Engineering Dynamics and Life Sciences

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Digital Signal Processing (Second Edition)

This book provides an account of the mathematical background, computational methods and software engineering associated with digital signal processing. The aim has been to provide the reader with the mathematical methods required for signal analysis which are then used to develop models and algorithms for processing digital signals and finally to encourage the reader to design software solutions for Digital Signal Processing (DSP). In this way, the reader is invited to develop a small DSP library that can then be expanded further with a focus on his/her research interests and applications. There are of course many excellent books and software systems available on this subject area. However, in many of these publications, the relationship between the mathematical methods associated with signal analysis and the software available for processing data is not always clear. Either the publications concentrate on mathematical aspects that are not focused on practical programming solutions or elaborate on the software development of solutions in terms of working ‘black-boxes’ without covering the mathematical background and analysis associated with the design of these software solutions. Thus, this book has been written with the aim of giving the reader a technical overview of the mathematics and software associated with the ‘art’ of developing numerical algorithms and designing software solutions for DSP, all of which is built on firm mathematical foundations. For this reason, the work is, by necessity, rather lengthy and covers a wide range of subjects compounded in four principal parts. Part I provides the mathematical background for the analysis of signals, Part II considers the computational techniques (principally those associated with linear algebra and the linear eigenvalue problem) required for array processing and associated analysis (error analysis for example). Part III introduces the reader to the essential elements of software engineering using the C programming language, tailored to those features that are used for developing C functions or modules for building a DSP library. The material associated with parts I, II and III is then used to build up a DSP system by defining a number of ‘problems’ and then addressing the solutions in terms of presenting an appropriate mathematical model, undertaking the necessary analysis, developing an appropriate algorithm and then coding the solution in C. This material forms the basis for part IV of this work. In most chapters, a series of tutorial problems is given for the reader to attempt with answers provided in Appendix A. These problems include theoretical, computational and programming exercises. Part II of this work is relatively long and arguably contains too much material on the computational methods for linear algebra. However, this material and the complementary material on vector and matrix norms forms the computational basis for many methods of digital signal processing. Moreover, this important and widely researched subject area forms the foundations, not only of digital signal processing and control engineering for example, but also of numerical analysis in general. The material presented in this book is based on the lecture notes and supplementary material developed by the author for an advanced Masters course ‘Digital Signal Processing’ which was first established at Cranfield University, Bedford in 1990 and modified when the author moved to De Montfort University, Leicester in 1994. The programmes are still operating at these universities and the material has been used by some 700++ graduates since its establishment and development in the early 1990s. The material was enhanced and developed further when the author moved to the Department of Electronic and Electrical Engineering at Loughborough University in 2003 and now forms part of the Department’s post-graduate programmes in Communication Systems Engineering. The original Masters programme included a taught component covering a period of six months based on two semesters, each Semester being composed of four modules. The material in this work covers the first Semester and its four parts reflect the four modules delivered. The material delivered in the second Semester is published as a companion volume to this work entitled Digital Image Processing, Horwood Publishing, 2005 which covers the mathematical modelling of imaging systems and the techniques that have been developed to process and analyse the data such systems provide. Since the publication of the first edition of this work in 2003, a number of minor changes and some additions have been made. The material on programming and software engineering in Chapters 11 and 12 has been extended. This includes some additions and further solved and supplementary questions which are included throughout the text. Nevertheless, it is worth pointing out, that while every effort has been made by the author and publisher to provide a work that is error free, it is inevitable that typing errors and various ‘bugs’ will occur. If so, and in particular, if the reader starts to suffer from a lack of comprehension over certain aspects of the material (due to errors or otherwise) then he/she should not assume that there is something wrong with themselves, but with the author

Vibration, Control and Stability of Dynamical Systems

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Hyperbolic Space Spectral Characteristics in a Network of Mechanical Linkages

We investigate the dynamic properties of elastic lattices defined by tessellations of a curved hyperbolic space. The lattices are obtained by projecting nodes of a regular hyperbolic tessellation onto a flat disk and then connecting those sites with simple linkages. Numerical and experimental investigations illustrate how their vibrational spectral properties are characterized by a high density of modes that are localized at the domain boundaries. Such properties govern the propagation of waves induced by broadband inputs. This suggests the potential for applications seeking the protection of bulk media from boundary-incident perturbations. We uncover the boundary-dominated nature of an exemplary hyperbolic lattice through the evaluation and analysis of its integrated density of states and vibrational spectrum. The dynamics of the lattice are also contextualized by comparing them with those of continuous disks characterized by Euclidean and hyperbolic property distributions, which confirms that the lattice retains the boundary-dominated spectrum observed in the hyperbolic plane. We then numerically investigate the response of the lattice to transient pulses incident on the boundary and find that edge-confined wave propagation occurs. The modal and transient pulse propagation behavior of the lattice is experimentally validated in a milled aluminum sample. By leveraging hyperbolic geometry, our mechanical lattice ushers in a novel class of mechanical metamaterials with boundary-dominated wave phenomena reminiscent of topologically protected systems suitable for applications in advanced wave control.Comment: 27 pages, 8 figure

