A 3D semi-analytical model to predict the behavior of ultrasonic bounded beam traveling in cylindrical solid bar embedded in a solid matrix

Abstract

A 3D semi-analytical model for predicting the behaviour of ultrasonic bounded beam travelling in cylindrical solid bar is presented. The bar is embedded in a solid matrix and the beam is emitted by an off-axis source for generating non-axisymmetric waves. Fourier series and Vector Hankel transform are combined to decompose the inside field into infinity of elementary cylindrical waves propagating into radial direction and planar waves propagating in axial direction. Global resolution method and Generalized Debye Series Expansion (GDSE) are used both to calculate the global reflection/transmission coefficients. A numerical model is implemented to demonstrate the validity of the present theoretical solution for predicting velocity signatures.