Lester W. Schmerr

Generation of the basis sets for multi-Gaussian ultrasonic beam models—An overview

By using a small number of Gaussian basis functions, one can synthesize the wave fields radiated from planar and focused piston transducers in the form of a superposition of Gaussian beams. Since Gaussian beams can be transmitted through complex geometries and media, such multi-Gaussian beam models have become powerful simulation tools. In previous studies the basis function expansion coefficients of multi-Gaussian beam models have been obtained by both spatial domain and k-space domain methods. Here, we will give an overview of these two methods and relate their expansion coefficients. We will demonstrate that the expansion coefficients that have been optimized for circular piston transducers can also be used to generate improved field simulations for rectangular probes. It will also be shown that because Gaussian beams are only approximate (paraxial) solutions to the wave equation, a multi-Gaussian beam model is ultimately limited in the accuracy it can obtain in the very near field.

An elastodynamic model for compressional and shear wave transducers

Elastodynamic models are developed for both contact ultrasonic compressional wave and shear wave transducers radiating into an elastic solid. Explicit high‐frequency asymptotic solutions are obtained for the major wave components present in the transducer responses. These solutions are compared, in both the frequency and time domains, with the response of a piston transducer radiating into a fluid. It is demonstrated that, within the main beam of the transducer and in the farfield, the fluid model accurately predicts the response in the elastic solid for both the compressional and shear wave cases. In the nearfield, the elastodynamic models provide a more complete description of the transducer radiated wave field.

Ultrasonic scattering by a flat-bottom hole in immersion testing: An analytical model

In ultrasonic nondestructive evaluation tests, a flat‐bottom hole is often used as a reference scatterer for calibration, sensitivity, and sizing studies. Here, an analytical model is derived for the response of a flat‐bottom hole in an immersion testing setup where the model is not restricted to the small hole, far‐field conditions required by previous theories. Tests of the model demonstrate that it is able to predict single frequency DGS curves for the hole that agree well with experiments, even in the very near field of the transducer. Thus, the model may serve as a new and useful theoretically based calibration ‘‘standard’’ for a variety of ultrasonic applications.

The time domain elastodynamic Kirchhoff approximation for cracks: The inverse problem

Abstract Obtaining the size, shape, and orientation of a crack from ultrasonic elastic wave scattering information is one example of the solution of an inverse problem. Here, we obtain the formal solution to this inverse problem for ideal, flat cracks using the Kirchhoff approximation for the scattered elastodynamic wavefield. Time and frequency domain verisions of the solution will be given, both in the general case and, in reduced form, for circular cracks. The time domain inverse formulation, in particular, will be shown to be equivalent to the method of projections, leading to a classical two-dimensional Radon transform. A method is also demonstrated for performing a constrained inversion to obtain the parameters of a flat crack that is assumed a priori to be of elliptical shape.

Ultrasonic modeling of benchmark problems

A series of ultrasonic benchmark problems have been defined for use in comparing different model-based approaches. Here, paraxial beam models are used in conjunction with approximate and exact flaw scattering models to demonstrate the effects of various modeling assumptions on the waveforms predicted for these benchmark problems.

A Unified Constrained Inversion Model for Ultrasonic Flaw Sizing

Equivalent flaw sizing using ultrasonic waves is an approach whereby shape and orientation information of a defect are obtained in terms of a best-fit simple geometry that is able to represent the major aspects of the flaw. Separate examples of this approach have previously been developed for volumetric flaws and cracks using the Born and Kirchhoff approximations, respectively. Here, these separate algorithms are unified into a single algorithm capable of sizing both volumetric flaws and cracks. Some examples of the performance of this unified algorithm on both synthetic and experimental data are also given.

Modeling Ultrasonic Problems for the 2002 Benchmark Session

In the 2001 RPQNDE conference, a series of ultrasonic benchmark problems were compared using different model‐based approaches [1–5]. Here, an extended set of benchmark problems are considered. Paraxial beam models are used in conjunction with various measurement models to demonstrate the effects of various modeling assumptions on the waveforms predicted for these benchmark problems.

Characterization of the system functions of ultrasonic linear phased array inspection systems.

This work characterizes the electrical and electromechanical aspects of an ultrasonic linear phased array inspection system, using a matrix of system functions that are obtained from the measured response of individual array elements in a simple reference experiment. It is shown that for the arrays tested all these system functions are essentially identical, allowing one to use a single system function to characterize the entire array, as done for an ordinary single element transducer. The variation of this single system function with the number of elements firing in the array or with changes of the delay law used is examined. It is also demonstrated that once such a single system function is obtained for an array, it can be used in a complete ultrasonic measurement model to accurately predict the array response measured from a reference reflector in an immersion setup.

Some exact solutions for the propagation of transient electroacoustic waves. I: Piezoelectric half-space

Abstract In piezoelectric materials, coupled electromagnetic and horizontally polarized shear surface wave disturbances can exist which have no purely elastic counterpart. The properties of these electroacoustic surface waves and similarly coupled body wave components have to date only been described by far-field approximations in the frequency domain. This article obtains exact transient solutions for the electroacoustic surface and body waves generated by a dipole source on a piezoelectric half-space. These solutions are obtained for both conducting and nonconducting surface boundary conditions using a modification of the Lamb-Cagniard-Pekeris technique previously applied to similar elastic and acoustic wave propagation problems. Explicit results for the separated surface and body wave contributions at the surface of the piezoelectric are given and discussed.

Multi-Gaussian Ultrasonic Beam Modeling for Multiple Curved Interfaces—an ABCD Matrix Approach

ABSTRACT A multi-Gaussian beam model uses a superposition of Gaussian beams to simulate the waves radiated from an ultrasonic transducer. We show that propagation and reflection/transmission laws for Gaussian beams in fluids and elastic solids can be written in the form of A , B , C , D matrices that are analogous to the A, B, C, D scalars used in Gaussian optics. This representation leads to simple expressions for a Gaussian beam even after that beam has been transmitted or reflected at multiple curved interfaces and produces a highly modular multi-Gaussian beam model that is also computationally very efficient. Some examples of the use of this model for both planar and curved interfaces are given.