合板的非线性动力稳定性问题。其研究成果不仅具有重要的学术价值,也具有非常重要的工程应用意义。本论文的主要研究工作如下。
基于粘弹性理论和连续介质损伤力学,采用Boltzmann叠加原理和应变能等效原理,建立了具正交各向异性损伤的粘弹性复合材料的本构关系。设每一单层沿厚度方向有相同的损伤程度,建立了适用于复合材料层合板整体分析的损伤粘弹性本构模型。根据复合材料力学和Von Kármán非线性板理论,建立了考虑损伤效应的粘弹性层合板的非线性运动控制方程。采用Kachanov损伤演化方程来表征损伤的发展规律,综合利用有限差分法、Newmark法、Newton-Cotes法和迭代法对整个问题进行求解。具体考察了损伤效应、载荷参数、结构几何参数、铺设状况和材料参数对损伤粘弹性层合板起裂的临界时间和非线性动力响应曲线的影响,并与有关文献的结果进行了比较。
根据Timoshenko-Mindlin中厚板理论、应变能等效原理和Boltzmann叠加原理,推导了考虑横向剪切变形和损伤效应的粘弹性层合中厚板的非线性动力学方程,采用Galerkin技术,将非线性积分—偏微分型方程组转化为非线性积分—常微分型方程组。在数值计算中,粘弹性材料取为标准线性固体,基于Kachanov损伤演化模型,讨论了不同跨厚比、长宽比和边界条件对损伤粘弹性层合中厚板的非线性自由振动幅频响应曲线的影响,以及横向剪切变形和材料参数对损伤粘弹性复合材料层合中厚板的非线性自由振动基频的影响,并与有关文献的结果进行了比较。
基于已建立的具损伤效应的粘弹性复合材料的本构方程,考虑几何非线性、横向剪切变形、损伤效应和初始几何缺陷,建立了正交铺设粘弹性层合圆柱曲板在轴向压力作用下的非线性微分平衡方程。算例中,仍然采用Kachanov型的损伤演化模型,但考虑拉压应力对材料的损伤演化率具有不同的贡献,讨论了几何非线性对粘弹性层合板蠕变后屈曲行为的影响,以及横向剪切变形、轴向压力、结构几何参数和铺设层数对具损伤粘弹性层合圆柱曲板的蠕变后屈曲性能和损伤演化行为的影响。
在有限变形条件下,对具损伤粘弹性层合中厚板的分岔与混沌特性进行了研究。采用Galerkin截断,并引进新的状态变量,综合应用非线性动力学中的近代
In this dissertation, considering fibre-reinforced composite laminated plates and piezoelectric laminated structures composed by the piezoelectric membranes and fibre-reinforced composite laminated plates as the subjects investigated, the nonlinear dynamic response, nonlinear vibration, creep postbuckling, bifurcation and chaos behaviors of viscoelastic laminated plates including damage effect, as well as the nonlinear dynamic stability of piezoelectric laminated plates with damage are systematically studied. The research results have an important meaning not only in the academic but also in the practical engineering. The main results contain as follows:Based on the viscoelastic theory and the continuum damage mechanics, and according to the Boltzmann superposition principle and strain energy equivalence, a constitutive model is established for viscoelastic composites with orthotropic damage. Suppose the damage variables remain constant throughout the thickness in each layer, then, the damage/viscoelastic constitutive model suited for the global analysis of the laminated plates is obtained. By using the composite mechanics and Von Karman's nonlinear theory, the nonlinear governing equations of motion for the viscoelastic laminated plates with damage are derived. The damage evolution law is characterized by the Kachanov damage evolution equations. Through applying the finite difference method, Newmark method, Newton-Cotes method and iterative procedure, the governing equations are solved. The comparative studies are carried out to validate the validity of the present method. The influences of damage effect, load parameters, geometric and material parameters as well as ply orientations on the critical time of failure initiation and nonlinear dynamic responses for the damage/viscoelastic laminated plates are discussed in detail.According to Timoshenko-Mindlin theory of thick plates, strain energy equivalence hypotheses and Boltzmann superposition principle, the nonlinear dynamic equations of viscoelastic laminated plates including the effects of damage and transverse shear deformation are given. By employing the Galerkin method, the original integro-partial-differential equations are transformed into a set of integro-ordinary equations. In the numerical calculations, the viscoelastic material is taken as a standard linear solid and the damage evolution model proposed by Kachanov is adopted. Firstly, the present result is compared with available data. Then, the influences of different span-thickness and aspect ratio as well as boundary condition on the nonlinear amplitude-frequency responses of the damage/viscoelastic
基于粘弹性理论和连续介质损伤力学,采用Boltzmann叠加原理和应变能等效原理,建立了具正交各向异性损伤的粘弹性复合材料的本构关系。设每一单层沿厚度方向有相同的损伤程度,建立了适用于复合材料层合板整体分析的损伤粘弹性本构模型。根据复合材料力学和Von Kármán非线性板理论,建立了考虑损伤效应的粘弹性层合板的非线性运动控制方程。采用Kachanov损伤演化方程来表征损伤的发展规律,综合利用有限差分法、Newmark法、Newton-Cotes法和迭代法对整个问题进行求解。具体考察了损伤效应、载荷参数、结构几何参数、铺设状况和材料参数对损伤粘弹性层合板起裂的临界时间和非线性动力响应曲线的影响,并与有关文献的结果进行了比较。
根据Timoshenko-Mindlin中厚板理论、应变能等效原理和Boltzmann叠加原理,推导了考虑横向剪切变形和损伤效应的粘弹性层合中厚板的非线性动力学方程,采用Galerkin技术,将非线性积分—偏微分型方程组转化为非线性积分—常微分型方程组。在数值计算中,粘弹性材料取为标准线性固体,基于Kachanov损伤演化模型,讨论了不同跨厚比、长宽比和边界条件对损伤粘弹性层合中厚板的非线性自由振动幅频响应曲线的影响,以及横向剪切变形和材料参数对损伤粘弹性复合材料层合中厚板的非线性自由振动基频的影响,并与有关文献的结果进行了比较。
基于已建立的具损伤效应的粘弹性复合材料的本构方程,考虑几何非线性、横向剪切变形、损伤效应和初始几何缺陷,建立了正交铺设粘弹性层合圆柱曲板在轴向压力作用下的非线性微分平衡方程。算例中,仍然采用Kachanov型的损伤演化模型,但考虑拉压应力对材料的损伤演化率具有不同的贡献,讨论了几何非线性对粘弹性层合板蠕变后屈曲行为的影响,以及横向剪切变形、轴向压力、结构几何参数和铺设层数对具损伤粘弹性层合圆柱曲板的蠕变后屈曲性能和损伤演化行为的影响。
在有限变形条件下,对具损伤粘弹性层合中厚板的分岔与混沌特性进行了研究。采用Galerkin截断,并引进新的状态变量,综合应用非线性动力学中的近代
In this dissertation, considering fibre-reinforced composite laminated plates and piezoelectric laminated structures composed by the piezoelectric membranes and fibre-reinforced composite laminated plates as the subjects investigated, the nonlinear dynamic response, nonlinear vibration, creep postbuckling, bifurcation and chaos behaviors of viscoelastic laminated plates including damage effect, as well as the nonlinear dynamic stability of piezoelectric laminated plates with damage are systematically studied. The research results have an important meaning not only in the academic but also in the practical engineering. The main results contain as follows:Based on the viscoelastic theory and the continuum damage mechanics, and according to the Boltzmann superposition principle and strain energy equivalence, a constitutive model is established for viscoelastic composites with orthotropic damage. Suppose the damage variables remain constant throughout the thickness in each layer, then, the damage/viscoelastic constitutive model suited for the global analysis of the laminated plates is obtained. By using the composite mechanics and Von Karman's nonlinear theory, the nonlinear governing equations of motion for the viscoelastic laminated plates with damage are derived. The damage evolution law is characterized by the Kachanov damage evolution equations. Through applying the finite difference method, Newmark method, Newton-Cotes method and iterative procedure, the governing equations are solved. The comparative studies are carried out to validate the validity of the present method. The influences of damage effect, load parameters, geometric and material parameters as well as ply orientations on the critical time of failure initiation and nonlinear dynamic responses for the damage/viscoelastic laminated plates are discussed in detail.According to Timoshenko-Mindlin theory of thick plates, strain energy equivalence hypotheses and Boltzmann superposition principle, the nonlinear dynamic equations of viscoelastic laminated plates including the effects of damage and transverse shear deformation are given. By employing the Galerkin method, the original integro-partial-differential equations are transformed into a set of integro-ordinary equations. In the numerical calculations, the viscoelastic material is taken as a standard linear solid and the damage evolution model proposed by Kachanov is adopted. Firstly, the present result is compared with available data. Then, the influences of different span-thickness and aspect ratio as well as boundary condition on the nonlinear amplitude-frequency responses of the damage/viscoelastic
