Analysis of Axisymmetric and Non-Axisymmetric Wave Propagation in a Homogeneous Piezoelectric Solid Circular Cylinder of Transversely Isotropic Material (original) (raw)
Related papers
Physics Procedia, 2010
Non-axisymmetric waves in a free homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization are investigated on the basis of the linear theory of elasticity and linear electromechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained through the application of the mechanical and two types of electric boundary conditions at the surface of the cylinder. A convenient method of calculating dispersion curves and phase velocities is discussed, and resulting curves are presented for propagating and evanescent waves for the piezoelectric ceramic material PZT-4 for non-axisymmetric modes of circumferential wave number m = 1. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the strength of the electromechanical coupling.
International Journal of Solids and Structures, 2009
A study concerning the propagation of free non-axisymmetric waves in a homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization is carried out on the basis of the linear theory of elasticity and linear electromechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained by the application of the mechanical and two types of electric boundary conditions at the surface of the piezoelectric cylinder. A novel method of displaying dispersion curves is described in the paper and the resulting dispersion curves are presented for propagating and evanescent waves for PZT-4 and PZT-7A piezoelectric ceramics for circumferential wave numbers m = 1, 2, and 3. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the measure of the electromechanical coupling of the material.
Axisymmetric Wave Propagation in Functionally Grade Cylinder with Isotropic Concentric Layers
Mechanics of Solids, 2020
The axisymmetric wave propagation is investigated in coaxially layered isotropic functionally graded cylinders with different mass and stiffness properties of the layers. Exact solutions of the governing equations of the wave propagation in the cylinders exist only for isotropic, transversely isotropic and piezoelectric transversely isotropic cylinders. In the case of the functionally graded cylinders exact solutions are not known. The authors developed a method of exact solution of the problem, which is based on matching of continuity and boundary conditions on junctions of the layers. The continuity and boundary conditions are formulated in terms of exact solutions for displacements and stresses in the layers obtained in Bessel functions. The spectral diagrams of the dispersion curves of frequencies versus wave numbers are plotted for both propagating and evanescent waves and graphs of the phase and group velocities are obtained from these diagrams.
Acoustic wave scattering from transversely isotropic cylinders
The Journal of the Acoustical Society of America, 1996
Mathematical expressions are derived for the far-field backscattering amplitude spectrum resulting from oblique insonification of an infinite, transversely isotropic elastic cylinder by a plane acoustic wave. The normal-mode solution is based on decoupling of the scalar potential representing the horizontally polarized shear wave from those of the compressional and vertically polarized waves. The solution degenerates to the well-known simple model for isotropic cylinders in the case of very weak anisotropy. The solution is used to study the influence of each element of the stiffness matrix on the various resonant modes of vibration. Perturbations of the elements c33 and c44, which characterize the cylinder along the axis, significantly affect resonant frequencies corresponding to axially guided waves. Perturbations of c11 and c12, which characterize the material on the transverse plane, predominantly affect the Rayleigh and Whispering Gallery resonance frequencies. Perturbations of ...
Analysis of multilayered piezoelectric cylinders with noncircular cross-section
The problem of ultraacoustic wave propagation in piezoceramic cylinders remain an interesting one since such materials are widely used in acoustoelectronics and ultrasonic nondestructive evaluation. In the current paper we study the wave propagation in piezoceramic multilayered cylindrical waveguides with noncircular cross-section. Infinite transversely isotropic cylinders considered here have circular or hollow cross-sections with sector cut of any angular measure arbitrary boundary conditions on surfaces. The method is based on exact analytical integration of wave equations of linear electroelastic medium by using wave potentials. Dispersion functions are obtained from boundary conditions in an analytical form of functional determinants and numerical analysis is carried out to illustrate the approach. The effect of various mechanical parameters is studied and the potential applications are discussed. Results are compared with those published earlier in order to check up the accuracy of the proposed approach, which is found to be very accurate and efficient.
Wave Motion, 2002
This paper studies wave propagation in the vicinity of a cylindrical solid formation submerged in an acoustic medium generated by point blast loads placed outside the inclusion. The full 3D solution is obtained first in the frequency domain as a discrete summation of responses for 2D problems defined by a spatial Fourier transform. Each 2D solution is computed using the Boundary Element Method, which makes use of two-and-a-half-dimensional Green's functions. This model is implemented to obtain Fourier spectra responses which make it possible to identify the behavior of both the axisymmetric and non-axisymmetric guided wave modes, when the cross-section of the elastic inclusion changes from circular to smooth oval.
Elastic wave propagation in circumferential direction in anisotropic cylindrical curved plates
Ultrasonic nondestructive inspection of large-diameter pipes is important for health monitoring of ailing infrastructure. Longitudinal stress-corrosion cracks are detected more efficiently by inducing circumferential waves; hence, the study of elastic wave propagation in the circumferential direction in a pipe wall is essential. The current state of knowledge lacks a complete solution of this problem. Only when the pipe material is isotropic a solution of the wave propagation problem in the circumferential direction exists. Ultrasonic inspections of reinforced concrete pipes and pipes retrofitted by fiber composites necessitate the development of a new theoretical solution for elastic wave propagation in anisotropic curved plates in the circumferential direction. Mathematical modeling of the problem to obtain dispersion curves for curved anisotropic plates leads to coupled differential equations. Unlike isotropic materials for which the Stokes-Helmholtz decomposition technique simplifies the problem, in anisotropic case no such general decomposition technique works. These coupled differential equations are solved in this paper. Dispersion curves for anisotropic curved plates of different curvatures have been computed and presented. Some numerical results computed by the new technique have been compared with those available in the literature.