Praveen Ailawalia, Naib Singh Narah. Effect of Rotation in Generalized Thermoelastic Solid Under the Influence of Gravity With an Overlying Infinite Thermoelastic Fluid[J]. Applied Mathematics and Mechanics, 2009, 30(12): 1415-1426. doi: 10.3879/j.issn.1000-0887.2009.12.003
Citation: Praveen Ailawalia, Naib Singh Narah. Effect of Rotation in Generalized Thermoelastic Solid Under the Influence of Gravity With an Overlying Infinite Thermoelastic Fluid[J]. Applied Mathematics and Mechanics, 2009, 30(12): 1415-1426. doi: 10.3879/j.issn.1000-0887.2009.12.003

Effect of Rotation in Generalized Thermoelastic Solid Under the Influence of Gravity With an Overlying Infinite Thermoelastic Fluid

doi: 10.3879/j.issn.1000-0887.2009.12.003
  • Received Date: 2009-04-24
  • Rev Recd Date: 2009-08-24
  • Publish Date: 2009-12-15
  • The present problem was concerned with the study of deformation of a rotating generalized thermoelastic solid with an overlying infinite thermoelastic fluid due to different forces acting along the interface under the influence of gravity.The components of displacement,force stress and temperature distribution were obtained in Laplace and Fourier domain by applying integral transforms.These components were then obtained in the physical domain by applying a numerical inversion method'some particular cases were also discussed in context of the problem.The results are also presented graphically to show the effect of rotation and gravity in the medium.
  • loading
  • [1]
    Chandrasekharaiah D S.Hyperbolic thermoelastic:a review of recent literature[J].Appl Mech Rev,1998,51(12):705-729. doi: 10.1115/1.3098984
    [2]
    Lord H W,Shulman Y.A generalized dynamical theory of thermoelasticity solids[J].J Mech Phy Solids,1967,15(5):299-309. doi: 10.1016/0022-5096(67)90024-5
    [3]
    Müller I.The coldness,a universal function in thermoelastic bodies[J].Arch Rat Mech Anal,1971,41(5):319-332.
    [4]
    Green A E,Laws N.On the entropy production inequality[J].Arch Rat Mech Anal,1972,45(1):45-47.
    [5]
    Green A E,Lindsay K A.Thermoelasticity[J].J Elasticity,1972,2(1):1-7. doi: 10.1007/BF00045689
    [6]
    Suhubi E S.Thermoelastic solids[A].In:Eringin A C,Ed.Continuum Physics[C].Vol Ⅱ Part Ⅱ,Chapter Ⅱ.New York:Acamadic Press,1975.
    [7]
    Green A E,Naghdi P M.On thermoelasticity without energy dissipation[J].J Elasticity,1993,31(3):189-208. doi: 10.1007/BF00044969
    [8]
    Barber J R,Martin-Moran C J.Green's functions for transient thermoelastic contact problems for the half-plane[J].Wear,1982,79:11-19. doi: 10.1016/0043-1648(82)90200-9
    [9]
    Barber J R.Thermoelastic displacements and stresses due to a heat source moving over the surface of a half plane[J].ASME,Transactions,Journal of Applied Mechanics,1984,51(3):636-640. doi: 10.1115/1.3167685
    [10]
    Sherief H H.Fundamental solution of the generalized thermoelastic problem for short times[J].J Thermal Stresses,1986,9(2):151-164. doi: 10.1080/01495738608961894
    [11]
    Dhaliwal R S,Majumdar S R,Wang J.Thermoelastic waves in an infinite solid caused by a line heat source[J].Int J Math & Math Sci,1997,20(2):323-334.
    [12]
    Chandrasekharaiah D S,Srinath K S.Thermoelastic interactions without energy dissipation due to a point heat source[J].J Elasticity,1998,50(2):97-108. doi: 10.1023/A:1007412106659
    [13]
    Sharma J N,Chauhan R S,Kumar R.Time-harmonic sources in a generalized thermoelastic continuum[J].J Thermal Stresses,2000,23(7):657-674. doi: 10.1080/01495730050130048
    [14]
    Sharma J N,Chauhan R S.Mechanical and thermal sources in a generalized thermoelastic half-space[J].J Thermal Stresses,2001,24(7):651-675. doi: 10.1080/014957301300194823
    [15]
    Sharma J N,Sharma P K,Gupta S K.Steady state response to moving loads in thermoelastic solid media[J].J Thermal Stresses,2004,27(10):931-951. doi: 10.1080/01495730490440181
    [16]
    德斯瓦尔 S,乔德哈瑞 S.带扩散的广义弹性固体中移动荷载引起的二维相互作用[J].应用数学和力学,2008,29(2):188-202.