引文
[1] Minahen T M, Knauss W G. Creep buckling of viscoelastic structures. International Journal of Solids and Structures, 1993, 30 (8): 1075-1092
[2] 杨挺青,张晓春.黏弹性薄板蠕变屈曲的载荷—时间特性研究.力学学报,2000,32(3):319-325
[3] 王颖坚,王震鸣.正交铺设层合圆柱曲板的蠕变失稳.应用数学和力学,1993,14(4):295-300
[4] 彭凡,傅衣铭.黏弹性结构蠕变屈曲特性的分析.力学学报,2003,35(3):353-356
[5] Hyasov M H, Akoz A Y. The vibration and dynamic stability of viscoelastic plates. International Journal of Engineering Science, 2000, 38:695-714
[6] Cederbaum G, Aboudi J, Elishakoff I. Dynamic instability of shear-deformable viscoelastic laminated plates by Lyapunov exponents. International Journal of Solids and Structures, 1991, 28(3): 317-327
[7] Aboudi J, Cederbaum G. Dynamic stability analysis of viscoelastic plates by Lyapunov exponents. Journal of Sound and Vibration, 1990, 139(3): 459-467
[8] Chandiramani N K, Librescu L. The theory of orthotropic viscoelastic shear deformable composite flat panels and their dynamic stability. International Journal of Solids and Structures, 1989, 25(5): 465-482
[9] Librescu L, Chandiramani N K. Dynamic stability of transversely isotropic viscoelastic plates. Journal of Sound and Vibration, 1989, 130(3): 467-486
[10] Touati D, Cederbaum G. Postbuckling analysis of imperfect nonlinear viscoelastic columns. International Journal of Solids and Structures, 1997, 34(14): 1751-1760
[11] Touati D, Cederbaum G. The effect of shear deformation on the post-buckling behavior of imperfect nonlinear viscoelastic columns. Archive of Applied Mechancis, 1997, 67:364-374
[12] Huang N N. Viscoelastic analysis of creep response for uniaxilly-compressed laminates with initial deflection including the effect of physical aging. International Journal of Solids and Structures, 1998, 35(4): 1515-1532
[13] Shalev D, Aboudi J. Postbuckling analysis of viscoelastic laminated plates using higher-order theory. International Journal of Solids and Structures, 1991, 27(14): 1747-1755
[14] Touati D, Cederbaum G. Postbuckling of non-linear viscoelastic imperfect laminated plates Part Ⅰ: material considerations. Composite Structures, 1998, 42: 33-41
[15] Touati D, Cederbaum G. Postbuckling of non-linear viscoelastic imperfect laminated plates, Part Ⅱ: Structural analysis. Composite Structures, 1998, (42): 43-51
[16] Cederbaum G, Touati D. Postbuckling analysis of imperfect non-linear viscoelastic cylindrical panels. International Journal of Non-linear Mechanics, 2002, 37:757-762
[17] Kim T W, Kim J H. Nonlinear vibration of viscoelastic laminated composite plates. International Journal of Solids and Structures, 2002, 39:2857-2870
[18] Yu S C, Huang S C. Vibration of a three-layered viscoelastic sandwich circular plate. International Journal of Mechanical Sciences, 2001(43): 2215-2236
[19] Chen L Q, Zu J W, Wu J. Steady-state response of the parametrically excited axially moving string constituted by the Boltzmann superposition principle. Atca Mechanica, 2003, 162:143-155
[20] 吴强,凌道盛,徐兴.粘弹性几何非线性夹层梁动响应分析.计算力学学报,1997,14(1):36-42
[21] Daya E M, Ferry M R. A numerical method for nonlinear eignvalue problems application to vibrations of viscoelastic structures. Computers and Structures, 2001, 79:533-541
[22] Rossikhin Y A, Shitikova M V. A new method for solving dynamic problems of fractional derivative viscoelasticity. International Journal of Engineering Science, 2001, 39:149-176
[23] Drozdov A D. Stability of viscoelastic shells under periodic and stochastic loading. Mechanics Research Communications, 1993, 20(6): 481-486
[24] Drozdov A D, et al. Stability of nonhomogeneous aging viscoelastic bodies under dynamic loading. Nonlinear Analysis, 1995, 24(9): 1361-1375
[25] Drozdov A D. Lyapunov stability of a class of operator integro-differential equations with applications to viscoelasticity. Mathematical Methods in the Applied Sciences, 1996, 19(5): 341-361
[26] Drozdov A D. Almost sure stability of viscoelastic structural members driven by random loads. Journal of Sound and Vibration, 1996, 197(3): 293-307
[27] Touati D, Cederbaum G. Dynamic stability of nonlinear viscoelastic plates. International Journal Solids and Structures, 1994, 31 (17): 2367-2376
[28] Touati D, Cederbaum G. Influence of large deflections on the dynamic stability of nonlinear viscoelastic plates. Acta Mechanica, 1995, 113: 215-231
[29] 朱媛媛,程昌钧.粘弹性矩形板的稳定性分析.固体力学学报,1996,17(3):257-261
[30] 程昌钧,范晓军.黏弹性环形板的临界载荷及动力稳定性.力学学报,2001,33(3):365-375
[31] 彭凡,傅衣铭.粘弹性板的非线性动力稳定特性分析.固体力学学报,2004,25(1):115-118
[32] Suire G, Cederbaum G. Periodic and chaotic behavior of viscoelastic nonlinear (elastica) bars under harmonic excitations. International Journal of Mechanical Sciences, 1995, 37(7): 753-772
[33] Suire G, Cederbaum G. Elastica type dynamic stability analysis of viscoelastic column. Archive of Applied Mechanics, 1994, 64:307-316
[34] Chen Li-Qun, Cheng Chang-Jun. Dynamical behaveor of nonlinear viscoelastic columns based on 2-order Galerkin truncation. Mechanics Research Communication, 2000, 27(4): 413-419
[35] Argyris J, Belubekian V, Ovakimyan N, et al. Chaotic vibrations of a nonlinear viscoelastic beam. Chaos, Solitons & Fractals, 1996, 7(2): 151-163
[36] 陈立群,程昌钧.非线性粘弹性柱的稳定性和混沌运动.应用数学和力学,2000,21(9):890-896
[37] 陈立群,程昌钧.非线性粘弹性梁的动力学行为.应用数学和力学,2000,21(9):897-902
[38] 陈立群,程昌钧,张能辉.具有几何和物理非线性粘弹性梁的混沌运动.工程力学,2001,18(1):1-6
[39] 李根国,朱正佑,程昌钧.非线性粘弹性Timoshenko梁动力学行为的分析.力学季刊,2001,22(3):346-351
[40] Ding Rui, Zhu Zheng-You, Cheng Chang-Jun. Dynamic properties of viscoelastic plates. In: Chien Wei-Zang, et al., ed. Proceeding 3rd Inter. Conf. on Nonlinear Mech., Shanghai: Shanghai Univ. Press, 1998:185-190
[41] Zhu Yan-Yan, Zhang Neng-Hui, Miura F. dynamical behavior of viscoelastic rectangular plates. In: Chien Wei-Zang, et al., ed. Proceeding 3rd Inter. Conf. on Nonlinear Mech., Shanghai: Shanghai Univ. Press, 1998:445-450
