Models, modelling and control design play important parts in automatic control. The contributions in this thesis concern topics in all three of these concepts. The poles are of fundamental importance when analyzing the behaviour of a system, and pole placement is an intuitive and natural approach for control design. A novel parameterization for state feedback gains for pole placement in the linear multiple input case is presented and analyzed. It is shown that when the open and closed loop poles are disjunct, every state feedback gain can be parameterized. Other properties are also investigated. Hammerstein models have a static non-linearity on the input. A method for exact compensation of such non-linearities, combined with introduction of integral action, is presented. Instead of inversion of the non-linearity the method utilizes differentiation, which in many cases is simpler. A partial differential equation (PDE) can be regarded as an infinite order model. Many model based control design techniques, like linear quadratic Gaussian control (LQG), require finite order models. Active damping of vibrations in a viscoelastic beam, modelled as a PDE, is considered. The beam is actuated by piezoelectric elements and its movements are measured by strain gauges. LQG design is used, for which different finite order models, approximating the PDE model, are constructed. The so obtained controllers are evaluated on the original PDE model. Minimization of the measured strain yields a satisfactory performance, but minimization of transversal deflection does not. The effect of the model accuracy of the finite order model approximations is also investigated. It turns out that a model with higher accuracy in a specified frequency interval gives controllers with better performance. The wave equation is another PDE. A PDE model, with one spatial dimension, is established. It describes wave propagation in a tube perforated with helical slots. The model describes waves of both extensional and torsional type, as well as the coupling between the two wave types. Experimental data are used for estimation of model parameters, and for assessment of the proposed model in two different cases. The model is found adequate when certain geometrical assumptions are valid.

The primary objective of this thesis was to gain a deeper understanding of acoustic wave propagation in phononic crystals, particularly those that include materials whose properties can be varied periodically in time. This research was accomplished in three ways. First, a 2D phononic crystal was designed, created, and characterized. Its properties closely matched those determined through simulation. The crystal demonstrated band gaps, dispersion, and negative refraction. It served as a means of elucidating the practicalities of phononic crystal design and construction and as a physical verification of their more interesting properties. Next, the transmission matrix method for analyzing 1D phononic crystals was extended to include the effects of time-varying material parameters. The method was then used to provide a closed-form solution for the case of periodically time-varying material parameters. Some intriguing results from the use of the extended method include dramatically altered transmission properties and parametric amplification. New insights can be gained from the governing equations and have helped to identify the conditions that lead to parametric amplification in these structures. Finally, 2D multiple scattering theory was modified to analyze scatterers with time-varying material parameters. It is shown to be highly compatible with existing multiple scattering theories. It allows the total scattered field from a 2D time-varying phononic crystal to be determined. It was shown that time-varying material parameters significantly affect the phononic crystal transmission spectrum, and this was used to switch an incident monochromatic wave. Parametric amplification can occur under certain circumstances, and this effect was investigated using the closed-form solutions provided by the new 1D method. The complexity of the extended methods grows logarithmically as opposed linearly with existing methods, resulting in superior computational complexity for large numbers of scatterers. Also, since both extended methods provide analytic solutions, they may give further insights into the factors that govern the behaviour of time-varying phononic crystals. These extended methods may now be used to design an active phononic crystal that could demonstrate new or enhanced properties.

The primary objective of this thesis was to gain a deeper understanding of acoustic wave propagation in phononic crystals, particularly those that include materials whose properties can be varied periodically in time. This research was accomplished in three ways. First, a 2D phononic crystal was designed, created, and characterized. Its properties closely matched those determined through simulation. The crystal demonstrated band gaps, dispersion, and negative refraction. It served as a means of elucidating the practicalities of phononic crystal design and construction and as a physical verification of their more interesting properties. Next, the transmission matrix method for analyzing 1D phononic crystals was extended to include the effects of time-varying material parameters. The method was then used to provide a closed-form solution for the case of periodically time-varying material parameters. Some intriguing results from the use of the extended method include dramatically altered transmission properties and parametric amplification. New insights can be gained from the governing equations and have helped to identify the conditions that lead to parametric amplification in these structures. Finally, 2D multiple scattering theory was modified to analyze scatterers with time-varying material parameters. It is shown to be highly compatible with existing multiple scattering theories. It allows the total scattered field from a 2D time-varying phononic crystal to be determined. It was shown that time-varying material parameters significantly affect the phononic crystal transmission spectrum, and this was used to switch an incident monochromatic wave. Parametric amplification can occur under certain circumstances, and this effect was investigated using the closed-form solutions provided by the new 1D method. The complexity of the extended methods grows logarithmically as opposed linearly with existing methods, resulting in superior computational complexity for large numbers of scatterers. Also, since both extended methods provide analytic solutions, they may give further insights into the factors that govern the behaviour of time-varying phononic crystals. These extended methods may now be used to design an active phononic crystal that could demonstrate new or enhanced properties.

