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Rough Scatterers in Acoustics and Elastodynamics

Doctoral thesis, 1995

The purpose of this thesis is to investigate the influence of roughness on wave scattering from finite-sized surfaces, in particular elastic wave scattering from cracks.
Acoustic scattering from a sphere is considered using the null field approach. The ensemble averaged T matrix of the sphere is obtained as a perturbation series where the small parameter is the ratio of the RMS height to the wavelength. The scattered far field and the scattering cross section are calculated for an incident plane wave.
The same method is applied to two-dimensional elastic wave scattering from an open nonplanar crack. The incident wave is taken to be a horizontally polarized shear wave. First an ordinary crack with zero volume is considered; then the solution is generalized to the case where the crack has a finite volume. The numerical results indicate that the influence of roughness is in most cases negligible compared to the effect of a finite volume. This is an expected result since roughness is a second order effect when ensemble averaged quantities are studied, while the volumetric effects are of first order. However, this does not necessarily mean that roughness is negligible for a specific crack of the ensemble.
Acoustic scattering from a rough circular disc immersed in a nonviscous fluid of infinite extent is studied using an integral equation method. A number of deterministic surfaces are constructed using a numerical simulation technique and the T matrix is determined for each surface by a first order perturbation method. Some numerical results for the back-scattered far-field amplitude are calculated.
Finally, the elastic wave scattering problem for a rough penny-shaped crack is solved using the same integral equation method. The stationary-phase approximation is used to determine the back-scattered far field. Numerical results are obtained for an incident plane longitudinal wave and a scattered longitudinal wave. For cracks with identical statistical properties there is a considerable spread in scattering data at oblique incidence except for low frequencies. Results are also given in the time domain, which means that pulse-echo testing is simulated.

acoustic scattering

penny-shaped crack

rough surfaces

elastodynamic scattering

T matrix

null field approach