Modeling ultrasonic transducer in homogeneous and non-homogeneous media using DPSM method

Abstract

Modeling ultrasonic transducers is an important aspect of research in nondestructive evaluation and testing. In most nondestructive evaluation applications, the ultrasonic transducers are traditionally modeled as: (1) point sources generating spherical wave fronts (2) line sources generating cylindrical wave fronts, or (3) planar surfaces generating plane wave fronts. In reality, the transducer front face has finite dimensions; it is neither point source nor planar source because the ultrasound that emits from a piezoelectric transducer does not originate from a point or an infinite plane, but instead originates from the finite surface of the piezoelectric element with flat or curved front face. Analytically modeling the fields radiated by ultrasonic transducers is a very difficult task because of the large number of possible transducer types, sizes and configurations that are used in practice. In this study, a semi analytical technique the Distributed Point Source Method (DPSM) is adapted to model ultrasonic transducers. The DPSM discretizes the transducer surface into a finite number of elemental surfaces. As a result, the complexity associated with the discretization of the three-dimensional problem geometry as done in the finite element technique is reduced. In the DPSM technique, the fundamental governing equations for elastic wave propagation in a fluid and in a solid are solved. For this reason, the DPSM technique is called a semi-analytical technique. In this research, computer codes for computing the ultrasonic field in a three dimensional inhomogeneous medium in front of a transducer of finite dimension have been written in MatLab. Two different cases are considered in this study, nonhomogeneous fluid and fluid-solid interface. Both normal and inclined incidence cases are investigated. This investigation shows that DPSM is an efficient technique for modeling ultrasonic transducers in nonhomogeneous media.