Single frame ultrasound B-mode image quality is largely governed by the ability to focus the ultrasound beam over a range in depths both in transmission and reception. By developing a comprehensive understanding of acoustic wave propagation two signal processing methods were identified for solving the transmission problem. We made use of both the impulse response using the classical point spread function (PSF) and the spatial sensitivity function (SSF) which describes the spatial distribution at a particular time. Using the angular spectrum method, an accurate analytical model was developed for the field distribution arising from a finite geometry, apodized and focused, plane piston transducer. While there is a thorough understanding of the radiated field arising from uniformly excited plane piston transducers, the focused equivalent (i.e., one that allows a continuous change in phase over the plane piston surface) is incomplete and assumes the Fresnel approximation. Our model addresses the effects of diffraction and evanescent waves without the use of the Fresnel approximation and is applicable at all near- and far-field locations in a lossless medium. The model was analyzed to identify new insights into wave propagation and compared with the Fresnel approximation and the spherically-focused, concave transducer. The piston transducer model was then extended to an attenuating and dispersive medium. After analysing existing models of power-law frequency dependent attenuation, a causal, spherical wave Green’s function was derived from the Navier-Stokes equation for a classical viscous medium. Modifications to the angular spectrum method were presented and used to analyze the radiated field of a focused, planar piston transducer. Finally, after presenting our signal processing strategy for improving imaging spatial resolution through minimization of the SSF, two signal processing methods were derived and analysed in simulation: a deconvolution technique to remove the effects of the ultrasound excitation wave and suppress additive noise from the received ultrasound signal, and a retrospective transmit focusing method that changed the response from a predefined transmit focus to an arbitrary transmit focal depth. Proof-of-concept simulations were presented using a variable number of scatterers and compared with the traditional matched filtering and envelope detection technique.

The majority of commercially available ultrasonic transducers used to excite and measure wave propagation in structures can be coupled only to a free surface. While convenient, this method is likely to excite multiple structural modes, making data interpretation difficult. Furthermore, the many modes excited make predicting the structure’s response a computationally intensive task. Here the dynamic radial displacement induced by a transient radial point load is calculated at more than 230,000 points on the outer surface of a virgin steel pipe to simulate a typical experiment. The radial component of the displacement field is calculated by convolving the Green’s functions of the pipe with the transient load. These functions are calculated on personal computers (in a distributed arrangement) by employing modal summation. The mode shapes are obtained from a Semi-Analytical Finite Element formulation used in conjunction with a separation of variables. The results are presented in a four dimensional animation, providing easier interpretations and insight into how to best select observation points for the detection of defects. The accuracy of the calculated displacements is verified experimentally. Agreement is good when magnitude and phase corrections are incorporated from the frequency response curves of the transducers used.

No description available.

