UBC Theses and Dissertations
Shadows created by an array of acoustically hard cylinders above a rigid plane Clark, David
Transient radiation from, and scattering by, objects of finite size is important for applications pertaining to antennas and to target identification. The goal of this thesis work was to study the waves scattered from an array of cylinders above a rigid plane by running experiments on real models using an acoustic scatter-mapping system developed by Garfield Mellema . The experiments were then simulated using MatLab 4.0 on a Sun Sparc 10 workstation. The first experiments were run on three different sized cylinders with a radius of 1.3 cm (0.35 wavelengths ), 5.7 cm (1.54 wavelengths), and 10.6 cm ( 3.15 wavelengths). The second set of experiments were run on a two cylinder array with each cylinder having a radius of 5.7 cm. The parallel cylinders were placed directly above each other at varying distances apart. The simulations used the method of images and an algorithm first presented by V. Twersky which calculated the incident and scattered fields in the wave-number domain. In this paper a time domain solution was obtained by applying the inverse Fourier transform to the wave-number domain data. Twersky used a modal expansion to represent the fields scattered by each cylinder. Then the boundary conditions on each cylinder were used to determine each cylinder’s scattering coefficients. To solve for the boundary conditions on each scatterer Twersky used the addition theorem for Hankel functions to translate cylindrical co-ordinate systems between cylinders. A problem with this method, however, was that it also used a modal expansion which converged slowly for values of ka much greater than unity (k represents the wave number, and a is the cylinder radius). To overcome this convergence problem a different translation formula was derived using the integral form of the Hankel function and employing the stationary phase approximation. In addition, it was found that there was a relation between the scattering coefficients of the image cylinders and the scattering coefficients of the real cylindrical scatterers. This result was also substantiated in a study of multiple scattering by two cylinders completed by J. W. Young and J. C. Bertrand . Before the field theory is presented, most of the arrival paths are determined using appropriate ray paths. Plots of the arrival path length versus speaker position are presented so that each arrival path on the real data sets and the simulations can be traced. The results of the real data sets along with the optical ray path distance plots confirm the correctness of the simulation algorithm. The simulations correctly predict the arrival distances and the destructive interference patterns found on the real data sets for the single and double cylinder case.
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