[42] 程昌钧,张能辉.粘弹性矩形板的混沌和超混沌行为.力学学报,1998,30 (6):690-699
[43] Cheng Chang-Jun, Zhang Neng-Hui. Buckling and multiple equilibrium states of viscoelastic rectangular plates. Journal of Shanghai University (English Edition), 1999, 3(3): 192-198
[44] Li Jing-Jing, Cheng Chang-Jun, Zhang Neng-Hui. Dynamic stability of viscoelastic plates with finite deformation and shear effects. Journal of Shanghai University (English Edition), 2002, 6(2): 115-124
[45] 李晶晶,程昌钧.粘弹性基础上粘弹性矩形板的非线性振动响应分析.上海大学学报,2000,6(3):231-236
[46] Zhang Neng-Hui, Cheng Chang-Jun. Chaos behavior of viscoelastic plates in supersonic flow. In: Chien Wei-Zang, et al., ed. Proceeding 3rd Inter. Conf. on Nonlinear Mech., Shanghai: Shanghai Univ. Press, 1998:432-436
[47] 程昌钧,范晓军.粘弹性圆薄板的动力学行为.固体力学学报,2000,21(4):306-312
[48] 陈立群,程昌钧.非线性粘弹性板的失稳条件.力学季刊,2001,22(2):247-251
[49] 陈立群,程昌钧.粘弹性板混沌振动的输出变量反馈线性化控制.应用数学和力学,1999,20(12):1229-1234
[50] 张能辉,程昌钧.粘弹性板动力稳定性分析中的两模态Galerkin逼近.应用数学和力学,2003,24(3):221-227
[51] Sun Y X, Zheng S Y. Chaotic dynamic analysis of viscoelastic plates. International Journal of Mechanical Sciences, 2001, 43:1195-1208
[52] Han Q, Hu H. Bifurcation analysis of a nonlinear viscoelastic panel. Europe Journal of Mechanics A/Solids, 2001, 20:827-839
[53] 吴晓.屈曲粘弹性矩形板的非线性振动分岔.力学与实践,2001,21(1):40-42
[54] 吴晓.屈曲粘弹性倾斜矩形板的非线性振动分岔.振动与冲击,2001,20(1):69-71
[55] 张能辉.粘弹性板壳结构的静动力分析:[博士学位论文].兰州大学,1998
[56] 程昌钧,张能辉.轴压作用下粘弹性柱壳的动力学行为.应用数学和力学,2001,22(1):1-8
[57] 张能辉,程昌钧.轴压作用下粘弹性柱壳的动力学行为.应用数学和力学,2001,22(10):1001-1007
[58] 杨挺青.粘弹性力学.武汉:华中理工大学出版社,1990
[59] 周光泉,刘孝敏.粘弹性理论.合肥:中国科技大学出版社,1996
[60] Christensen R M. Theory of viscoelasticity: an introduction. New York: Academic Press, 1992
[61] 张义同.热粘弹性理论.天津:天津大学出版社,2002
[62] Kachanov L M. Time of the rupture process under creep conditions. TVZ Akad. Nauk. SSR, Otd. Tech. Nauk., 1958, 8:26-31
[63] Rabotnov Y N. On the equations of state for creep. In: Progress in Applied Mechanics, The Prager Anniversary Volume. MacMillan, New York, 1963, 307-315
[64] Lemaitre J. How to use damage mechanics. Nuclear Engineering and Design Journal, 1984, 80:233-245
[65] Lemaitre J. A course on damage mechanics. Berlin, Springer-Verlag, 1996
[66] Lemaitre J, Chaboche J L. Mechanics of solid materials. Cambridge University Press, 1990
[67] Janson J, Hult J. Fracture mechanics and damage mechanics: a combined approach. Journal de Mecanique Appliquee, 1977, 1(1): 69-84
[68] Hayhurst D R, Leckie F A. The effect of creep constitutive and damage relationships upon the rupture time of a solid circular torsion bar. Journal of Mechanics and Physics of Solids, 1973, 21:431-446
[69] Murakami S. Notion of continuum damage mechanics and its application to anisotropic creep damage theory. Journal of Engineering Material Technology, 1983, 105:99-105
[70] Murakami S, Sanomura Y. Analysis of the coupled effect of plastic damage and creep damage in Nimonic 80A at finite deformation. Engineering Fracture Mechancis, 1986, 25(5/6): 693-704
[71] Murakami, S. Mechanical modeling of material damage. Journal of Applied Mechancis, 1988, 55:280-286
[72] Lemaitre J, etc. Damage mechanics. Euromech 147, Cachan, France, 1981
[73] Kachanov L M. Introduction to continuum damage mechanics. Maritinus Nijhoff Publishers, 1986
[74] Chow C L, Wang J. An anisotropic theory of elasticity for continuum damage mechanics. International Journal of Fracture, 1987, 33: 3-16
[75] Chow C L, Wang J. An anisotropic theory of continuum damage mechanics for ductile fracture. Engineering Fracture Mechanics, 1987, 27(5): 547-558
[76] Valliappan S, Murit V, Zhang W H. Finite element analysis of anisotropic damage mechanics problems. Engineering Fracture Mechanics, 1990, 35(6): 1061-1071
[77] 李兆霞.损伤力学及其应用.北京:科学出版社,2002
[78] Reifsnider K L. Some foundamental aspects of the fatigue and fracture response of composite materials. Proceedings 14th Annual Meeting of Society of Engineering Science, Bethlehem: Lehigh Univ., 1977:14-16
[79] Reifsnider K L. Damage in composite materials/Stp 775. Philadelphia: American Society for Testing & Materials, 1982, 103-117
[80] Talreja R. Transverse crackling and stiffness reduction in composite laminates. Journal of Composite Materials, 1985, 19:355-375
[81] Talreja R. Stiffness properties of composite laminates with matrix cracking and internal delaminations. Engineering Fracture Mechanics, 1986, 25(6): 751-762
[82] Talreja R. Damage development in composites: Mechanics and Modeling. Journal of Strain Analysis for Engineering Design, 1989, 24(4): 215-222
[83] Allen D H, Harris C E, Groves S E. A thermomechanical constitutive theory for elastic composites with distributed damage-part Ⅰ: theoretical development. International Journal of Solids and Structures, 1987, 23 (9): 1301-1318
[84] Allen D H, Harris C E, Groves S E. A thermomechanical constitutive theory for elastic composites with distributed damage-part Ⅱ: theoretical development. International Journal of Solids and Structures, 1987, 23(9): 1319-1338
[85] Ladeveze P, Dantec E. Damage modeling of the elementary ply for laminated composites. Composites Science & Technology, 1992, 43(2): 257-267
[86] Allix O, Ladeveze P. Interlaminar interface modeling for the prediction of delaminating. Composite Structures, 1992, 22(3): 235-242
[87] 迈勒特J.损伤力学教程.倪金刚,陶春虎译.北京:科学出版社,1996
[88] Talreja R. Damage mechanics of composite materials. New York: Elsevier, 1994
[89] 杨光松.损伤力学与复合材料损伤.北京:国防工业出版社,1995
[90] Schapery R A. Models for damage growth and fracture in nonlinear viscoelastic particulate composite. Proceeding 9th U. S. National Congress of Applied Mechanics, the American Society of Mechanical Engineering, 1982, 237-245
[91] Park S W, Schapery R A. A viscoelastic constitutive model for particulate composite with growing damage. International Journal of Solids and Structures, 1997, 34(8): 931-947
[92] Ha K, Schapery R A. A three-dimensional viscoelastic constitutive model for particulate composite with growing damage and its experimental validation. International Journal of Solids and Structures, 1998, 35(26/27): 3497-3517
[93] Tawab K A, Weitsman Y L. A strain-based formulation for the coupled viscoelastic/damage behavior. Journal of Applied Mechanics, 2001, 86:304-311
[94] Kumar R S, Talreja R. Linear viscoelastic behavior of matrix cracked cross-ply laminates. Mechanics of Materials, 2001, 33:139-154
[95] Kumar RS, Talreja R. A continuum damage model for linear viscoelastic composite materials. Mechanics of Materials, 2003, 35:463-480
