Volume 108, Issue 3, September 2000
Index of content:
- GENERAL LINEAR ACOUSTICS 
A three-dimensional, two-way, parabolic equation model for acoustic backscattering in a cylindrical coordinate system108(2000); http://dx.doi.org/10.1121/1.1286074View Description Hide Description
A new PE model for solving three-dimensional, forward and backward sound propagation in a cylindrical coordinate system is presented. The model marches a wave field in the radial direction including the azimuthal diffraction effects, and solves for a backscattered field based on a three-dimensional, single scattering approach. A periodic sidewall boundary condition is applied for computations in a 360-degree sector, while an approximate sidewall boundary condition is used for calculation in a sector less than 360 degrees. These two sidewall boundary conditions are verified by the numerical results. The major drawback of using the cylindrical coordinate system, when the backscattering solution is valid within a limited area, is analyzed using a geometrical-optical interpretation. The model may be useful for studying three-dimensional backscattering phenomena comprising azimuthal diffraction effects.
108(2000); http://dx.doi.org/10.1121/1.1285919View Description Hide Description
An inverse scattering method that uses eigenfunctions of a scattering operator at a single frequency is extended to include the full range of frequencies present in the incident pulse waveform. The resulting so-called time-domain eigenfunction method is shown to yield a modulated version of the scattering potential. The potential is recovered by a demodulation process using cross correlation with a reference. Including an adaptive delay in the reference is shown to compensate partially for the linearization of the Born approximation and to extend its valid range. The -space window of the time-domain solution is expressed in terms of the incident waveform and shown to be smoother than that of a single-frequency solution. The time-domain method is examined using both calculated and measured data. In the calculations, an exact solution for scattering from one or multiple nonconcentric cylinders is used to obtain the scattered field. In the measurements, a novel ring-transducer system was employed to obtain the incident and total fields. The results of simulations and experiments show that the method is robust and accurate for the size of objects considered and that the point resolution approaches one-half the wavelength at the pulse center frequency.
108(2000); http://dx.doi.org/10.1121/1.1287028View Description Hide Description
Following a well-established formula used by many researchers, the scattering of an anti-plane shear wave by an infinite elastic cylinder of arbitrary relative radius centered in a traction-free two-dimensional isotropic plate has been examined. The plate is divided into three regions by introducing two imaginary planes located symmetrically away from the surface of the cylinder and perpendicular to surfaces of the plate. The wave field is expanded into cylinder wave modes in the central bounded region containing the cylinder, while the fields in the other two outer regions are expanded into plate wave modes. A system of equations determining the expansion coefficients is obtained according to the traction-free boundary conditions on the plate walls and the stress and displacement continuity conditions across the imaginary planes. By taking an appropriate finite number of terms of the infinite expansion series and a few selected points on the two properly chosen virtual planes and the surfaces of the plate through convergence and precision tests, a matrix equation to numerically evaluate the expansion coefficients is found. The method of how to choose the locations of the imaginary planes and the terms of the expansion series as well as the points on each respective boundary is given in Sec. III in detail. Curves of the reflection and transmission coefficients against the relative radius of the cylinder in welded and slip or cracked interfacial conditions are shown. Analysis on the contrast variations of the reflection and transmission coefficients for a cylinder in bonded and debonded interfacial situations is made. The relative errors estimated by the deviation of the numerical results from the principle of the conservation of energy are found to be less than
On approximating guided waves in plates with thin anisotropic coatings by means of effective boundary conditions108(2000); http://dx.doi.org/10.1121/1.1286882View Description Hide Description
In this paper, effective boundary conditions for elastic wave propagation in plates with thin coatings are derived. These effective boundary conditions are used to obtain an approximate dispersion relation for guided waves in an isotropic plate with thin anisotropiccoating layers. The accuracy of the effective boundary conditions is investigated numerically by comparison with exact solutions for two different material systems. The systems considered consist of a metallic core with thin superconductingcoatings. It is shown that for wavelengths long compared to the coating thickness there is excellent agreement between the approximate and exact solutions for both systems. Furthermore, numerical results presented might be used to characterize coatingproperties by ultrasonic techniques.