Anthony J. Mulholland

Tapered transmission line technique based graded matching layers for thickness mode piezoelectric transducers

Conventionally, in order to acoustically match thickness mode piezoelectric transducers to a low acoustic impedance load medium, multiple quarter wavelength (QW) matching layers are employed at the front face of the device. Typically a number of layers, 2–4 in number, are employed resulting in discrete impedance steps within the acoustic matching scheme. This can result in impedance matching with limited bandwidth characteristics. This paper investigates the application of tapered transmission line filter theory to implement a graded impedance profile, through the thickness of the matching layer scheme, to solve the impedance mismatch problem whilst accounting for enhanced transducer sensitivity and bandwidth.

Wave propagation in 0-3/3-3 connectivity composites with complex microstructure.

This work presents a study of the properties of particulate composites. The whole range of particle volume fraction (0-1) and ideal 0-3, 3-3 and intermediate 0-3/3-3 connectivities are analysed. Two different approaches to produce a realistic model of the complex microstructure of the composites are considered. The first one is based on a random location of mono-dispersed particles in the matrix; while the second incorporates a size distribution of the particles based on experimental measurements. Different particle shapes are also considered. A commercial finite element package was used to study the propagation of acoustic plane waves through the composite materials. Due to the complexity of the problem, and as a first step, a two-dimensional model was adopted. The results obtained for the velocity of sound propagation from the finite element technique are compared with those from other theoretical approaches and with experimental data. The study validates the use of this technique to model acoustic wave propagation in 0-3/3-3 connectivity composites. In addition, the finite element calculations, along with the detailed description of the microstructure of the composite, provide valuable information about the micromechanics of the sample and the influence of the microstructure on macroscopic properties.

Piezoelectric ultrasonic transducers with fractal geometry

Piezoelectric ultrasonic transducers typically employ composite structures to improve their transmission and reception sensitivities. The geometry of the composite is regular with one dominant length scale and, since these are resonant devices, this dictates the central operating frequency of the device. In order to construct a wide bandwidth device it would seem natural therefore to utilize resonators that span a range of length scales. In this article we consider such a device and build a theoretical model to predict its performance. A fractal medium is used as this contains a wide range of length scales and yields to a renormalization approach. The propagation of an ultrasonic wave in this heterogeneous medium is then analyzed and used to construct expressions for the electrical impedance, and the transmission and reception sensitivities of this device as a function of the driving frequency. The results presented show a marked increase in the reception sensitivity of the device.

A model-based approach to crack sizing with ultrasonic arrays

Ultrasonic phased array systems have become increasingly popular in the last 10 years as tools for flaw detection and characterization within the nondestructive testing industry. The existence and location of flaws can often be deduced via images generated from the data captured by these arrays. A factor common to these imaging techniques is the subjective thresholding required to estimate the size of the flaw. This paper puts forward an objective approach which employs a mathematical model. By exploiting the relationship between the width of the central lobe of the scattering matrix and the crack size, an analytical expression for the crack length is reached via the Born approximation. Conclusions are then drawn on the minimum resolvable crack length of the method and it is thus shown that the formula holds for subwavelength defects. An analytical expression for the error that arises from the discrete nature of the array is then derived and it is observed that the method becomes less sensitive to the discretization of the array as the distance between the flaw and array increases. The methodology is then extended and tested on experimental data collected from welded austenitic plates containing a lack-of-fusion crack of 6 mm length. An objective sizing matrix (OSM) is produced by assessing the similarity between the scattering matrices arising from experimentally collected data with those arising from the Born approximation over a range of crack lengths and frequencies. Initially, the global minimum of the OSM is taken as the objective estimation of the crack size, giving a measurement of 7 mm. This is improved upon by the adoption of a multifrequency averaging approach, with which an improved crack size estimation of 6.4 mm is obtained.

Analysis of ultrasonic transducers with fractal architecture

Ultrasonic transducers composed of a periodic piezoelectric composite are generally accepted as the design of choice in many applications. Their architecture is normally very regular and this is due to manufacturing constraints rather than performance optimization. Many of these manufacturing restrictions no longer hold due to new production methods such as computer controlled, laser cutting, and so there is now freedom to investigate new types of geometry. In this paper, the plane wave expansion model is utilized to investigate the behavior of a transducer with a self-similar architecture. The Cantor set is utilized to design a 2-2 configuration, and a 1-3 configuration is investigated with a Sierpinski carpet geometry. Ideally a single longitudinal mode in the thickness direction will drive the transducer in a piston-like fashion. In this paper it was found that by increasing the fractal generation level, the bandwidth surrounding the main thickness mode will increase, but there will be a corresponding reduction in the amplitude of the electrical conductance. It is also shown that a shift in the frequency of operation of the device can be achieved by altering the spatial periodicity of the electrical excitation.

Calculation of chemical and phase equilibria via simulated annealing

We present a new class of techniques for the solution of the chemical and phase equilibria problem for reacting species in a closed system. The minimisation of the Gibbs free energy for all the species in the system is conducted using the technique of simulated annealing (SA). The SA objective function incorporates non‐ideal equations of state. This new approach is demonstrably able to solve multi‐species and multi‐phase LTCE problems in ideal‐gas solutions, ideal solutions and mixtures of ideal and non‐ideal solutions.

Integrated modelling of process heat transfer with combustion and fouling

Abstract This paper provides a summary of the main project topics which contribute to a major study aimed at integrating fouling and combustion activities. Brief outlines of the aims of the 14 main activities are provided along with examples of results from work on time-dependent fouling, industrial measurements, particle deposition tests, engineering combustion modelling, CFB modelling, sonic control and optimisation tests. Application of the results will lead to improved energy efficiency in a wide range of industries.

The detection of flaws in austenitic welds using the decomposition of the time reversal operator

The non-destructive testing of austenitic welds using ultrasound plays an important role in the assessment of the structural integrity of safety critical structures. The internal microstructure of these welds is highly scattering and can lead to the obscuration of defects when investigated by traditional imaging algorithms. This paper proposes an alternative objective method for the detection of flaws embedded in austenitic welds based on the singular value decomposition of the time-frequency domain response matrices. The distribution of the singular values is examined in the cases where a flaw exists and where there is no flaw present. A lower threshold on the singular values, specific to austenitic welds, is derived which, when exceeded, indicates the presence of a flaw. The detection criterion is successfully implemented on both synthetic and experimental data. The datasets arising from welds containing a flaw are further interrogated using the decomposition of the time-reversal operator (DORT) method and the total focusing method (TFM), and it is shown that images constructed via the DORT algorithm typically exhibit a higher signal-to-noise ratio than those constructed by the TFM algorithm.

A fractional Fourier transform analysis of the scattering of ultrasonic waves

Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification.

A RENORMALIZATION APPROACH TO REACTION-DIFFUSION PROCESSES ON FRACTALS

Of fundamental importance to wave propagation in a wide range of physical phenomena is the structural geometry of the supporting medium. Recently, there have been several investigations on wave propagation in fractal media. We present here a renormalization approach to the study of reaction-diffusion (RD) wave propagation on finitely ramified fractal structures. In particular we will study a Rinzel-Keller (RK) type model, supporting travelling waves on a Sierpinski gasket (SG), lattice.