Partial saturation of porous rock by two fluids substantially affects compressional wave propagation. In particular, partial saturation causes significant attenuation and dispersion due to wave-induced fluid flow. Such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids. When partial saturation is mesoscopic, i.e. existing on a length scale much greater than pore scale but less than wavelength scale, significant attenuation can arise for frequencies 10-1000 Hz. Models for attenuation and dispersion due to mesoscale heterogeneities mostly assume fluids are distributed in a regular way. Recent experiments indicate mesoscopic heterogeneities have less idealised distributions and distribution affects attenuation/dispersion. Thus, theoretical models are required to simulate effects due to realistic fluid distributions. / The thesis focus is to model attenuation and dispersion due to realistic mesoscopic fluid distributions and fluid contrasts. First X-ray tomographic images of partially saturated rock are analysed statistically to identify spatial measures useful for describing fluid distribution patterns. The correlation function and associated correlation length for a specific fluid type are shown to be of greatest utility. Next a new model, called 3DCRM (CRM stands for continuous random media) is derived, utilizing a correlation function to describe the fluid distribution pattern. It is a random media model, is accurate for small fluid contrast and approximate for large fluid contrast. Using 3DCRM attenuation and dispersion are shown to depend on fluid distribution. / Next a general framework for partial saturation called APS (acoustics of partial saturation) is extended enabling estimation of attenuation and dispersion due to arbitrary 1D/3D fluid distributions. The intent is to construct a versatile model enabling attenuation and dispersion to be estimated for arbitrary fluid distributions, contrasts and saturations. Two crucial parameters within APS called shape and frequency scaling parameters are modified via asymptotic analysis using several random media models (which are accurate for only certain contrasts in fluid bulk moduli and percent saturation). For valid fluid contrasts and saturations, which satisfy certain random media conditions there is good correspondence between modified APS and the random media models, hence showing that APS can be utilized to model attenuation and dispersion due to more realistic fluid distributions. / Finally I devise a numerical method to test the accuracy of the analytical shape parameters for a range of fluid distributions, saturations and contrasts. In particular, the analytical shape parameter for randomly distributed spheres was shown to be accurate for a large range of saturations and fluid contrasts.

Biot's theory when applied to homogeneous media (involving the macroscopic flow mechanism) cannot explain the high level of attenuation observed in natural porous media over the seismic frequency range. However, several successful mesocopic inhomogeneity models have been developed to account for P wave attenuation. In this thesis I further develop the approaches to tackle S wave velocity and attenuation, to simulate transient wave propagation in poroelastic media, and to construct new models for determining the effective parameters of porous media containing mesoscopic inhomogeneities. As an important application of the double-porosity dual-permeability (DPDP) model, I have reformulated the effective Biot model using the total-field variables. This gives rise to new and more general governing equations than the previous approach based on the host phase field variables (which become a special case of the more general treatment). The analytical transient solution and dispersion characteristics for the double-porosity model and also for a poro-viscoacoustic model are derived over the entire frequency range for a homogeneous medium. The comparison between the results of the two models shows that dissipation by local mesoscopic flow of the double porosity model is very hard to fit by a single Zener element over a broad band. I chose the relaxation function to approximate the dispersion behaviour of the double porosity model just around the source centre frequency. It is shown that for most water-filled sandstones having a double porosity structure, wave propagation can be well described by the poro-viscoaoustic model with a single Zener element in the seismic frequency range. The transient solution for heterogeneous double porosity media is obtained by a numerical pseudospectral time splitting technique. This method is extended to 2.5-D poro-viscoelastic media to capture both P and S wave behaviour. I also demonstrate that if the frequency is below several Hz, then a single Kelvin-Voigt element gives an even better result than a single Zener element. I propose a two-phase permeability spherical inclusion model and obtain the dispersion curves of phase velocity and dissipation factor for the composite. I then determine the effective dynamic permeability of porous media with mesoscopic heterogeneities over the whole frequency range. This result is used to check the validity of other measures of effective dynamic permeability, deduced from the effective hydraulic permeability by replacing the permeability of the components with their dynamic values as determined from the Johnson, Koplik and Dashen (JKD) model. I also investigate the scattering of plane transverse waves by a spherical porous inclusion embedded in an infinite poroelastic medium. The vector displacement wave equations of Biot’s theory are solved as an infinite series of vector spherical harmonics for the case of a plane S-wave incidence. Then, the non-self-consistent theory is used to derive the dispersion characteristics of shear wave velocity and attenuation for a porous rock having mesoscopic spherical inclusions which are designed to represent either the patchy saturation model or the double porosity model with dilute concentrations of identical inclusions. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1457632 / Thesis (Ph.D.) -- University of Adelaide, School of Chemistry and Physics, 2009

Diss. ETH No. 14577. Eidgenöss. Techn. Hochsch., Diss.--Zürich, 2002.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1994. / Vita. Abstract. Includes index. Includes bibliographical references (leaves 137-142). Also available via the Internet.