Ultrasonic scattering from imperfect interfaces: A quasi-static model

TLDR: In this article, a quasi-static model for ultrasonic transmission and reflection at imperfect interfaces is developed, where the interface is represented by a distributed spring determined by the change in static compliance of the medium with respect to one with a perfect interface, and a distributed mass, representing excess mass at the interface.

Abstract: A quasi-static model for the ultrasonic transmission and reflection at imperfect interfaces is developed. The interface is represented by a distributed spring, determined by the change in static compliance of the medium with respect to one with a perfect interface, and a distributed mass, representing excess mass at the interface. Comparison of the model predictions to exact solutions for two simple cases illustrates its accuracy at low frequencies. The spring stiffnesses can be derived from existing solutions for the elastic displacement of materials containing cracks and inclusions under static load. Results for a variety of cases are reviewed. Applications of the model to study the characteristics of partially contacting surfaces in several problem areas of current interest are discussed.