Wave propagation in a homogenous piezoelectric solid cylinder of transversely isotropic material
Yenwong-Fai, Alfred Sevidzem
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.