Location

La Jolla, CA

Start Date

1-1-1998 12:00 AM

Description

In elastic materials the propagation of ultrasonic waves is governed by the Christoffers equation, which relates the displacement vector as a function of time and position to the stiffness tensor at that point. If the material is inhomogeneous, an analytical solution of the partial differential equation becomes exceedingly difficult or impossible, especially in the presence of non-trivial boundary or initial conditions. Finite Difference Equations (FDE) provide a very convenient tool for the solution of partial differential equations (PDE’s) in media, in which the physical properties are homogeneous or vary continuously, such as Epstein Layers. Otherwise the use of FDE’s may be justified only as an approximation. In fact, for the conversion of derivatives into finite differences, a “smoothing” of the variables across the interfaces is required and, if the discontinuity is sharp, severe errors or ambiguities may result [1,2].

Book Title

Review of Progress in Quantitative Nondestructive Evaluation

Volume

17A

Chapter

Chapter 4: NDE Sensors and Fields

Section

UT Sensors, Transducers and Fields

Pages

971-977

DOI

10.1007/978-1-4615-5339-7_125

Language

en

File Format

application/pdf

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Jan 1st, 12:00 AM

Simulation of Ultrasound Propagation across Interfaces with Imperfect Contact

La Jolla, CA

In elastic materials the propagation of ultrasonic waves is governed by the Christoffers equation, which relates the displacement vector as a function of time and position to the stiffness tensor at that point. If the material is inhomogeneous, an analytical solution of the partial differential equation becomes exceedingly difficult or impossible, especially in the presence of non-trivial boundary or initial conditions. Finite Difference Equations (FDE) provide a very convenient tool for the solution of partial differential equations (PDE’s) in media, in which the physical properties are homogeneous or vary continuously, such as Epstein Layers. Otherwise the use of FDE’s may be justified only as an approximation. In fact, for the conversion of derivatives into finite differences, a “smoothing” of the variables across the interfaces is required and, if the discontinuity is sharp, severe errors or ambiguities may result [1,2].