Torsional wave propagation in non‐homogeneous layer between non‐homogeneous half‐spaces

The study of surface wave in a layered medium has their possible application in geophysical prospecting. In the present work, dispersion equation for torsional wave in an inhomogeneous isotropic layer between inhomogeneous isotropic half‐spaces has been derived. Two cases are discussed separately for torsional wave propagation in inhomogeneous layer between homogeneous and non‐homogeneous half‐spaces, respectively. Further, two possible modes for torsional wave propagation are obtained in case of inhomogeneous layer sandwiched between non‐homogeneous half‐spaces. Closed form solutions for displacement in the layer and half‐spaces are obtained in each case. The study reveals that the layer width, layer inhomogeneity, frequency of inhomogeneity, as well as inhomogeneity in the half‐space has significant effect on the propagation of torsional surface waves. Displacement and implicit dispersion equation for torsional wave velocities are expressed in terms of Heun functions and their derivatives. Effects of inhomogeneity on torsional wave velocity are also discussed graphically by plotting the dimensionless phase velocity against dimensionless and scaled wave number for different values of inhomogeneity parameter. Copyright © 2012 John Wiley & Sons, Ltd.

[1]  Arthur Beiser,et al.  Elastic Waves in Layered Media , 2015 .

[2]  S. Gupta,et al.  Propagation of torsional waves in an inhomogeneous layer over an inhomogeneous half-space , 2011 .

[3]  Chun-li Zhang,et al.  Torsional wave propagation in a circumferentially poled piezoelectric cylindrical transducer with unattached electrodes , 2010, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[4]  B. Kennett,et al.  Dynamic Earth: crustal and mantle heterogeneity , 2008 .

[5]  R. Paroni,et al.  An asymptotic approach to the torsion problem in thin rectangular domains , 2008 .

[6]  Christophe Bacon,et al.  Finite element modeling of torsional wave modes along pipes with absorbing materials , 2006 .

[7]  H. Yuan,et al.  A Study on the Torsional Wave of Fiber-reinforced Composite Materials , 2006 .

[8]  R. G. Payton,et al.  Green’s function for torsional waves in a cylindrically monoclinic material , 2005 .

[9]  A. Gupta,et al.  Propagation of Torsional Surface Waves in an Elastic Layer with Void Pores over an Elastic Half Space with Void Pores , 2003 .

[10]  C. Sarı,et al.  Analysis of gravity anomalies with hyperbolic density contrast: An application to the gravity data of Western Anatolia , 2002 .

[11]  Ioannis Vardoulakis,et al.  Torsional surface waves in a gradient-elastic half-space , 2000 .

[12]  A. Gupta,et al.  Torsional surface waves in nonhomogeneous and anisotropic medium , 1996 .

[13]  A. Gupta,et al.  Propagation of torsional surface waves in a homogeneous substratum over a heterogeneous half-space , 1996 .

[14]  A. Gupta,et al.  Propagation of torsional surface waves in viscoelastic medium , 1996 .

[15]  A. Gupta,et al.  Torsional surface wave in an elastic half-space with void pores , 1993 .

[16]  C. Vrettos.  In-plane vibrations of soil deposits with variable shear modulus: II. Line load , 1990 .

[17]  D. Gubbins.  Seismology and Plate Tectonics , 1990 .

[18]  C. Vrettos.  In-plane vibrations of soil deposits with variable shear modulus: I. Surface waves , 1990 .

[19]  Kazumi Watanabe.  Plane SH-waves in harmonically inhomogeneous elastic media , 1984 .

[20]  I. Vardoulakis.  Torsional surface waves in inhomogeneous elastic media , 1984 .

[21]  G. Ronca,et al.  Study of the propagation of a torsional wave in a curved wire , 1970 .

[22]  F. Birch.  Elasticity and Constitution of the Earth's Interior , 1952 .

[23]  K. E. Bullen,et al.  The problem of the earth's density variation , 1940 .

[24]  A. Chattopadhyay,et al.  Torsional Waves in Self-Reinforced Medium , 2009 .

[25]  N. Tanimoto.  An Analysis of Combined Longitudinal and Torsional Elastic-Plastic-Viscoplastic Waves in a Thin-Walled Tube , 2007 .

[26]  R. Meissner.  The little book of planet Earth , 2002 .

[27]  A. Gupta,et al.  Propagation of torsional surface waves in a heterogeneous half-space under a rigid layer , 2001 .

[28]  A. Ronveaux,et al.  Heun's differential equations , 1995 .