留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

无限非均质横观各向同性黏弹性介质中具有圆柱孔洞时的振动

D·P·阿查亚 因德拉吉·罗伊 P·K·比沃斯

D·P·阿查亚, 因德拉吉·罗伊, P·K·比沃斯. 无限非均质横观各向同性黏弹性介质中具有圆柱孔洞时的振动[J]. 应用数学和力学, 2008, 29(3): 331-341.
引用本文: D·P·阿查亚, 因德拉吉·罗伊, P·K·比沃斯. 无限非均质横观各向同性黏弹性介质中具有圆柱孔洞时的振动[J]. 应用数学和力学, 2008, 29(3): 331-341.
D. P. Acharya, Indrajit Roy, P. K. Biswas. Vibration of an Infinite Inhomogeneous Trasversely Isotropic Viscoelastic Medium With a Cylindrical Hole[J]. Applied Mathematics and Mechanics, 2008, 29(3): 331-341.
Citation: D. P. Acharya, Indrajit Roy, P. K. Biswas. Vibration of an Infinite Inhomogeneous Trasversely Isotropic Viscoelastic Medium With a Cylindrical Hole[J]. Applied Mathematics and Mechanics, 2008, 29(3): 331-341.

无限非均质横观各向同性黏弹性介质中具有圆柱孔洞时的振动

详细信息
  • 中图分类号: O343.8;O345

Vibration of an Infinite Inhomogeneous Trasversely Isotropic Viscoelastic Medium With a Cylindrical Hole

  • 摘要: 在无限介质中,研究了横截面为圆的柱形孔洞表面上瞬时径向力或扭转引起的扰动,讨论了高阶黏弹性和横观各向同性弹性参数的非均匀性对扰动产生的影响.根据高阶黏弹性Voigt模型,将非零应力分量简化为径向位移分量项表示,这对横观各向同性和高阶黏弹性固体介质是合宜的.导出了含有弹性和黏弹性参数以幂律变化时的应力方程.在瞬时力和扭转边界条件下,求解该方程,求得径向位移分量以及和它相关的应力分量,用修正的Bessel函数项来表示.对瞬时径向力作用问题进行了数值分析,并给出了不同阶的黏弹性和非均质性时的位移和应力变化图形.扭转作用时扰动的数值解可以用类似的方法研究,这里不再深入讨论.
  • [1] Flugge W.Viscoelasticity[M].London:Blasdell Publishing Co,1967.
    [2] Ezzat M A. Fundamental solution in generalized magneto thermoelasticity with two relaxation times for perfect conductor cylindrical region[J].Internat J Engrg Sci,2004,42(13/14):1503-1519. doi: 10.1016/j.ijengsci.2003.09.013
    [3] Bullen K E.An Introduction to Theory of Seismology[M].Cambridge: Cambridge University Press,1963.
    [4] Nowacki W.Dynamics of Elastic System[M].London: Chapman and Hall,1963.
    [5] 约塞夫·H·M. 带球形空腔的广义热弹性无限大材料的弹性模量和传热系数与材料参考温度的相关性[J].应用数学和力学,2005,26(4):431-436.
    [6] Sengupta P R, De N, Kar M,et al.Rotatory vibration of sphere of higher order viscoelastic solid[J].Internat J Math Math Sci,1994,17(4):799-806. doi: 10.1155/S0161171294001110
    [7] Biswas P K, Sengupta P R.Torsional vibration of a non-homogeneous viscoelastic circular cylinder involving strain and stress rate of higher order[J].Acta Ciencia Indica,1991,17M(4):747-754.
    [8] Biswas P K, Sengupta P R.Disturbances in an infinite visco-elastic medium by transient radial forces and twist on the surface of a cylindrical hole considering rate of stress and rate of strain of higher order[J].Indian J Theo Phys,1989,37(1):61-70.
    [9] Das T K, Sengupta P R.Effect of damping on the torsional vibration of a homogeneous viscoelastic circular cylinder including strain rate stress rate[J].Acta Ciencia Indica,1991,17M(2):271-280.
    [10] Bhattacharya S,Sengupta P R. Disturbances in a general viscoelastic medium due to impulsive forces on a spherical cavity[J].Gerlands Beitr Geophysik, Leipzig,1978,87Ⅰ(8):57-62.
    [11] Biswas P K, Das T K. Propagation of waves in a higher order infinite visco-elastic medium by transient radial forces and twist on the surface of a cylinder[J].Acta Ciencia Indica,1991,17M(3):457-462.
    [12] Ghosh N C, Sengupta S. Radial deformation of a linearly varying non-homogeneous spherically anisotropic elastic spherical nodule with concentric spherical inclusion[J].Bull Calcutta Math Soc,1997,89(2):115-126.
    [13] Gaikwad M N,Deshmukh K C. Thermal stresses in anisotropic cylinder[J].Bull Calcutta Math Soc,2004,96(6):447-452.
    [14] Mukherjee J.Radial vibration of an inhomogeneous aeolotropic cylindrical shell[J].Indian J Mech Maths,1969,7(2):76-82.
    [15] Mondal A K, Sengupta S.Twisting of a hollow circular cylinder of cylindrically aeolotropic non-homogeneous material[J].J Bihar Math Soc,1999,19(1):41-50.
    [16] Voigt W. Theortische student über die elasticitatsverhalinisse krystalle [J].Abh Ges Wiss Goettingen,1887,34.
    [17] Mukherjee J.The disturbances in an infinite inhomogeneous medium due to transient forces and twists on the surface of a buried spherical source[J].Pure and Appl Geoph(PAGEOPH),1969,76(5):65-70. doi: 10.1007/BF00877837
    [18] Allam M N, Elsibai K A, AbouElregal A E. Thermal stresses in a harmonic field for an infinite body with a circular cylindrical hole without energy dissipation[J].Journal of Thermal Stresses,2002,25(1):57-67. doi: 10.1080/014957302753305871
    [19] Mukhopadhyay S.A problem on thermoelastic interactions without energy dissipation in an unbounded body with a spherical cavity subjected to harmonically varying stress[J].Bull Calcutta Math Soc,2007,99(3):261-270.
    [20] Arfken G B, Weber H J.Mathematical Methods for Physicists[M].Fifth Ed.New Delhi:Academic Press,2001,709-716.
    [21] Yang J, Shen H S.Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions[J].Composites Part B: Engineering,2003,34(2):103-115. doi: 10.1016/S1359-8368(02)00083-5
    [22] Zhang N H, Wang M L. Thermoviscoelastic deformations of functionally graded thin plates[J].European Journal of Mechanics-A/Solids,2007,26(5):872-886. doi: 10.1016/j.euromechsol.2007.03.002
    [23] Ghosh M K. Stresses in a semi-infinite non-homogeneous elastic medium due to torsion[J].J Indian Acad Math,2003,25(2):371-381.
  • 加载中
计量
  • 文章访问数:  2771
  • HTML全文浏览量:  84
  • PDF下载量:  480
  • 被引次数: 0
出版历程
  • 收稿日期:  2007-06-01
  • 修回日期:  2007-12-28
  • 刊出日期:  2008-03-15

目录

    /

    返回文章
    返回