An axi symmetric numerical elastic contact model for application to the transmission of ultrasound across a rough interface

摘要

The authors are currently investigating convenient coupling of transducers to improve the ultrasonic technique when inspecting concrete structures. The work has taken a number of ideas from a previous project at Imperial College where experiments on the use of rubber as an ultrasonic coupling medium were performed. In that work the deformations of a solid pressed onto a rough surface were predicted using a numerical elastic line contact model. Predictions of the change in surface separation as a function of load were applied to quasi static contact models to estimate reflection or transmission coefficients for a given interface. The current work considers various axi-symmetric solid contact designs that would attach to the face of a cylindrical transducer. When modelling the contact of such devices with a rough surface, three dimensional solutions were found to take considerable computational time. Line contact is more suitable for modelling contact of parallel rollers and assumes that the surface roughness is parallel. It was therefore decided to derive more appropriate models where the solid bodies and hence the surface roughness are assumed axi-symmetric in profile. Solution techniques for solving such equations are given in (4,6). In this paper the authors derive the equations for a deformable body in contact with a rough surface and present an alternative iterative technique for solution.