Rajneesh Kumar, Manjeet Singh. Propagation of Plane Waves in Thermoelastic Cubic Crystal Material With Two Relaxation Times[J]. Applied Mathematics and Mechanics, 2007, 28(5): 561-574.
Citation: Rajneesh Kumar, Manjeet Singh. Propagation of Plane Waves in Thermoelastic Cubic Crystal Material With Two Relaxation Times[J]. Applied Mathematics and Mechanics, 2007, 28(5): 561-574.

Propagation of Plane Waves in Thermoelastic Cubic Crystal Material With Two Relaxation Times

  • Received Date: 2006-02-16
  • Rev Recd Date: 2007-02-06
  • Publish Date: 2007-05-15
  • A problem concerning with the reflection and refraction of thermoelastic plane waves at an imperfect interface between two generalized thermally conducting cubic crystal solid half-spaces of different elastic and thermal properties with two relaxation times has been investigated.The generalized thermoelastic theory with two relaxation times developed by Green and Lindsay has been used to study the problem in 1972.The expressions for the reflection and refraction coefficients which are the ratios of the amplitudes of reflected and refracted waves to the amplitude of incident waves were obtained for an imperfect boundary and deduced for normal stiffness,transverse stiffness,thermal contact conductance,slip and welded boundaries.Amplitude ratios of different reflected and refracted waves for different boundaries with angle of emergence were compared graphically for different incident waves.It is observed that the amplitude ratios of reflected and refracted waves are affected by the stiffness and thermal properties of the media.
  • loading
  • [1]
    Jones J P, Whittier J P. Waves in a flexible bonded interface[J].J Appl Mech,1967,34(4):905-909. doi: 10.1115/1.3607854
    Murty G S. A theoretical model for the attenuation and dispersion of Stonley waves at the loosely bonded interface of elastic half-space[J].Phys Earth and Planetary Interiors,1975,11(1):65-79. doi: 10.1016/0031-9201(75)90076-X
    Nayfeh A H, Nassar E M. Simulation of the influence of bonding materials on the dynamic behaviour of laminated composites[J].J Appl Mech,1978,45(4):822-828. doi: 10.1115/1.3424426
    Schoenberg M. Elastic wave behavior across linear slip interfaces[J].J Acoust Soc Amer,1980,68(5):1516-1521. doi: 10.1121/1.385077
    Rokhlin S I, Hefets M, Rosen M. An elastic interface wave guided by a thin film between two solids[J].J Appl Phys,1980,51(7):3579-3582. doi: 10.1063/1.328208
    Rokhlin S I. Adhesive Joint characterization by ultrasonic surface and interface waves[A].In:Mittal K L Ed.Adhesive Joints:Formation, Characteristics and Testing[C].New York:Plenum,1984:307-345.
    Pilarski A, Rose J L. A transverse wave ultrasonic oblique-incidence technique for interface weakness detection in adhesive bonds[J].J Appl Phys,1988,63(2):300-307. doi: 10.1063/1.340294
    Baik J M, Thompson R B. Ultrasonic scattering from imperfect interfaces a quasi-static model[J].J Nondestr Eval,1984,4(3/4):177-196. doi: 10.1007/BF00566223
    Angel Y C, Achenbach J D. Reflection and transmission of elastic waves by a periodic array of crack[J].J Appl Mech,1985,52(1):33-41. doi: 10.1115/1.3169023
    Cheng Z Q, Jemah A K, Williams F W. Theory for multilayered anisotropic plates with weakened interfaces[J].J Appl Mech,1996,63(4):1019-1026. doi: 10.1115/1.2787221
    Lavrentyev A I, Rokhlin S I. Ultrasonic spectroscopy of imperfect contact interfaces between a layer and two solids[J].J Acoust Soc Amer,1998,103(2):657-664. doi: 10.1121/1.423235
    Cheng Z Q, He L H, Kitipornchai S. Influence of imperfect interfaces on bending and vibration of laminated composite shells[J].Internat J Solids and Structures,2000,37(15):2127-2150. doi: 10.1016/S0020-7683(98)00294-7
    Chen W Q, Ying J, Cai J B,et al. Benchmark solution of imperfect angle-ply laminated rectangular plated in cylindrical bending with surface piezoelectric layers as actuator and sensor[J].Computers and Structures,2004,82(22):1773-1784. doi: 10.1016/j.compstruc.2004.05.011
    Chen W Q, Wang Y F, Cai J B,et al. Three-dimensional analysis of cross-ply laminated cylindrical panels with weak interfaces[J].Internat J Solids and Structures,2004,41(9/10):2429-2446. doi: 10.1016/j.ijsolstr.2003.12.018
    Chen W Q, Cai J B, Ye G R. Responses of cross-ply laminates with viscous interfaces in cylindrical bending[J].Computer Methods in Appl Mech and Engng,2005,194(6/8):823-835. doi: 10.1016/j.cma.2004.06.016
