Rajneesh Kumar, Mahabir Barak. Wave Propagation in a Liquid-Saturated Porous Solid With Micropolar Elastic Skeleton at Boundary Surface[J]. Applied Mathematics and Mechanics, 2007, 28(3): 305-316.
Citation: Rajneesh Kumar, Mahabir Barak. Wave Propagation in a Liquid-Saturated Porous Solid With Micropolar Elastic Skeleton at Boundary Surface[J]. Applied Mathematics and Mechanics, 2007, 28(3): 305-316.

Wave Propagation in a Liquid-Saturated Porous Solid With Micropolar Elastic Skeleton at Boundary Surface

  • Received Date: 2005-05-17
  • Rev Recd Date: 2007-01-18
  • Publish Date: 2007-03-15
  • The reflection and transmission of plane waves at an interface between homogenous inviscid liquid half space and a micropolar liquid-saturated porous solid half space are studied.The reflection and transmission coefficients of various reflected and transmitted waves with the angle of incident were obtained.Numerical calculation were performed for amplitude ratios of variously reflected and transmitted waves.Micropolarity and porosity effects on the reflection and transmission coefficients were depicted graphically.Some particular cases were deduced from the present formulation.
  • loading
  • [1]
    Biot M A.General solutions of the equations of elasticity and consolidation for a porous material[J].J Appl Mech,1956,23:91-96.
    [2]
    Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid I.Low-frequency range,II.Higher frequency range[J].J Acoust Soc Am,1956,28:168-191. doi: 10.1121/1.1908239
    [3]
    Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].J Appl Phys,1962,33:1482-1498. doi: 10.1063/1.1728759
    [4]
    Deresiewicz H.The effect of boundaries on wave propagation in a liquid-filled porous solid-I:Reflection of plane waves at a free plane boundary(non-dissipative case)[J].Bull Seism Soc Am,1960,50:599-607.
    [5]
    Deresiewicz H,Rice J T.The effect of boundaries on wave propagation in a liquid-filled porous solid-Ⅲ:Reflection of plane waves at a free plane boundary(genaral case)[J].Bull Seism Soc Am,1962,52:595-625.
    [6]
    Eringen A C,Suhubi E S.Non-linear theory of simple microelastic solids Ⅰ[J].Int J Engg Sci,1964,2:189-203. doi: 10.1016/0020-7225(64)90004-7
    [7]
    Suhubi E S,Eringen A C.Non-linear theory of simple microelastic solids Ⅱ[J].Int J Engg Sci,1964,2:389-404. doi: 10.1016/0020-7225(64)90017-5
    [8]
    Eringen A C.Mechanics of micromorphic materials[A].In:Proc 11th Int Congress Appl Mech[C].Gortler H,Ed.New York:Springer-Verlag,1964.
    [9]
    Eringen A C.Linear theory of micropolar elasticity[J].J Math Mech,1966,15:909-923.
    [10]
    Gauthier R D.Mechanics of Micropolar Media[M].Brulin O,Hsieh R K T,Eds.Singapore:World Scientific,1982.
    [11]
    Yang,Lakes,Biomech J.Experimental study of micropolar and couple stress elasticity in bone in bending[J].J Biomechanics,1982,15:91-98. doi: 10.1016/0021-9290(82)90040-9
    [12]
    Parfitt V R,Eringen A C.Reflection of plane waves from the flat boundary of a micropolar elastic half-space[J].J Acoust Soc Am,1969,45(5):1258-1272. doi: 10.1121/1.1911598
    [13]
    Tomar S K,Gogna M L.Reflection and refraction of coupled transverse and microrotational waves at an interface between two different micropolar elastic media in welded contact[J].Int J Engg Sci,1995,33(4):485-496. doi: 10.1016/0020-7225(94)00077-8
    [14]
    Tomar S K,Kumar R.Reflection and refraction of longitudinal displacement wave at a liquid micropolar solid interface[J].Int J Engg Sci,1995,33(10):1507-1515. doi: 10.1016/0020-7225(95)00015-P
    [15]
    Konczak Z.Thermo-mechanical effects in fluid-saturated porous media with a micropolar viscoelastic skeletion[J].ZAMM Z angew,Math Mech,1986,66(4):152-154.
    [16]
    Konczak Z.On wave propagation in fluid-saturated porous media with a micropolar viscoelastic skeleton[J].ZAMM Z angew Math Mech,1987,67(1):201-203.
    [17]
    Kumar R,Singh B.Reflection and refraction of micropolar elastic waves at an interface between porous elastic solid and micropolar elastic solid[J].Proc Nat Acad Sci India,2000,70(A)(4):397-410.
    [18]
    Kumar R,Deswal S.Wave propagation in micropolar liquid-saturated porous solid[J].Indian J Pure and Appl Math,2000,31(10):1317-1337.
    [19]
    Kumar R,Deswal S.Surface wave propagation in a micropolar liquid-saturated porous solid lying under a uniform layer of liquid[J].Bult of Calcutta Mathematical Society, Calcutta,2000,92:99-110.
    [20]
    Kumar R,Tomar S K.Reflection and transmission of elastic waves at viscous liquid/micropolar elastic solid interface[J].Int J Math and Math Sci,2001,26(11):685-694. doi: 10.1155/S0161171201005415
    [21]
    Eringen A C.Theory of Micropolar Elasticity in Fracture[M].Chapter 7 of Fracture,Vol Ⅱ.Liebowitz H,Ed.New York:Academic Press,1968.
    [22]
    Yew C H,Jogi P N.Study of wave motions in fluid saturated porous rocks[J].J Acoust Soc Am,1976,60:2-8. doi: 10.1121/1.381045
    [23]
    Fatt I.The Biot-Willis elastic Co-efficients for a Sandstone[J].J Appl Mech,1959,26:296-297.
  • 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 (2324) PDF downloads(562) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return