Numerical Simulations

This book will interest researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modeling and computer simulation. Although it represents only a small sample of the research activity on numerical simulations, the book will certainly serve as a valuable tool for researchers interested in getting involved in this multidisciplinary field. It will be useful to encourage further experimental and theoretical researches in the above mentioned areas of numerical simulation

ELECTROMECHANICAL MODELING OF A HONEYCOMB CORE INTEGRATED VIBRATION ENERGY CONVERTER WITH INCREASED SPECIFIC POWER FOR ENERGY HARVESTING APPLICATIONS

Innovation in integrated circuit technology along with improved manufacturing processes has resulted in considerable reduction in power consumption of electromechanical devices. Majority of these devices are currently powered by batteries. However, the issues posed by batteries, including the need for frequent battery recharge/replacement has resulted in a compelling need for alternate energy to achieve self-sufficient device operation or to supplement battery power. Vibration based energy harvesting methods through piezoelectric transduction provides with a promising potential towards replacing or supplementing battery power source. However, current piezoelectric energy harvesters generate low specific power (power-to-weight ratio) when compared to batteries that the harvesters seek to replace or supplement. In this study, the potential of integrating lightweight cellular honeycomb structures with existing piezoelectric device configurations (bimorph) to achieve higher specific power is investigated. It is shown in this study that at low excitation frequency ranges, replacing the solid continuous substrate of a conventional piezoelectric bimorph with honeycomb structures of the same material results in a significant increase in power-to-weight ratio of the piezoelectric harvester. In order to maximize the electrical response of vibration based power harvesters, the natural frequency of these harvesters is designed to match the input driving frequency. The commonly used technique of adding a tip mass is employed to lower the natural frequency (to match driving frequency) of both, solid and honeycomb substrate bimorphs. At higher excitation frequency, the natural frequency of the traditional solid substrate bimorph can only be altered (to match driving frequency) through a change in global geometric design parameters, typically achieved by increasing the thickness of the harvester. As a result, the size of the harvester is increased and can be disadvantageous especially if the application imposes a space/size constraint. Moreover, the bimorph with increased thickness will now require a larger mechanical force to deform the structure which can fall outside the input ambient excitation amplitude range. In contrast, the honeycomb core bimorph offers an advantage in terms of preserving the global geometric dimensions. The natural frequency of the honeycomb core bimorph can be altered by manipulating honeycomb cell design parameters, such as cell angle, cell wall thickness, vertical cell height and inclined cell length. This results in a change in the mass and stiffness properties of the substrate and hence the bimorph, thereby altering the natural frequency of the harvester. Design flexibility of honeycomb core bimorphs is demonstrated by varying honeycomb cell parameters to alter mass and stiffness properties for power harvesting. The influence of honeycomb cell parameters on power generation is examined to evaluate optimum design to attain highest specific power. In addition, the more compliant nature of a honeycomb core bimorph decreases susceptibility towards fatigue and can increase the operating lifetime of the harvester. The second component of this dissertation analyses an uncoupled equivalent circuit model for piezoelectric energy harvesting. Open circuit voltage developed on the piezoelectric materials can be easily computed either through analytical or finite element models. The efficacy of a method to determine power developed across a resistive load, by representing the coupled piezoelectric electromechanical problem with an external load as an open circuit voltage driven equivalent circuit, is evaluated. The lack of backward feedback at finite resistive loads resulting from such an equivalent representation is examined by comparing the equivalent circuit model to the governing equations of a fully coupled circuit model for the electromechanical problem. It is found that the backward feedback is insignificant for weakly coupled systems typically seen in micro electromechanical systems and other energy harvesting device configurations with low coupling. For moderate to high coupling systems, a correction factor based on a calibrated resistance is presented which can be used to evaluate power generation at a specific resistive load

Analysis of Nonlinear Behaviors, Design and Control of Sigma Delta Modulators

M PhilSigma delta modulators (SDMs) have been widely applied in analogue-to-digital (A/D) conversion for many years. SDMs are becoming more and more popular in power electronic circuits because it can be viewed and applied as oversampled A/D converters with low resolution quantizers. The basic structure of an SDM under analytical investigation consists of a loop filter and a low bit quantizer connected by a negative feedback loop. Although there are numerous advantages of SDMs over other A/D converters, the application of SDMs is limited by the unboundedness of the system states and their nonlinear behaviors. It was found that complex dynamical behaviors exist in low bit SDMs, and for a bandpass SDM, the state space dynamics can be represented by elliptic fractal patterns confined within two trapezoidal regions. In all, there are three types of nonlinear behaviors, namely fixed point, limit cycle and chaotic behaviors. Related to the unboundedness issue, divergent behavior of system states is also a commonly discovered phenomenon. Consequently, how to design and control the SDM so that the system states are bounded and the unwanted nonlinear behaviors are avoided is a hot research topic worthy of investigated. In our investigation, we perform analysis on such complex behaviors and determine a control strategy to maintain the boundedness of the system states and avoid the occurrence of limit cycle behavior. For the design problem, we impose constraints based on the performance of an SDM and determine an optimal design for the SDM. The results are significantly better than the existing approaches

An investigation of stress wave propagation through rock joints and rock masses

Tese de doutoramento. Engenharia Civil. Faculdade de Engenharia. Universidade do Porto, Laboratório Nacional de Engenharia Civil. 201