[96] Akshantala N V, Brinson L C. A damage evolution model for viscoelastic composite laminates. Journal of Composites Technology & Research, 2001, 23(10): 3-14
[97] 沈为.损伤力学.武汉:华中理工大学出版社,1993
[98] 沈为,乐运国,彭立华.树脂基复合材料板的粘弹性损伤本构关系,固体力学学报,1993,14(2):198-162
[99] 樊建平,沈为.树脂基复合材料粘弹性损伤本构及试验测定,应用力学学报,1996,13(1):54-58
[100] Adolfson E, Gudmundson P. Thermoelastic properties in combined bending and extension of thin composite laminates with transverse matrix cracks. International Journal of Solids and Structures, 1997, 34(16); 2035-2060
[101] Adolfsson E, Gudmundson P. Matrix crack initiation and propregress in composite laminates subjected to bending and extension. International Journal of Solids and Structures, 1999, 36(21): 3131-3169
[102] Schapery R A. Homogenized constitutive equations for linear viscoelastic unidirectional composites with growing transverse cracks. Mechanics of Time-Dependent Material, 2002, 6:101-131
[103] Jong G S, Dale G K. Propagation of continuum damage in nonlinear viscoelastic bar by finite difference method, 1990, ASME AMD, 109
[104] 张我华,金荑,陈云敏.损伤材料的动力响应特征.振动工程学报,2000,13(3):413-425
[105] Krishnamurthy K S, Mahajan P, Mittal R K. A parametric study of the impact response and damage of laminated cylindrical composite shells. Composites Science and Technology, 2001, 61:1655-1669
[106] 盛冬发.损伤粘弹性理论及其结构的静、动力学行为分析:[博士学位论文].上海大学,2003
[107] 孙慷,张福学.压电学(上下册).北京:国防工业出版社,1984
[108] Crawley E F, Deluis J. Use of piezoelectric actuators as elements of intelligent structures. AIAA Journal, 1987, 25:1373-1385
[109] Wang B T, Rogers C A. Laminate plate theory for spatially distributed induced strain actuators. Journal of Composite Material, 1991, 25: 433-452
[110] Mitchell J A, Reddy J N. A refined hybrid plate theory for composite laminates with piezoelectric lamina. International Journal of Solids and Structures, 1995, 32:2345-2367
[111] Ha S K, Chang F K. Finite element analysis of composite structures containing distributed piezoelectric sensors and actuators. AIAA Journal, 1992, 30(3): 772-780
[112] Ray M C, Samanta B. Exact solution for static analysis of intelligent structures. AIAA Journal, 1993, 31 : 1684-1691
[113] Ray M C, Rao K M. Exact solution for static analysis of an intelligent structure under cylindrical bending. Computer and Structure, 1993, 47:1031-1042
[114] Sosa H A, Castro M A. Electroelastic analysis of piezoelectric laminated structures. Applied Mechanics Review, 1993, 46:21-28
[115] 王子昆,陈庚超.压电材料空间轴对称通解及其应用.应用数学和力学,1994,15(7):587-598
[116] Pagano N J. Exact solution for rectangular bi-directional composites and sandwich plates. Journal of Composite Materials, 1970, 4:20-34
[117] Heyliger P, Brooks S. Exact solutions for laminated piezoelectric plates in cylindrical bending. Journal of Applied Mechanics, 1996, 63:903-907
[118] Heyliger P. Exact solutions for simply supported laminated piezoelectric plates. Journal of Applied Mechanics, 1997, 64:299-306
[119] Bisegna P, Maceri F. An exact three-dimensional solution for simply supported rectangular piezoelectric plates. Journal of Applied Mechanics, 1996, 63: 628-637
[120] Vel S S, Batra R C. Three-dimensional analytical solution for hybrid multilayered piezoelectric plates. Journal of Applied Mechanics, 2000, 67: 558-567
[121] Heyliger P, Brooks S. Free vibration of piezoelectric laminates in cylindrical bending. International Journal of Solids and Structures, 1995, 32:2945-2960
[122] Brata R C, Liang X Q. The vibration of a rectangular laminated elastic plate with embedded piezoelectric sensors and actuators. Computer and Structure, 1997, 63:203-216
[123] 高坚新,沈亚鹏,王子昆.有限长压电层合简支板自由振动的三维精确解.力学学报,1998,30(2):168-177
[124] Benjeddou A, Deu J F, Letombe S. Free vibrations of simply-supported piezoelectric adaptive plates: an exact sandwich formulation. Thin-walled Structures 2002, 40:573-593
[125] 章建国,刘正兴,林启荣.压电弹性层合板静力机电耦合特性的解析解.力学学报,2000,32(3):326-332
[126] 丁皓江,池毓蔚,国凤林等.压电材料轴对称有限元分析.计算力学学报,2000,17(1):1-7
[127] Ding H J, Xu R Q, Guo F L. Exact axisysmetric solutions for laminated transversely isotropic piezoelectric circular plate (Ⅰ). Science in China (Series E), 1999, 42(4): 388-395
[128] 丁皓江,国凤林,侯鹏飞.横观各向同性热电材料简支矩形板的自由振动.力学学报,2000,32(4):402-411
[129] Baumhauer J C, Tiersten H F. Nonlinear electroelastic equations for small fields superposed on a bias. Journal of Acoustic Society of America, 1973, 54(4): 1017-1033
[130] Pai P F, Nafeh A H, Mook D T. A refined nonlinear model of piezoelectric plate with integrated piezoelectric actuators and sensors. International Journal of Solids and Structures, 1993, 30(11): 1603-1630
[131] Lee C K. Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part Ⅰ: governing equations and reciprocal relationships. Journal of Acoustic Soc Am, 1990, 87(3): 1144-1158
[132] Yu Y Y. Some recent advances in linear and nonlinear dynamical modeling of elastic and piezoelectric plates. Adaptive Structures and Material System, 1993, 35:185-195
[133] Tzou H S, Gradre M. Theoretical analysis of a multi-layered thin shell couple with piezoelectric shell actuators for distributed vibration controls. Journal of Sound and Vibration, 1989, 132(3): 433-450
[134] Tzou H S. Piezoelectric shells (Distributed sensing and control of continua). Kluwer Academic Publishers, 1993
[135] Tzou H S, Bao Y. Nonlinear piezothermoelasticity and multifield actuations, part Ⅰ: Nonlinear anisotropic piezothermoelastic shell laminates. Journal of Vibration and Acoustics, 1997, 119 (3): 374-381
[136] Tzou H S, Zhou Y H. Dynamics and control of nonlinear circular plates with piezoelectric actuators. Journal of Sound and Vibration, 1995,188(2): 189-207
[137] Li H Y, Lin Q L, Liu Z X, et al. Free vibration of piezoelastic laminated cylindrical shells under hydrostatic pressure. International Journal of Solids and Structures, 2001, 38:7571-7585
[138] 李红云,林启荣,刘正兴,等.静力压力下压电弹性圆柱振动的主动控制.应用数学和力学,2003,24(2):163-174
[139] 李红云,刘正兴.考虑静力压力的压电弹性层合圆柱壳动力响应的控制模型.复合材料学报,2002,19(6):13-19
[140] Varelis D, Saravanos D A. Mechanics and finite element for nonlinear response of active laminated piezoelectric plates. AIAA Journal, 2004, 42(6): 1227-1235
[141] Zhou Y H, Tzou H S. Active control of nonlinear piezoelectric circular shallow spherical shells. International Journal of Solids and Structures, 2000, 37: 1663-1677
[142] Li Y Y, Cheng L, Yam L H, et al. Numerical modeling of a damaged plate with piezoelectric actuation. Smart Materials and Structures, 2003, 12:524-532
