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

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

1.
班加巴斯英宁学院,加尔各答 700 009,西孟,印度;2.卡亚尼大学数学系,卡亚尼,那迪,西孟,印度;3.甘杰拉巴拉学院数学系,741248,743145 西孟,印度

详细信息

中图分类号: O343.8；O345
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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

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

1.
Bangabasi Morning College, Kolkata 700 009, WB, India;

摘要

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．
- 高阶黏弹性 /
- 非均质和横观各向同性 /
- 瞬时力和扭转 /
- 径向位移 /
- 应力分量 /
- 修正的Bessel函数
Abstract: The influences of higher order viscoela sticity and the inhomo geneities of the transversely isotropic elastic parameters on the disturbances in an infinite medium, caused by the presence of a transient radial force or twist on the surface of a cylindrical hole with circular cross section are investigated. Following Voigt's model for higher order viscoelasticity the nonvanishing stress components valid for a transversely isotropic and higher or derviscoelastic solid medium were deduced in terms of radial displacement component. Considering the power law variation of elastic and viscoelastic parameters, the stress equation of motion was developed. Solving this equation under suitable boundary conditions due to transient forces and twists radial displacement and relevant stress components were found out in terms of modified Bessel functions. The problem for the presence of transient radial force was numerically analysed. Modulations of displacement and stresses due to different order of viscoelasticity and inhomogeneity were graphically depicted. The numerical study of the disturbance caused by the presence of twist on the surface may be similarly done and is not pursued.
- higher order viscoelasticity /
- inhomogeneity and transversely isotropy /
- transient force and twist /
- radial displacement /
- stress component /
- modified Bessel function

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参考文献(23)

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