    [17]
    Chand D,Sharma J N,Sud S P.Transient generalized magneto-thermoelastic waves in a rotating half space[J].Int J Engg Sci,1990,28(6):547-556. doi: 10.1016/0020-7225(90)90057-P
    [18]
    Schoenberg M,Censor D.Elastic waves in rotating media[J].Quart Appl Math,1973,31:115-125.
    [19]
    Clarke N S,Burdness J S.Rayleigh waves on a rotating surface[J].ASME J Appl Mech,1994,61:724-726. doi: 10.1115/1.2901524
    [20]
    Destrade M.Surface waves in rotating rhombic crystal[J].Proc Royal Soc London,Series A,2004,460:653-665. doi: 10.1098/rspa.2003.1192
    [21]
    Roychoudhuri S K,Mukhopadhyay S.Effect of rotation and relaxation times on plane waves in generalized thermo-visco-elasticity[J].Int J Math Math Sci,2000,23(7):497-505. doi: 10.1155/S0161171200001356
    [22]
    Ting T C T.Surface waves in a rotating anisotropic elastic half-space[J].Wave Motion,2004,40(4):329-346. doi: 10.1016/j.wavemoti.2003.10.005
    [23]
    Sharma J N,Thakur D.Effect of rotation on Rayleigh-Lamb waves in magneto-thermoelastic media[J].J Sound Vib,2006,296(4/5):871-887. doi: 10.1016/j.jsv.2006.03.014
    [24]
    Sharma J N,Walia V.Effect of rotation on Rayleigh-Lamb waves in piezothermoelastic half space[J].J Solid Structures,2007,44(3/4):1060-1072. doi: 10.1016/j.ijsolstr.2006.06.005
    [25]
    Sharma J N,Othman M I A.Effect of rotation on generalized thermo-viscoelastic Rayleigh-Lamb waves[J].J Solid Structures,2007,44(13):4243-4255. doi: 10.1016/j.ijsolstr.2006.11.016
    [26]
    Sharma J N,Walia V,Gupta S K.Effect of rotation and thermal relaxation on Rayleigh waves in piezothermoelastic half space[J].Int J Mech Sci,2008,50(3):433-444. doi: 10.1016/j.ijmecsci.2007.10.001
    [27]
    Othman M I A,Song Y.Effect of rotation on plane waves of generalized electro-magneto-thermoviscoelasticity with two relaxation times[J].Appl Math Modelling,2008,32(5):811-825. doi: 10.1016/j.apm.2007.02.025
    [28]
    Bromwich T J J A.On the influence of gravity on elastic waves and in particular on the vibrations of an elastic globe[J].Proc London Math Soc,1898,30(1):98-120. doi: 10.1112/plms/s1-30.1.98
    [29]
    Love A E H.Some Problems of Geodynamics[M].New York:Dover,1911.
    [30]
    De S N,Sengupta P R.Plane Lamb's problem under the influence of gravity[J].Gerland Beitr Geophysics (Leipzig),1973,82:421-426.
    [31]
    De S N,Sengupta P R.Influence of gravity on wave propagation in an elastic layer[J].J Acoust Soc Am,1974,55(5):919-921. doi: 10.1121/1.1914662
    [32]
    De S N,Sengupta P R.Surface waves under the influence of gravity[J].Gerland Beitr Geophysics (Leipzig),1976,85:311-318.
    [33]
    Sengupta P R,Acharya D.The influence of gravity on the propagation of waves in a thermoelastic layer[J].Rev Roum Sci Technol Mech Appl Tome,1979,24:395-406.
    [34]
    Das S C,Acharya D P,Sengupta P R.Surface waves in an inhomogeneous elastic medium under the influence of gravity[J].Rev Roum Des Sci Tech,1992,37(5):539-551.
    [35]
    Abd-Alla A M,Ahmed S M.Rayleigh waves in an orthotropic thermoelastic medium under gravity field and initial stress[J].J Earth Moon Planets,1996,75(3):185-197. doi: 10.1007/BF02592996
    [36]
    Abd-Alla A M,Ahmed S M.Stonley and Rayleigh waves in a nonhomogeneous orthotropic elastic medium under the influence of gravity[J].Appl Math Comp,2003,135:187-200. doi: 10.1016/S0096-3003(01)00329-0
    [37]
    Youssef H M.Problem of generalized thermoelastic infinite medium with cylindrical cavity subjected to ramp-type heating and loading[J].Arch Appl Mech,2006,75:553-565. doi: 10.1007/s00419-005-0440-3
    [38]
    Sinha S B,Elsibai K A.Reflection and refraction of thermoelastic waves at an interface of two semi-infinite media with two relaxation times[J].J Thermal Stresses,1997,20(2):129-145. doi: 10.1080/01495739708956095
    [39]
    Sharma J N,Kumar V.Plane strain problems of transversely isotropic thermoelastic media[J].J Thermal Stresses,1997,20(5):463-476. doi: 10.1080/01495739708956113
  • 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 (1532) PDF downloads(704) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return