[143] Ray M C, Reddy J N. Effect of delamination on active constrained layer damping of smart composite beams. AIAA Journal, 2004, 42(6): 1219-1226
[144] Yan Y J, Yam L H. Online detection of crack damage in composite plates using embedded piezoelectric actuators/sensors and wavelet analysis. Composite Structures, 2002, 58:29-38
[145] Wei Z, Yam L H, Cheng L. Detection of internal delamination in multi-layer composite using wavelet packets combined with modal parameter analysis. Composite Structures, 2004, 64:377-387
[146] Yang X M, Shen Y P. Dynamic instability of laminated piezoelectric shell. International Journal of Solids and Structures, 2001, 38:2291-2303
[147] 朱军强,沈亚鹏,杨新迈.电场及双向压缩下含压电层的对称层合圆柱壳体的动力稳定性.航空学报,2003,24(1):21-27
[148] Zhu J Q, Chen C Q, Shen Y P. Three dimensional analysis of the dynamic stability of piezoelectric circular cylindrical shells. European Journal of Mechanics A/Solids, 2003, 22:401-411
[149] Wang S Y, Quek S T, Ang K K. Dynamic stability analysis of finite element modeling of piezoelectric composite plates. International Journal of Solids and Structures, 2004, 41 : 745-764
[150] Chen L W, Lin C Y, Wang C C. Dynamic stability analysis and control of a composite beam with piezoelectric layers. Composite Structures, 2002, 56: 97-109
[151] Chia C Y. Nonlinear analysis of plates. McGraw-Hill, New York, 1980
[152] 李灏.损伤力学基础.济南:山东科学技术出版社,1992
[153] Geoge Z, Voyiadjis G, Teoayo P. Local and interfacial damage analysis of metal matrix composites using the finite element method. Engineering Fracture Mechanics, 1997, 56:483-511
[154] Pipkin A C. Lectures on viscoelasticity theory. Springer-Verlag, New York, 1986
[155] Zhang W H. Numerical analysis of continuum damage mechanics: [dissertation]. Australia: the University of New South Wales, 1992
[156] Mindlin R D. Influences of rotatory inertia and shear inflexural motion of isotropic, elastic plates. Journal of Applied Mechanics, 1951, 18:1031-1036
[157] 傅衣铭.结构非线性动力学分析.广州:暨南大学出版社,1997
[158] Reddy J N. Geometrically nonlinear transient analysis of laminated composite plates. AIAA Journal, 1983, 21 : 621-629
[159] Khdeir A A, Reddy JN. Free vibrations of laminated composite plates using second-order shear deformation theory. Computers and Structures, 1999, 71: 617-626
[160] Librescu L, Khdeir A A, Frederick D. A shear deformable theory of laminated composite shallows shell-type panels and their response analysis, Ⅰ: free vibration and buckling. Acta Mechanica, 1989, 76:1-33
[161] Fu Y M, Chia C Y. Nonlinear analysis of unsymmetrically laminated imperfect thick panels on elastic foundation. Composite Structures, 1989, 13:289-314
[162] Fu Y M, Chia C Y. Multi-mode non-linear vibration and postbuckling of anti-symmetric imperfect angle-ply cylindrical thick panels. International Journal of Non-Linear Mechanics, 1989, 24(5): 365-381
[163] Betten J, Sklepus S, Zolochevsky A. A creep damage model for initially isotropic materials with different properties on tension and compression. Engineering Fracture Mechanics, 1998, 59 (5): 623-631
[164] Betten J, Sklepus S, Zolochevsky A. A constitutive theory for creep behanior of initially isotropic materials sustaining unilateral damage. Mechanics Research Communications, 2003, 30:251-256
[165] Voyiadjis G Z, Zolochevsky A. Creep theory for transversely isotropic solids sustaining unilateral damage. Mechanics Research Communications, 1998, 25(3): 299-304
[166] Prabhakara D L, Datta P K. Vibration and static stability characteristics of rectangular plates with a localized flaw. Computers and Structures, 1993, 49(5): 825-836
[167] Prabhakara D L, Datta P K. Parametric instability characteristics of rectangular
[2] 杨挺青,张晓春.黏弹性薄板蠕变屈曲的载荷—时间特性研究.力学学报,2000,32(3):319-325
[3] 王颖坚,王震鸣.正交铺设层合圆柱曲板的蠕变失稳.应用数学和力学,1993,14(4):295-300
[4] 彭凡,傅衣铭.黏弹性结构蠕变屈曲特性的分析.力学学报,2003,35(3):353-356
[5] Hyasov M H, Akoz A Y. The vibration and dynamic stability of viscoelastic plates. International Journal of Engineering Science, 2000, 38:695-714
[6] Cederbaum G, Aboudi J, Elishakoff I. Dynamic instability of shear-deformable viscoelastic laminated plates by Lyapunov exponents. International Journal of Solids and Structures, 1991, 28(3): 317-327
[7] Aboudi J, Cederbaum G. Dynamic stability analysis of viscoelastic plates by Lyapunov exponents. Journal of Sound and Vibration, 1990, 139(3): 459-467
[8] Chandiramani N K, Librescu L. The theory of orthotropic viscoelastic shear deformable composite flat panels and their dynamic stability. International Journal of Solids and Structures, 1989, 25(5): 465-482
[9] Librescu L, Chandiramani N K. Dynamic stability of transversely isotropic viscoelastic plates. Journal of Sound and Vibration, 1989, 130(3): 467-486
[10] Touati D, Cederbaum G. Postbuckling analysis of imperfect nonlinear viscoelastic columns. International Journal of Solids and Structures, 1997, 34(14): 1751-1760
[11] Touati D, Cederbaum G. The effect of shear deformation on the post-buckling behavior of imperfect nonlinear viscoelastic columns. Archive of Applied Mechancis, 1997, 67:364-374
[12] Huang N N. Viscoelastic analysis of creep response for uniaxilly-compressed laminates with initial deflection including the effect of physical aging. International Journal of Solids and Structures, 1998, 35(4): 1515-1532
[13] Shalev D, Aboudi J. Postbuckling analysis of viscoelastic laminated plates using higher-order theory. International Journal of Solids and Structures, 1991, 27(14): 1747-1755
[14] Touati D, Cederbaum G. Postbuckling of non-linear viscoelastic imperfect laminated plates Part Ⅰ: material considerations. Composite Structures, 1998, 42: 33-41
[15] Touati D, Cederbaum G. Postbuckling of non-linear viscoelastic imperfect laminated plates, Part Ⅱ: Structural analysis. Composite Structures, 1998, (42): 43-51
[16] Cederbaum G, Touati D. Postbuckling analysis of imperfect non-linear viscoelastic cylindrical panels. International Journal of Non-linear Mechanics, 2002, 37:757-762
[17] Kim T W, Kim J H. Nonlinear vibration of viscoelastic laminated composite plates. International Journal of Solids and Structures, 2002, 39:2857-2870
[18] Yu S C, Huang S C. Vibration of a three-layered viscoelastic sandwich circular plate. International Journal of Mechanical Sciences, 2001(43): 2215-2236
[19] Chen L Q, Zu J W, Wu J. Steady-state response of the parametrically excited axially moving string constituted by the Boltzmann superposition principle. Atca Mechanica, 2003, 162:143-155
