扭轉表面波在初始應力作用下於非均質與異向性及飽和液體孔隙彈性半空間之傳播

Torsional Surface Wave in Nonhomogeneous Anisotropic Medium and Fluid Saturated Poroelastic Medium under Initial Stress

陳昱良(Yu-Liang Chen)

指導教授 ： 葉超雄

國立臺灣大學/工學院/應用力學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.10253

摘要

由文獻中可以知道扭轉表面波無法在均質的彈性半空間中傳播，本文主要是要探討有初始應力作用下扭轉表面波在非均質異向性彈性介質與液體飽和孔隙彈性介質的可能性與其波傳特性。
本文的分析方法，主要是利用Biot增量變形彈性理論及孔隙彈性理論來分析扭轉表面波的波傳問題，首先我們由Biot彈性理論中得到問題的控制方程式，解出其位移場後，將邊界條件代入位移場中，可以得到扭轉表面波的相速度方程式並加以分析。
本文的問題主要分成兩個部分，第一部分是扭轉表面波在有初始應力作用下的非均質異向性彈性半空間中的波傳特性分析；第二部分是扭轉表面波在有初始應力作用下的液體飽和孔隙彈性半空間的波傳特性分析。
研究的結果顯示出扭轉表面波可以在非均質與液體飽和孔隙彈性半空間中傳播，而初始應力的存在會降低扭轉表面波的波速，其他因素，例如:非均質性、異向性因子、孔隙率等也會影響扭轉表面波的傳遞波速。

關鍵字

扭轉表面波 ； 初始應力 ； 異向性 ； 非均質 ； 孔隙材料 ； Biot彈性理論

並列摘要

It is well known that torsional surface wave cannot propagate in the homogeneous elastic half space. The present article studies the propagation of torsional surface wave in nonhomogeneous anisotropic medium and fluid saturated poroelastic medium under initial stress.
In this article, we try to use Biot’s incremental deformation theory of elasticity and poroelastic theory analyzing the wave propagation problem. Firstly, we obtaine the governing equations from Biot’s theory. By solving the governing equations, we can obtain the displacement field. Taking the displacement field into the boundary condition ,we can get the velocity equation of torsional surface wave.
The problem of this paper is divided into two parts. The first part is that propagation of torsional surface wave in nonhomogeneous anisotropic medium under initial stress; the second part is that propagation of torsional surface wave in fluid saturated poroelastic medium under initial stress.
The results of the study show that torsional surface wave can propagate in nonhomogeneous anisotropic medium and fluid saturated poroelastic medium under initial stress. The presence of initial stress diminishes the velocity of torsional surface wave. The other factors also influence the velocity of torsional surface wave as non-homogeneity, anisotropy factor etc.

並列關鍵字

torsional surface wave ； initial stress ； anisotropic ； inhomogeneous ； porous medium ； Biot’s theory

參考文獻

[1] Weiskopf, W.H. (1945), “Stresses in soils under a foundation”, Journal of the Franklin Institute , Vol. 239, pp.445-465.

[2] Biot, M.A. (1955),“Theory of elasticity and consolidation for a porous anisotropic solid”, Journal of Applied Physics, Vol. 26, pp.182-185.

[3] Biot, M.A. (1956), “Theory of deformation of a porous viscoelastic anisotropic solid”, Journal of Applied Physics, Vol. 27, pp.459-467.

[4] Biot, M.A. (1956), “Theory of propagation of elastic waves in fluid saturated porous solid”, Journal of the Acoustical Society of America Vol. 28, pp.168-178.

[5] Biot, M.A. (1962), “Mechanics of deformation and acoustic propagation in porous media”, Journal of Applied Physics, Vol. 33, pp.1482-1498.