Focused Ultrasonic Beam Behavior at a Stress-Free Boundary and Applicability for Measuring Nonlinearity Parameter in a Reflection Mode

Thumbnail Image
Jeong, Hyunjo
Zhang, Shuzeng
Kim, Jongboem
Li, Xiongbing
Major Professor
Committee Member
Journal Title
Journal ISSN
Volume Title
Research Projects
Organizational Units
Journal Issue
Is Version Of
Review of Progress in Quantitative Nondestructive Evaluation
Center for Nondestructive Evaluation

Begun in 1973, the Review of Progress in Quantitative Nondestructive Evaluation (QNDE) is the premier international NDE meeting designed to provide an interface between research and early engineering through the presentation of current ideas and results focused on facilitating a rapid transfer to engineering development.

This site provides free, public access to papers presented at the annual QNDE conference between 1983 and 1999, and abstracts for papers presented at the conference since 2001.


Measurements of the acoustic nonlinearity parameter β are frequently made for early detection of damage in various materials. The practical implementation of the measurement technique has been limited to the through-transmission setup for determining the nonlinearity parameter of the second harmonic wave. For the purpose of practical applications, a pulse-echo measurement technique is more desirable which enables the single-side access of test components. The issue with using the second harmonic wave reflected from the stress-free interface is that such a boundary destructively alters the nonlinear generation process and consequently makes it difficult to obtain the reliable results of β.

In this work, we employ a focused beam theory to modify the phase reversal at the stress-free boundary, and consequently enhance the second harmonic generation during its back-propagation toward the initial source position. We first confirm this concept through experiment by using a spherically focused beam at the water-air interface, and measuring the reflected second harmonic and comparing with a planar wave reflected from the same stress-free or a rigid boundary. In order to test the feasibility of this idea for measuring the nonlinearity parameter of solids in a reflection mode, an array transducer beam is modeled for focusing at and reflection from a stress-free boundary. A nonlinearity parameter expression is then defined together with diffraction and attenuation corrections.