波在分数Maxwell流体饱和孔隙介质界面的反射和透射  

Reflection and Transmission of Elastic Waves at an Interface between Solid and Fractional Maxwell Fluid-saturated Porous Medium

作　　者：张秀娥 康永刚 ZHANG Xiu-e;KANG Yong-gang(Department of Basic Courses Teaching,Institute of Disaster Prevention,Sanhe 065201,China)

机构地区：[1]防灾科技学院基础课教学部,三河065201

出　　处：《科学技术与工程》2022年第36期15881-15888,共8页Science Technology and Engineering

基　　金：廊坊市科技支撑计划(2021013161,2021013073)。

摘　　要：为了准确描述弹性波在流体饱和孔隙介质中的频散和衰减特征,需要研究流体的非牛顿效应。作为当前一种热门的非牛顿流体模型,分数Maxwell模型还没有应用到孔隙介质的弹性波领域。通过对分数Maxwell流体在周期性振动圆管中流动的分析,给出黏滞系数修正因子,由此来表示孔隙流体非牛顿效应的影响。推导了波从弹性固体射向孔隙介质时,在两个半空间分界面的反射和透射系数,其中孔隙介质充满数Maxwell流体。以往研究波在孔隙介质界面反射和透射时,由Snell定理会给出物理意义不明确的复数角度。按照非均匀波讨论,由Snell定理给出的角度为实数,物理意义明确。发现波由弹性固体射向孔隙介质时,孔隙介质中3种类型波的传播方向不同,但衰减方向均垂直于界面。通过数值算例,以及与牛顿流体饱和的情况对比,考察了孔隙流体非牛顿效应对反射和透射系数的影响。结果表明:当孔隙介质充满分数Maxwell流体时,波在界面的反射和透射情况,明显不同于充满牛顿流体的时候。In order to accurately describe the dispersion and attenuation characteristics of elastic waves in fluid-saturated porous media,it is necessary to study the non-Newtonian effects of porous fluid.As a popular model of the non-Newtonian fluid,the fractional Maxwell model has not been applied to the field of elastic waves in porous medium.To study the non-Newtonian effect of the porous fluid,the viscosity correction factor was deduced by analyzing the oscillating fractional Maxwell fluid in a cylindrical tube.The reflection and transmission coefficients of plane waves from an elastic solid half-space to a fractional Maxwell fluid-saturated porous medium half-space were investigated.In previous study,the complex angles with unclear physical meaning are often obtained by Snell Theorem.The inhomogeneous waves in porous medium were supposed,the angles given by Snell Theorem was real value and has clear physical meaning.When the elastic wave propagates from solid to porous medium,the direction of propagation of three kinds of wave in porous medium were different,but the directions of attenuation of them were all perpendicular to the interface.Through comparing with these coefficients predicted by Biot’s theory for ordinary Newtonian fluid-saturated porous medium,the non-Newtonian effect of the porous fluid on the reflection and transmission coefficients were investigated.The results show that the reflection and transmission of elastic waves at the interface of the fractional Maxwell fluid-saturated porous medium are distinctly different from the result obtained at the interface of the Newtonian fluid-saturated porous medium.

关 键 词：非均匀波 非牛顿流体 分数阶导数 反射和透射 

分 类 号：O347.4[理学—固体力学]