[20] 吴强,凌道盛,徐兴.粘弹性几何非线性夹层梁动响应分析.计算力学学报,1997,14(1):36-42
[21] Daya E M, Ferry M R. A numerical method for nonlinear eignvalue problems application to vibrations of viscoelastic structures. Computers and Structures, 2001, 79:533-541
[22] Rossikhin Y A, Shitikova M V. A new method for solving dynamic problems of fractional derivative viscoelasticity. International Journal of Engineering Science, 2001, 39:149-176
[23] Drozdov A D. Stability of viscoelastic shells under periodic and stochastic loading. Mechanics Research Communications, 1993, 20(6): 481-486
[24] Drozdov A D, et al. Stability of nonhomogeneous aging viscoelastic bodies under dynamic loading. Nonlinear Analysis, 1995, 24(9): 1361-1375
[25] Drozdov A D. Lyapunov stability of a class of operator integro-differential equations with applications to viscoelasticity. Mathematical Methods in the Applied Sciences, 1996, 19(5): 341-361
[26] Drozdov A D. Almost sure stability of viscoelastic structural members driven by random loads. Journal of Sound and Vibration, 1996, 197(3): 293-307
[27] Touati D, Cederbaum G. Dynamic stability of nonlinear viscoelastic plates. International Journal Solids and Structures, 1994, 31 (17): 2367-2376
[28] Touati D, Cederbaum G. Influence of large deflections on the dynamic stability of nonlinear viscoelastic plates. Acta Mechanica, 1995, 113: 215-231
[29] 朱媛媛,程昌钧.粘弹性矩形板的稳定性分析.固体力学学报,1996,17(3):257-261
[30] 程昌钧,范晓军.黏弹性环形板的临界载荷及动力稳定性.力学学报,2001,33(3):365-375
[31] 彭凡,傅衣铭.粘弹性板的非线性动力稳定特性分析.固体力学学报,2004,25(1):115-118
[32] Suire G, Cederbaum G. Periodic and chaotic behavior of viscoelastic nonlinear (elastica) bars under harmonic excitations. International Journal of Mechanical Sciences, 1995, 37(7): 753-772
[33] Suire G, Cederbaum G. Elastica type dynamic stability analysis of viscoelastic column. Archive of Applied Mechanics, 1994, 64:307-316
[34] Chen Li-Qun, Cheng Chang-Jun. Dynamical behaveor of nonlinear viscoelastic columns based on 2-order Galerkin truncation. Mechanics Research Communication, 2000, 27(4): 413-419
[35] Argyris J, Belubekian V, Ovakimyan N, et al. Chaotic vibrations of a nonlinear viscoelastic beam. Chaos, Solitons & Fractals, 1996, 7(2): 151-163
[36] 陈立群,程昌钧.非线性粘弹性柱的稳定性和混沌运动.应用数学和力学,2000,21(9):890-896
[37] 陈立群,程昌钧.非线性粘弹性梁的动力学行为.应用数学和力学,2000,21(9):897-902
[38] 陈立群,程昌钧,张能辉.具有几何和物理非线性粘弹性梁的混沌运动.工程力学,2001,18(1):1-6
[39] 李根国,朱正佑,程昌钧.非线性粘弹性Timoshenko梁动力学行为的分析.力学季刊,2001,22(3):346-351
[40] Ding Rui, Zhu Zheng-You, Cheng Chang-Jun. Dynamic properties of viscoelastic plates. In: Chien Wei-Zang, et al., ed. Proceeding 3rd Inter. Conf. on Nonlinear Mech., Shanghai: Shanghai Univ. Press, 1998:185-190
[41] Zhu Yan-Yan, Zhang Neng-Hui, Miura F. dynamical behavior of viscoelastic rectangular plates. In: Chien Wei-Zang, et al., ed. Proceeding 3rd Inter. Conf. on Nonlinear Mech., Shanghai: Shanghai Univ. Press, 1998:445-450
[42] 程昌钧,张能辉.粘弹性矩形板的混沌和超混沌行为.力学学报,1998,30 (6):690-699
[43] Cheng Chang-Jun, Zhang Neng-Hui. Buckling and multiple equilibrium states of viscoelastic rectangular plates. Journal of Shanghai University (English Edition), 1999, 3(3): 192-198
[44] Li Jing-Jing, Cheng Chang-Jun, Zhang Neng-Hui. Dynamic stability of viscoelastic plates with finite deformation and shear effects. Journal of Shanghai University (English Edition), 2002, 6(2): 115-124
[45] 李晶晶,程昌钧.粘弹性基础上粘弹性矩形板的非线性振动响应分析.上海大学学报,2000,6(3):231-236
[46] Zhang Neng-Hui, Cheng Chang-Jun. Chaos behavior of viscoelastic plates in supersonic flow. In: Chien Wei-Zang, et al., ed. Proceeding 3rd Inter. Conf. on Nonlinear Mech., Shanghai: Shanghai Univ. Press, 1998:432-436
[47] 程昌钧,范晓军.粘弹性圆薄板的动力学行为.固体力学学报,2000,21(4):306-312
[48] 陈立群,程昌钧.非线性粘弹性板的失稳条件.力学季刊,2001,22(2):247-251
[49] 陈立群,程昌钧.粘弹性板混沌振动的输出变量反馈线性化控制.应用数学和力学,1999,20(12):1229-1234
[50] 张能辉,程昌钧.粘弹性板动力稳定性分析中的两模态Galerkin逼近.应用数学和力学,2003,24(3):221-227
[51] Sun Y X, Zheng S Y. Chaotic dynamic analysis of viscoelastic plates. International Journal of Mechanical Sciences, 2001, 43:1195-1208
[52] Han Q, Hu H. Bifurcation analysis of a nonlinear viscoelastic panel. Europe Journal of Mechanics A/Solids, 2001, 20:827-839
[53] 吴晓.屈曲粘弹性矩形板的非线性振动分岔.力学与实践,2001,21(1):40-42
[54] 吴晓.屈曲粘弹性倾斜矩形板的非线性振动分岔.振动与冲击,2001,20(1):69-71
[55] 张能辉.粘弹性板壳结构的静动力分析:[博士学位论文].兰州大学,1998
[56] 程昌钧,张能辉.轴压作用下粘弹性柱壳的动力学行为.应用数学和力学,2001,22(1):1-8
[57] 张能辉,程昌钧.轴压作用下粘弹性柱壳的动力学行为.应用数学和力学,2001,22(10):1001-1007
[58] 杨挺青.粘弹性力学.武汉:华中理工大学出版社,1990
[59] 周光泉,刘孝敏.粘弹性理论.合肥:中国科技大学出版社,1996
[60] Christensen R M. Theory of viscoelasticity: an introduction. New York: Academic Press, 1992
[61] 张义同.热粘弹性理论.天津:天津大学出版社,2002
[62] Kachanov L M. Time of the rupture process under creep conditions. TVZ Akad. Nauk. SSR, Otd. Tech. Nauk., 1958, 8:26-31
[63] Rabotnov Y N. On the equations of state for creep. In: Progress in Applied Mechanics, The Prager Anniversary Volume. MacMillan, New York, 1963, 307-315
[64] Lemaitre J. How to use damage mechanics. Nuclear Engineering and Design Journal, 1984, 80:233-245
[65] Lemaitre J. A course on damage mechanics. Berlin, Springer-Verlag, 1996
[66] Lemaitre J, Chaboche J L. Mechanics of solid materials. Cambridge University Press, 1990
[67] Janson J, Hult J. Fracture mechanics and damage mechanics: a combined approach. Journal de Mecanique Appliquee, 1977, 1(1): 69-84
[68] Hayhurst D R, Leckie F A. The effect of creep constitutive and damage relationships upon the rupture time of a solid circular torsion bar. Journal of Mechanics and Physics of Solids, 1973, 21:431-446
[69] Murakami S. Notion of continuum damage mechanics and its application to anisotropic creep damage theory. Journal of Engineering Material Technology, 1983, 105:99-105
[70] Murakami S, Sanomura Y. Analysis of the coupled effect of plastic damage and creep damage in Nimonic 80A at finite deformation. Engineering Fracture Mechancis, 1986, 25(5/6): 693-704
[71] Murakami, S. Mechanical modeling of material damage. Journal of Applied Mechancis, 1988, 55:280-286
[72] Lemaitre J, etc. Damage mechanics. Euromech 147, Cachan, France, 1981
[73] Kachanov L M. Introduction to continuum damage mechanics. Maritinus Nijhoff Publishers, 1986
[74] Chow C L, Wang J. An anisotropic theory of elasticity for continuum damage mechanics. International Journal of Fracture, 1987, 33: 3-16
[75] Chow C L, Wang J. An anisotropic theory of continuum damage mechanics for ductile fracture. Engineering Fracture Mechanics, 1987, 27(5): 547-558
[76] Valliappan S, Murit V, Zhang W H. Finite element analysis of anisotropic damage mechanics problems. Engineering Fracture Mechanics, 1990, 35(6): 1061-1071
[77] 李兆霞.损伤力学及其应用.北京:科学出版社,2002
[78] Reifsnider K L. Some foundamental aspects of the fatigue and fracture response of composite materials. Proceedings 14th Annual Meeting of Society of Engineering Science, Bethlehem: Lehigh Univ., 1977:14-16
[79] Reifsnider K L. Damage in composite materials/Stp 775. Philadelphia: American Society for Testing & Materials, 1982, 103-117
[80] Talreja R. Transverse crackling and stiffness reduction in composite laminates. Journal of Composite Materials, 1985, 19:355-375
[81] Talreja R. Stiffness properties of composite laminates with matrix cracking and internal delaminations. Engineering Fracture Mechanics, 1986, 25(6): 751-762
[82] Talreja R. Damage development in composites: Mechanics and Modeling. Journal of Strain Analysis for Engineering Design, 1989, 24(4): 215-222
[83] Allen D H, Harris C E, Groves S E. A thermomechanical constitutive theory for elastic composites with distributed damage-part Ⅰ: theoretical development. International Journal of Solids and Structures, 1987, 23 (9): 1301-1318
[84] Allen D H, Harris C E, Groves S E. A thermomechanical constitutive theory for elastic composites with distributed damage-part Ⅱ: theoretical development. International Journal of Solids and Structures, 1987, 23(9): 1319-1338
[85] Ladeveze P, Dantec E. Damage modeling of the elementary ply for laminated composites. Composites Science & Technology, 1992, 43(2): 257-267
[86] Allix O, Ladeveze P. Interlaminar interface modeling for the prediction of delaminating. Composite Structures, 1992, 22(3): 235-242
[87] 迈勒特J.损伤力学教程.倪金刚,陶春虎译.北京:科学出版社,1996
[88] Talreja R. Damage mechanics of composite materials. New York: Elsevier, 1994
[89] 杨光松.损伤力学与复合材料损伤.北京:国防工业出版社,1995
[90] Schapery R A. Models for damage growth and fracture in nonlinear viscoelastic particulate composite. Proceeding 9th U. S. National Congress of Applied Mechanics, the American Society of Mechanical Engineering, 1982, 237-245
[91] Park S W, Schapery R A. A viscoelastic constitutive model for particulate composite with growing damage. International Journal of Solids and Structures, 1997, 34(8): 931-947
[92] Ha K, Schapery R A. A three-dimensional viscoelastic constitutive model for particulate composite with growing damage and its experimental validation. International Journal of Solids and Structures, 1998, 35(26/27): 3497-3517
[93] Tawab K A, Weitsman Y L. A strain-based formulation for the coupled viscoelastic/damage behavior. Journal of Applied Mechanics, 2001, 86:304-311
[94] Kumar R S, Talreja R. Linear viscoelastic behavior of matrix cracked cross-ply laminates. Mechanics of Materials, 2001, 33:139-154
[95] Kumar RS, Talreja R. A continuum damage model for linear viscoelastic composite materials. Mechanics of Materials, 2003, 35:463-480
[96] Akshantala N V, Brinson L C. A damage evolution model for viscoelastic composite laminates. Journal of Composites Technology & Research, 2001, 23(10): 3-14
[97] 沈为.损伤力学.武汉:华中理工大学出版社,1993
[98] 沈为,乐运国,彭立华.树脂基复合材料板的粘弹性损伤本构关系,固体力学学报,1993,14(2):198-162
[99] 樊建平,沈为.树脂基复合材料粘弹性损伤本构及试验测定,应用力学学报,1996,13(1):54-58
[100] Adolfson E, Gudmundson P. Thermoelastic properties in combined bending and extension of thin composite laminates with transverse matrix cracks. International Journal of Solids and Structures, 1997, 34(16); 2035-2060
[101] Adolfsson E, Gudmundson P. Matrix crack initiation and propregress in composite laminates subjected to bending and extension. International Journal of Solids and Structures, 1999, 36(21): 3131-3169
[102] Schapery R A. Homogenized constitutive equations for linear viscoelastic unidirectional composites with growing transverse cracks. Mechanics of Time-Dependent Material, 2002, 6:101-131
[103] Jong G S, Dale G K. Propagation of continuum damage in nonlinear viscoelastic bar by finite difference method, 1990, ASME AMD, 109
[104] 张我华,金荑,陈云敏.损伤材料的动力响应特征.振动工程学报,2000,13(3):413-425
[105] Krishnamurthy K S, Mahajan P, Mittal R K. A parametric study of the impact response and damage of laminated cylindrical composite shells. Composites Science and Technology, 2001, 61:1655-1669
[106] 盛冬发.损伤粘弹性理论及其结构的静、动力学行为分析:[博士学位论文].上海大学,2003
[107] 孙慷,张福学.压电学(上下册).北京:国防工业出版社,1984
[108] Crawley E F, Deluis J. Use of piezoelectric actuators as elements of intelligent structures. AIAA Journal, 1987, 25:1373-1385
[109] Wang B T, Rogers C A. Laminate plate theory for spatially distributed induced strain actuators. Journal of Composite Material, 1991, 25: 433-452
[110] Mitchell J A, Reddy J N. A refined hybrid plate theory for composite laminates with piezoelectric lamina. International Journal of Solids and Structures, 1995, 32:2345-2367
[111] Ha S K, Chang F K. Finite element analysis of composite structures containing distributed piezoelectric sensors and actuators. AIAA Journal, 1992, 30(3): 772-780
[112] Ray M C, Samanta B. Exact solution for static analysis of intelligent structures. AIAA Journal, 1993, 31 : 1684-1691
[113] Ray M C, Rao K M. Exact solution for static analysis of an intelligent structure under cylindrical bending. Computer and Structure, 1993, 47:1031-1042
[114] Sosa H A, Castro M A. Electroelastic analysis of piezoelectric laminated structures. Applied Mechanics Review, 1993, 46:21-28
[115] 王子昆,陈庚超.压电材料空间轴对称通解及其应用.应用数学和力学,1994,15(7):587-598
[116] Pagano N J. Exact solution for rectangular bi-directional composites and sandwich plates. Journal of Composite Materials, 1970, 4:20-34
[117] Heyliger P, Brooks S. Exact solutions for laminated piezoelectric plates in cylindrical bending. Journal of Applied Mechanics, 1996, 63:903-907
[118] Heyliger P. Exact solutions for simply supported laminated piezoelectric plates. Journal of Applied Mechanics, 1997, 64:299-306
[119] Bisegna P, Maceri F. An exact three-dimensional solution for simply supported rectangular piezoelectric plates. Journal of Applied Mechanics, 1996, 63: 628-637
[120] Vel S S, Batra R C. Three-dimensional analytical solution for hybrid multilayered piezoelectric plates. Journal of Applied Mechanics, 2000, 67: 558-567
[121] Heyliger P, Brooks S. Free vibration of piezoelectric laminates in cylindrical bending. International Journal of Solids and Structures, 1995, 32:2945-2960
[122] Brata R C, Liang X Q. The vibration of a rectangular laminated elastic plate with embedded piezoelectric sensors and actuators. Computer and Structure, 1997, 63:203-216
[123] 高坚新,沈亚鹏,王子昆.有限长压电层合简支板自由振动的三维精确解.力学学报,1998,30(2):168-177
[124] Benjeddou A, Deu J F, Letombe S. Free vibrations of simply-supported piezoelectric adaptive plates: an exact sandwich formulation. Thin-walled Structures 2002, 40:573-593
[125] 章建国,刘正兴,林启荣.压电弹性层合板静力机电耦合特性的解析解.力学学报,2000,32(3):326-332
[126] 丁皓江,池毓蔚,国凤林等.压电材料轴对称有限元分析.计算力学学报,2000,17(1):1-7
[127] Ding H J, Xu R Q, Guo F L. Exact axisysmetric solutions for laminated transversely isotropic piezoelectric circular plate (Ⅰ). Science in China (Series E), 1999, 42(4): 388-395
[128] 丁皓江,国凤林,侯鹏飞.横观各向同性热电材料简支矩形板的自由振动.力学学报,2000,32(4):402-411
[129] Baumhauer J C, Tiersten H F. Nonlinear electroelastic equations for small fields superposed on a bias. Journal of Acoustic Society of America, 1973, 54(4): 1017-1033
[130] Pai P F, Nafeh A H, Mook D T. A refined nonlinear model of piezoelectric plate with integrated piezoelectric actuators and sensors. International Journal of Solids and Structures, 1993, 30(11): 1603-1630
[131] Lee C K. Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part Ⅰ: governing equations and reciprocal relationships. Journal of Acoustic Soc Am, 1990, 87(3): 1144-1158
[132] Yu Y Y. Some recent advances in linear and nonlinear dynamical modeling of elastic and piezoelectric plates. Adaptive Structures and Material System, 1993, 35:185-195
[133] Tzou H S, Gradre M. Theoretical analysis of a multi-layered thin shell couple with piezoelectric shell actuators for distributed vibration controls. Journal of Sound and Vibration, 1989, 132(3): 433-450
[134] Tzou H S. Piezoelectric shells (Distributed sensing and control of continua). Kluwer Academic Publishers, 1993
[135] Tzou H S, Bao Y. Nonlinear piezothermoelasticity and multifield actuations, part Ⅰ: Nonlinear anisotropic piezothermoelastic shell laminates. Journal of Vibration and Acoustics, 1997, 119 (3): 374-381
[136] Tzou H S, Zhou Y H. Dynamics and control of nonlinear circular plates with piezoelectric actuators. Journal of Sound and Vibration, 1995,188(2): 189-207
[137] Li H Y, Lin Q L, Liu Z X, et al. Free vibration of piezoelastic laminated cylindrical shells under hydrostatic pressure. International Journal of Solids and Structures, 2001, 38:7571-7585
[138] 李红云,林启荣,刘正兴,等.静力压力下压电弹性圆柱振动的主动控制.应用数学和力学,2003,24(2):163-174
[139] 李红云,刘正兴.考虑静力压力的压电弹性层合圆柱壳动力响应的控制模型.复合材料学报,2002,19(6):13-19
[140] Varelis D, Saravanos D A. Mechanics and finite element for nonlinear response of active laminated piezoelectric plates. AIAA Journal, 2004, 42(6): 1227-1235
[141] Zhou Y H, Tzou H S. Active control of nonlinear piezoelectric circular shallow spherical shells. International Journal of Solids and Structures, 2000, 37: 1663-1677
[142] Li Y Y, Cheng L, Yam L H, et al. Numerical modeling of a damaged plate with piezoelectric actuation. Smart Materials and Structures, 2003, 12:524-532
[143] Ray M C, Reddy J N. Effect of delamination on active constrained layer damping of smart composite beams. AIAA Journal, 2004, 42(6): 1219-1226
[144] Yan Y J, Yam L H. Online detection of crack damage in composite plates using embedded piezoelectric actuators/sensors and wavelet analysis. Composite Structures, 2002, 58:29-38
[145] Wei Z, Yam L H, Cheng L. Detection of internal delamination in multi-layer composite using wavelet packets combined with modal parameter analysis. Composite Structures, 2004, 64:377-387
[146] Yang X M, Shen Y P. Dynamic instability of laminated piezoelectric shell. International Journal of Solids and Structures, 2001, 38:2291-2303
[147] 朱军强,沈亚鹏,杨新迈.电场及双向压缩下含压电层的对称层合圆柱壳体的动力稳定性.航空学报,2003,24(1):21-27
[148] Zhu J Q, Chen C Q, Shen Y P. Three dimensional analysis of the dynamic stability of piezoelectric circular cylindrical shells. European Journal of Mechanics A/Solids, 2003, 22:401-411
[149] Wang S Y, Quek S T, Ang K K. Dynamic stability analysis of finite element modeling of piezoelectric composite plates. International Journal of Solids and Structures, 2004, 41 : 745-764
[150] Chen L W, Lin C Y, Wang C C. Dynamic stability analysis and control of a composite beam with piezoelectric layers. Composite Structures, 2002, 56: 97-109
[151] Chia C Y. Nonlinear analysis of plates. McGraw-Hill, New York, 1980
[152] 李灏.损伤力学基础.济南:山东科学技术出版社,1992
[153] Geoge Z, Voyiadjis G, Teoayo P. Local and interfacial damage analysis of metal matrix composites using the finite element method. Engineering Fracture Mechanics, 1997, 56:483-511
[154] Pipkin A C. Lectures on viscoelasticity theory. Springer-Verlag, New York, 1986
[155] Zhang W H. Numerical analysis of continuum damage mechanics: [dissertation]. Australia: the University of New South Wales, 1992
[156] Mindlin R D. Influences of rotatory inertia and shear inflexural motion of isotropic, elastic plates. Journal of Applied Mechanics, 1951, 18:1031-1036
[157] 傅衣铭.结构非线性动力学分析.广州:暨南大学出版社,1997
[158] Reddy J N. Geometrically nonlinear transient analysis of laminated composite plates. AIAA Journal, 1983, 21 : 621-629
[159] Khdeir A A, Reddy JN. Free vibrations of laminated composite plates using second-order shear deformation theory. Computers and Structures, 1999, 71: 617-626
[160] Librescu L, Khdeir A A, Frederick D. A shear deformable theory of laminated composite shallows shell-type panels and their response analysis, Ⅰ: free vibration and buckling. Acta Mechanica, 1989, 76:1-33
[161] Fu Y M, Chia C Y. Nonlinear analysis of unsymmetrically laminated imperfect thick panels on elastic foundation. Composite Structures, 1989, 13:289-314
[162] Fu Y M, Chia C Y. Multi-mode non-linear vibration and postbuckling of anti-symmetric imperfect angle-ply cylindrical thick panels. International Journal of Non-Linear Mechanics, 1989, 24(5): 365-381
[163] Betten J, Sklepus S, Zolochevsky A. A creep damage model for initially isotropic materials with different properties on tension and compression. Engineering Fracture Mechanics, 1998, 59 (5): 623-631
[164] Betten J, Sklepus S, Zolochevsky A. A constitutive theory for creep behanior of initially isotropic materials sustaining unilateral damage. Mechanics Research Communications, 2003, 30:251-256
[165] Voyiadjis G Z, Zolochevsky A. Creep theory for transversely isotropic solids sustaining unilateral damage. Mechanics Research Communications, 1998, 25(3): 299-304
[166] Prabhakara D L, Datta P K. Vibration and static stability characteristics of rectangular plates with a localized flaw. Computers and Structures, 1993, 49(5): 825-836
[167] Prabhakara D L, Datta P K. Parametric instability characteristics of rectangular