    Chen W Q, Lee K Y. Benchmark solution of angle-ply piezoelectric-laminated cylindrical panels in cylindrical bending with weak interfaces[J].Arch Appl Mech,2005,74(7):466-476. doi: 10.1007/s00419-004-0357-2
    Lord H W, Shulman Y. A generalized dynamical theory of Thermoelasticity[J].J Mech Phys Solids,1967,15(5):299-309. doi: 10.1016/0022-5096(67)90024-5
    Green A E, Lindsay K A. Thermoelasticity[J].J Elasticity,1972,2(1):1-7. doi: 10.1007/BF00045689
    Dhaliwal R S, Sherief H H. Generalized thermoelasticity for anisotropic media[J].Q Appl Math,1980,38(1):1-8.
    Deresiewicz H. Effect of boundaries on waves in a thermoelastic solid:Reflexion of plane waves from a plane boundary[J].J Mech Phys Solids,1960,8(3):164-172. doi: 10.1016/0022-5096(60)90035-1
    Deresiewicz H. Corrections and additions:effect of boundaries on waves in a thermoelastic solid[J].J Mech Phys Solids,1962,10(2):179-181. doi: 10.1016/0022-5096(62)90020-0
    Sinha A N, Sinha S B. Reflection of thermoelastic waves at a solid half-space with thermal relaxation[J].J Phys Earth,1974,22:237-244. doi: 10.4294/jpe1952.22.237
    Beevers C E, Bree J. A note on wave reflection problems in linear thermoelasticity[J].J Math Phys Sci,1975,9:355-362.
    Sharma J N. Reflection of thermoelastic waves from the stress-free insulated boundary of an anisotropic half-space[J].Indian J Pure Appl Math,1988,19(3):294-304.
    Sinha S B, Elsibai S A. Reflection of thermoelastic waves at a solid half-space with two relaxation times[J].J Thermal Stresses,1996,19(7):749-762. doi: 10.1080/01495739608946205
    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
    Singh B, Kumar R. Reflection of plane waves from the flat boundary of a micropolar generalized thermoelastic half-space[J].Internat J Engrg Sci,1998,36(7/8):865-890. doi: 10.1016/S0020-7225(97)00079-7
    Singh B, Kumar R. Reflection of plane waves from the flat boundary of a micropolar generalized thermoelastic half-space with stretch[J].Indian J Pure Appl Math,1998,29(6):657-669.
    Singh B, Kumar R. Wave propagation in a generalized thermo-microstretch elastic solid[J].Internat J Engng Sci,1998,36(7/8):891-912. doi: 10.1016/S0020-7225(97)00099-2
    Abd-Alla Abo-El-Nour N, Al-Dawy A S Amira. The reflection phenomena of SV-waves in generalized thermoelastic medium[J].Internat J Math Math Sci,2000,23(8):529-546. doi: 10.1155/S0161171200004221
    Singh B. Wave Propagation in an anisotropic generalized thermoelastic solid[J].Indian J Pure Applied Math,2003,34(10):1479-1485.
    Singh B. Plane waves in a thermally conducting viscous liquid[J].Sadhana,2004,29(1):27-34. doi: 10.1007/BF02706999
    Kumar R, Sharma J N. Reflection of plane waves from the boundaries of a micropolar thermoelastic half-space without energy dissipation[J].Internat J Appl Mech Engrg,2005,10(4):631-645.
    Henneke II Edmund G. Reflection-Refraction of a stress wave at a plane boundary between anisotropic media[J].J Acoust Soc Amer,1972,51(1):210-217. doi: 10.1121/1.1912832
    Velasco V R, Garcia-Moliner F. Theory of surface waves in anisotropic cubic crystals[J].J Phys C:Solid St Phys,1980,13:2237-2256. doi: 10.1088/0022-3719/13/11/024
    Atalar A. Reflection of ultrasonic waves at a liquid-cubic-solid interface[J].J Acoust SocAmer,1983,73(2):435-439. doi: 10.1121/1.388991
    Sharma J N, Singh H. Propagation of generalized thermoelastic waves in cubic crystal[J].Arch Mech,1990,42(1):19-30.
    Kumar R, Rani R. Elastodynamics of time harmonic sources in a thermally conducting cubic crystal[J].Internat J Appl Mech Engrg,2003,8(4):637-650.
    Kumar R, Rani L. Deformation due to mechanical and thermal sources in generalized orthorhombic thermoelastic metrial[J].Sadhana,2004,29(5):429-447. doi: 10.1007/BF02703254
    Kumar R, Ailawalia P. Time harmonic sources at micropolar thermoelastic medium possessing cubic symmetry with one relaxation time[J].European J Mech A/Solids,2006,25(2):271-282. doi: 10.1016/j.euromechsol.2005.09.004
    库玛 R, 额拉瓦尼亚 P. 具有立方对称性及两个弛豫时间的微极热弹性介质中调和时间源引起的变形[J].应用数学和力学,2006,27(6):690-700.
    Sharma J N, Kumar V, Sud S P. Plane harmonic waves in orthorhombic thermoelastic materials[J].J Acoust Soc Amer,2000,107(1):293-305. doi: 10.1121/1.428347
  • 加载中


    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 (2728) PDF downloads(578) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint