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.
The influences of higher order viscoelasticity and the inhomogeneities 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 nonvanisbing stress components valid for a transversely isotropic and higher order viscoelastic 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.
出处
《应用数学和力学》
CSCD
北大核心
2008年第3期331-341,共11页
Applied Mathematics and Mechanics
关键词
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
higher order viscoelasticity
inhomogeneity and transversely isotropy
transient force and twist
radial displacement
stress component
modified Bessel function
