Research Article
The Effects of Piezoelectricity on the Interaction of
Waves in Fluid-Loaded Poroelastic Half-Space
Vishakha Gupta
1
and Anil K. Vashishth
2
1
Department of Mathematics, Dyal Singh College, Karnal 132001, India
2
Department of Mathematics, Kurukshetra University, Kurukshetra 36119, India
Correspondence should be addressed to Vishakha Gupta; vi shu85@yahoo.co.in
Received 21 October 2013; Revised 9 February 2014; Accepted 6 March 2014; Published 17 April 2014
Academic Editor: Manas C. Ray
Copyright © 2014 V. Gupta and A. K. Vashishth. Tis is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Te efects of piezoelectricity on the interaction of waves at fuid-poroelastic interface are studied. Te constitutive equations and
governing equations are formulated and their solution is obtained. Te boundary conditions are described at fuid-solid interface.
Te efects of various parameters on the angle of refraction, amplitude ratios, displacements, electric potentials, and vertical
component of slowness are studied numerically for a particular model. Te results obtained are in agreement with the general
laws of physics.
1. Introduction
It is well known that piezoelectric materials produce an
electric feld when deformed and undergo deformation when
subjected to an electric feld. Piezoelectric materials are
acting as very important functional components in sonar
projectors, fuid monitors, pulse generators, and surface
acoustic wave devices. Te feld of piezoelectric materi-
als has advanced rapidly due to an increasing awareness
about capabilities of such materials, the development of new
materials and transducer designs, and increasingly stringent
design and control specifcations in aerospace, aeronautics,
industrial, automotive, biomedical, and nanosystems. Engi-
neering applications in surface acoustic waves (SAW) devices,
materials characterizations, and smart structures require the
analysis of elastic wave interaction with piezoelectric mate-
rials. Te problem of refection-transmission in piezoelectric
materials has been attracting unceasing attention in view of
its theoretical interest and from application points of view
also. Te characteristics of the refected and refracted waves
at such boundaries give information about the resolution
characteristics of acoustic transducers [1]. Te refection
and refraction of plane waves in piezoelectric anisotropic
materials have been mentioned in the texts of Auld [2],
Dieulesaint and Royer [3], and Parton and Kudryavtsev [4].
Noorbehesht and Wade [5] obtained the analytical expres-
sions for refection and transmission coefcients of the waves
at a boundary between piezoelectric materials and water
and studied the efects of angle of incidence and material
properties on these coefcients. Auld [6] studied the wave
propagation in piezoelectric materials. Te refection ofa
transverse wave from the surface of a piezoelectric crystal of
class 6 was studied by Alshits et al. [7]. Nayfeh and Chien
[8] made an analytical study on ultrasonic wave interaction
with fuid-loaded anisotropic piezoelectric substrates. Te
analytical expressions for the refection and transmission
coefcients were derived and propagation characteristics of
the leaky wave and free wave are also identifed. Every
and Neiman [9] analyzed the refection of electroacoustic
waves at the boundary of a piezoelectric half-space. Zinchuk
and Podlipenets [10, 11] obtained dispersion equations for
acoustoelectric Rayleigh wave in a periodic layer piezoelectric
half-space in a study for the 6 mm crystal class. Zaitsev
and Kuznetsova [12] performed a detailed analysis of energy
characteristics of bulk, surface, and plane acoustic waves
in piezoelectric materials and structures. Le Clezio and
Shuvalov [13] dealt theoretically and experimentally with
the transmission of acoustic waves through a piezoelectric
plate. Burkov et al. [14, 15] derived the basic equations
describing the wave at the interface between acentric crystals
Hindawi Publishing Corporation
Smart Materials Research
Volume 2014, Article ID 281013, 9 pages
http://dx.doi.org/10.1155/2014/281013