Mathematical model for internal ultrasonic inspection of cylindrically layered structures

Abstract

An efficient numerical model is described for predicting the pulse-echo response of an ultrasonic transducer insonifying a cylindrically layered medium from the inside. A rigorous 3-D formulation of the problem is first developed. Reduction to an approximate but computationally much more efficient form is accomplished based on several general assumptions regarding the geometrical properties of the transducer and the cylindrically symmetric layered medium. Within these constraints, the model accurately accounts for diffraction, attenuation, and dispersion in the interior immersing fluid and for reflection from the multilayered annular region that may contain strong internal resonances. Calibration of the temporal response of the transducer and associated measurement electronics is an integral part of the model, which is formulated using reciprocity relations for cylindrical coordinates. The principal application for the model is the ultrasonic internal inspection of pipes.