Wave propagation in a homogenous piezoelectric solid cylinder of transversely isotropic material
Date
2009-02-04T08:53:36Z
Authors
Yenwong-Fai, Alfred Sevidzem
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Abstract
The ultrasonic nondestructive evaluation (NDE) of composite cylinders is dependent on
the thorough understanding of the propagation characteristics of the wave modes in these
materials. In this dissertation the propagation of free harmonic non-axisymmetric (flexural)
waves in a homogeneous piezoelectric solid cylinder of transversely isotropic material is
studied, on the basis of the linear theory of elasticity and linear electromechanical coupling
of the elastic and electric variables. The equations of motion of the cylinder are developed
using the constitutive relations of a piezoelectric material possessing transversely isotropic
symmetry properties, with the symmetry direction collinear with the axis of the cylinder. The
physically allowed boundary conditions are derived from Hamilton’s variational principle.
Four displacement and three electric potentials satisfying Helmholtz’s equation are used
to solve the equations of motion of the cylinder. The characteristic equation (dispersion
relation) is obtained by the application of the boundary conditions satisfied by the elastic
and electric variables. The characteristic equation is solved numerically by a novel method
which makes use of the three dimensional plot of the log of the modulus of the left hand side
of the characteristic equation. The results are numerically illustrated via dispersion curves
of a sample PZT-4 composite cylinder. Significant changes in the propagating wave modes
are revealed by the dispersion curves, when compared with a corresponding non-piezoelectric
model of a PZT-4 cylinder. It is also observed that the dispersion curves are sensitive to the
form of the electric boundary conditions.