The distributed point source method is commonly used to predict the complex acoustic field emitted by ultrasonic transducers. In this paper, it is presented as an alternative to conventional approaches often used when solving rough surface scattering problems. Surface shadowing and multiple scattering effects are inherently included in the mesh-free semi-analytical simulation method through matrix manipulation making it very efficient and simple to implement. Results are presented which illustrate the improvement in accuracy gained over the Kirchhoff approximation and the decrease in computational load over the finite element method, culminating in greater than an order of magnitude decrease in required simulation time. The method is applied to the practical problem of online wall thickness monitoring within corrosive environments, illustrating the variability in reflected pulse shape that could be expected from rough surfaces with similar statistics. Three commonly implemented time-of-flight algorithms are used to analyze a large number of simulated signals from which it is concluded that those based on first arrival time are more stable under increasing roughness conditions than those which are based on reflected pulse shape.
The challenge of accurately simulating how incident scalar waves interact with rough boundaries has made it an important area of research within many scientific disciplines. Conventional methods, which in the majority of cases focus only on scattering in two dimensions, often suffer from long simulation times or reduced accuracy, neglecting phenomena such as multiple scattering and surface self-shadowing. A simulation based on the scalar wave distributed point source method (DPSM) is presented as an alternative which is computationally more efficient than fully meshed numerical methods while obtaining greater accuracy than approximate analytical techniques. Comparison is made to simulated results obtained using the finite element method for a sinusoidally periodic surface where scattering only occurs in two dimensions, showing very good agreement (<0.2 dB). In addition to two-dimensional scattering, comparison to experimental results is also carried out for scattering in three dimensions when the surface has a Gaussian roughness distribution. Results indicate that for two-dimensional scattering and for rough surfaces with a correlation length equal to the incident wavelength (λ) and a root mean square height less than 0.2λ, the scalar wave approximation predicts reflected pulse shape change and envelope amplitudes generally to within 1 dB. Comparison between transducers within a three-element array also illustrate the sensitivity pulse amplitude can have to sensor position above a rough surface, differing by as much as 17 dB with a positional change of just 1.25λ.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.