Rajneesh Kumar, Tarun Kansal. Propagation of Rayleigh Waves at the Free Surface of Transversely Isotropic Generalized Thermoelastic Diffusion[J]. Applied Mathematics and Mechanics, 2008, 29(11): 1314-1324.
Citation: Rajneesh Kumar, Tarun Kansal. Propagation of Rayleigh Waves at the Free Surface of Transversely Isotropic Generalized Thermoelastic Diffusion[J]. Applied Mathematics and Mechanics, 2008, 29(11): 1314-1324.

Propagation of Rayleigh Waves at the Free Surface of Transversely Isotropic Generalized Thermoelastic Diffusion

  • Received Date: 2008-02-07
  • Rev Recd Date: 2008-09-26
  • Publish Date: 2008-11-15
  • The propagation of Rayleigh waves in a homogeneous, transversely isotropic, thermoelastic diffusive half-space subjected to stress free, thermally insulated/isothermal and chemical potential boundary conditions, in the context of generalized theory of thermoelastic diffusion is studied. Green and Lindsay(GL) theory, in which, thermodiffusion and thermodiffusion-mechanical relaxations are governed by four different time constants, was selected for study. Secular equations for surface wave propagation in the considered media were derived. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient were presented graphically in order to illustrate and compare the analytically results. Some special cases of frequency equations were also deduced from the present investigation.
  • loading
  • [1]
    Lord H W, Shulman Y. A generalized dynamical theory of thermoelasticity[J].J Mech Phys Solid,1967,15(5): 299-309. doi: 10.1016/0022-5096(67)90024-5
    [2]
    Green A E, Lindsay K A. Thermoelasticity[J].J Elasticity,1972,2(1):1-7. doi: 10.1007/BF00045689
    [3]
    Dhaliwal R S, Sherief H. Generalized thermoelasticity for anisotropic media[J]. Quarterly Appl Math,1980,33:1-8. doi: 10.1093/qjmam/33.1.1
    [4]
    Chanderashekhariah D S. Thermoelasticity with second: a review[J]. Appl Mech Rev,1986,39(3):355-376. doi: 10.1115/1.3143705
    [5]
    Hetnarski R B, Ignaczak J. Generalized thermoelasticity[J].J Thermal Stresses,1999,22(4/5): 451-476. doi: 10.1080/014957399280832
    [6]
    Nowacki W. Dynamical problems of thermodiffusion in solids—I[J]. Bull Acad Pol Sci Ser Sci Tech,1974,22:55-64.
    [7]
    Nowacki W. Dynamical problems of thermodiffusion in solids—II[J]. Bull Acad Pol Sci Ser Sci Tech, 1974,22:129-135.
    [8]
    Nowacki W. Dynamical problems of thermodiffusion in solids—III[J]. Bull Acad Pol Sci Ser Sci Tech,1974,22:275-276.
    [9]
    Nowacki W. Dynamical problems of thermodiffusion in solids[J].Proc Vib Prob,1974,15:105-128.
    [10]
    Dudziak W, Kowalski S J. Theory of thermodiffusion for solids[J].Internat J Heat and Mass Transfer,1989,32(11):2005-2013. doi: 10.1016/0017-9310(89)90107-5
    [11]
    Olesiak Z S, Pyryev Y A. A coupled quasi-stationary problem of thermodiffu-sion for an elastic cylinder[J].Internat J Engrg Sci,1995,33(6): 773-780. doi: 10.1016/0020-7225(94)00099-6
    [12]
    Sherief H H, Saleh H, Hamza F. The theory of generalized thermoelastic diffusion[J].Internat J Engrg Sci, 2004,42(5/6): 591-608. doi: 10.1016/j.ijengsci.2003.05.001
    [13]
    Sherief H H, Saleh H. A half space problem in the theory of generalized ther moelastic diffusion[J]. Internat J Solids Structure,2005,42(15): 4484-4493. doi: 10.1016/j.ijsolstr.2005.01.001
    [14]
    Singh B. Reflection of P and SV waves from free surface of an elastic solid with generalized thermodiffusion[J]. J Earth Syst Sci, 2005,114(2): 159-168. doi: 10.1007/BF02702017
    [15]
    Singh B. Reflection of SV waves from free surface of an elastic solid in generalized thermodiffusion[J].J Sound Vibration, 2006,291(3/5): 764-778. doi: 10.1016/j.jsv.2005.06.035
    [16]
    Aouadi M. Variable electrical and thermal conductivity in the theory of generalized thermodiffusion[J].ZAMP,2006,57(2):350-366. doi: 10.1007/s00033-005-0034-5
    [17]
    Aouadi M. A generalized thermoelastic diffusion problem for an infinitely long solid cylinder[J].Internat J Math Math Sci,2006,(13):1-15.
    [18]
    Aouadi M. A problem for an infinite elastic body with a spherical cavity in the theory of generalized thermoelastic diffusion[J]. Internat J Solids Structure,2007,44(17): 5711-5722. doi: 10.1016/j.ijsolstr.2007.01.019
    [19]
    Aouadi M. Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion[J].J Thermal Stresses, 2007,30(7):665-678. doi: 10.1080/01495730701212815
    [20]
    Aouadi M. Generalized theory of thermoelastic diffusion for anisotropic media[J]. J Thermal Stresses, 2008,31(3): 270-285. doi: 10.1080/01495730701876742
    [21]
    Sharma J N, Walia V, Gupta S K. Effect of rotation and thermal relaxations on Rayleigh waves in piezothermoelastic half space[J].Internat J Mech Sci, 2008,50(3): 433-444. doi: 10.1016/j.ijmecsci.2007.10.001
    [22]
    Sharma J N. Generalized thermoelastic diffusive waves in heat conducting materials[J].J Sound Vibration,2007,301: 979-993. doi: 10.1016/j.jsv.2006.11.001
    [23]
    Sharma J N, Sharma Y D, Sharma P K. On the propagation of elasto- thermodiffusive surface waves in heat-conducting materials[J].J Sound Vibration, 2008,351(4): 927-938.
    [24]
    Kumar R, Kansal T. Propagation of Lamb waves in transversely isotropic thermo elastic diffusion plate[J].Internat J Solids Structure,2008,4(22/23):5890-5913.
    [25]
    Sharma J N, Singh D, Kumar R. Generalized thermoelastic waves in transversely isotropic plates[J].Indian J Pure Appl Math,2003,34(6): 841-852.
    [26]
    Sharma J N, Pal M, Chand D. Propagation characteristics of Rayleigh waves in transversely isotropic piezothermoelastic materials[J].J Sound Vibration,2005,284(1/2): 227-248. doi: 10.1016/j.jsv.2004.06.036
    [27]
    Ewing W M, Jardetzky W S, Press F.Elastic Layers in Layered Media[M]. New York, Toronto, London: McGraw-Hill Company, Inc, 1957.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (3279) PDF downloads(632) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return