横观各向同性广义热弹性扩散Rayleigh波在自由表面上的传播

R·库玛; T·坎赛

横观各向同性广义热弹性扩散Rayleigh波在自由表面上的传播

库卢谢特拉大学数学系,库卢谢特拉_136119,哈里亚拉邦,印度

基金项目: 印度科学和工业研究委员会(CSIR)资助项目

详细信息

中图分类号: O343.6
计量
- 文章访问数: 3437
- HTML全文浏览量: 155
- PDF下载量: 636
- 被引次数: 0
出版历程
- 收稿日期: 2008-02-07
- 修回日期: 2008-09-26
- 刊出日期: 2008-11-15

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

Department of Mathematics, Kurukshetra University, Kurukshetra-136 119, India

摘要

摘要: 基于广义热弹性扩散理论，边界无应力作用、绝热/恒温和化学势边界条件作用下，研究均匀、横观各向同性、热弹性扩散半空间Rayleigh波的传播．采用Green和Lindsay(GL)理论，热扩散和热扩散-力学松弛条件采用4个不同的时间常数加以控制．导出了所研究介质中表面波传播的久期方程．为了说明和比较分析结果，用图形示出了各向异性和扩散对相速度、衰减系数的影响．同时，还推导了某些特殊情况下的频率方程．
- 波传播 /
- 横观各向同性 /
- 广义热弹性扩散 /
- 相速度 /
- 衰减系数
Abstract: 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.
- wave propagation /
- transversely isotropic /
- generalized thermoelastic diffusion /
- phase velocity /
- attenuation coefficient

HTML全文

参考文献(27)

[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.