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基于表面阻抗张量的界面滑移波动态失稳分析

李楠 汪越胜 于桂兰

李楠, 汪越胜, 于桂兰. 基于表面阻抗张量的界面滑移波动态失稳分析[J]. 应用数学和力学, 2004, 25(9): 935-942.
引用本文: 李楠, 汪越胜, 于桂兰. 基于表面阻抗张量的界面滑移波动态失稳分析[J]. 应用数学和力学, 2004, 25(9): 935-942.
LI Nan, WANG Yue-sheng, YU Gui-lan. Analysis of Dynamic Instability of Interfacial Slip Waves Based on the Surface Impedance Tensor[J]. Applied Mathematics and Mechanics, 2004, 25(9): 935-942.
Citation: LI Nan, WANG Yue-sheng, YU Gui-lan. Analysis of Dynamic Instability of Interfacial Slip Waves Based on the Surface Impedance Tensor[J]. Applied Mathematics and Mechanics, 2004, 25(9): 935-942.

基于表面阻抗张量的界面滑移波动态失稳分析

基金项目: 国家自然科学基金资助项目(49974007);国家杰出青年科学基金资助项目(10025211)
详细信息
    作者简介:

    李楠(1974- ),男,河南省郑州市人,博士(Tel:+86-10-84920401;Fax:+86-10-51682094;E-mail:jason-nan-li@yahoo.com.cn);汪越胜(联系人.Tel:+86-10-51688417;Fax:+86-10-51682094;E-mail:yswang@center.njtu.edu.cn).

  • 中图分类号: O347

Analysis of Dynamic Instability of Interfacial Slip Waves Based on the Surface Impedance Tensor

  • 摘要: 基于Stroh公式和表面阻抗张量理论,提出了研究界面滑移波动态失稳问题的一种新的方法.该方法将表面阻抗张量概念推广到复波速域,并将摩擦接触界面上的边界条件以表面阻抗张量表示.最终将边值问题化归为求解一个复多项式在单位圆内的根.以弹性半空间与刚体平面相对稳态摩擦滑移为例进行了详细的分析,导出了一个4次复特征方程并讨论了方程在单位圆内解的特性,给出了滑移界面波失稳条件的显式解析表达式.
  • [1] 汪越胜,于桂兰,章梓茂,等.复杂界面(界面层)条件下的弹性波传播问题研究综述[J].力学进展,2000,30(3):378—390.
    [2] Adams G G.Self-excited oscillations of two elastic half-space4s sliding with a constant coefficient of friction[J].ASME Journal of Applied Mechanics,1995,62(4):867—872. doi: 10.1115/1.2896013
    [3] Martins J A C,Guimares J,Faria L O.Dynamic surface solutions in linear elasticity and viscoelasticity with frictional boundary conditions[J].ASME Journal of Vibration and Acoustics,1995,117(4):445—451. doi: 10.1115/1.2874477
    [4] Simōes F M F,Martins J A C.Instability and ill-posedness in some friction problems[J].International Journal of Engineering Science,1998,36(11):1265—1293. doi: 10.1016/S0020-7225(98)00024-X
    [5] Ranjith K,Rice I R.Slip dyanamics at an interface between dissimilar materials[J].Journal of the Mechanics and Physics of Solids,2001,49(2):341—361. doi: 10.1016/S0022-5096(00)00029-6
    [6] Chadwick P,Smith G D.Foundations of the theory of surface waves in anisotropic elastic materials[J].Advances in Applied Mechanics,1977,17:303—376. doi: 10.1016/S0065-2156(08)70223-0
    [7] Barnett D M,Lothe J.Free surface(Rayleigh) waves in anisotropic elastic half-spaces:the surface impedance method[J].Proc R Soc Lond,Ser A,1985,402:135—152. doi: 10.1098/rspa.1985.0111
    [8] Barnett D M,Lothe J,et al.Considerations of existence of interfacial(Stoneley) waves in bonded anisotropic elastic half-spaces[J].Proc Roy Soc London,Ser A,1985,402:153—166. doi: 10.1098/rspa.1985.0112
    [9] Barnett D M,Gavazza S D,Lothe J.Slip waves along the interface between two anisotropic elastic half-spaces in sliding contact[J].Proc Roy Soc London,Ser A,1988,415:389—419. doi: 10.1098/rspa.1988.0020
    [10] Stroh A N.Steady state problems in anisotropic elasticity[J].J Math Phys,1962,41(1):77—103.
    [11] 王竹溪,郭敦仁.特殊函数概论[M].北京:北京大学出版社,2000.
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出版历程
  • 收稿日期:  2002-09-13
  • 修回日期:  2004-06-08
  • 刊出日期:  2004-09-15

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