Book Review
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David Wagg and Simon Neild |
Nonlinear Vibration with Control for Flexible and Adaptive Structures
Series: Solid Mechanics and Its Applications, Vol. 170
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A Springer-SBM - Canopus Academic Publishing Ltd co-publication |
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354 pages, $149.00 (hard cover) |
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This book on nonlinear vibration is a welcome addition to the literature in this area. It fills a gap in the book market, in that it tackles the subject from the viewpoint of engineering and control. This contrasts with many other books in the area of nonlinear vibration, which have a heavy bias towards theory, which make them less accessible to engineers. The book is written by two academics from the University of Bristol in the UK, and reflects their interests in the modelling and control of engineering systems that are inherently nonlinear. The emphasis is on continuous structural elements, such as beams, cables and plates. The style throughout the book is the presentation of linear systems, and then the inclusion of nonlinearities; the systems are then either explored in detail in terms of their dynamics and/or control techniques are then applied. The book, therefore, will suit a reader who has some familiarity with linear vibrations and control, which is acknowledged by the authors in the preface. It should also be noted that this is very much a book on nonlinear vibrations rather than a book on control. Having said that, it does contain useful information for the vibration engineer who is contemplating the use of active control – and the effect that would have on the system dynamics - but not enough information to implement a working active control system. The methods of analysis and control are really well described using simple systems such as the Duffing oscillator. This is helpful for a basic understanding of the methods, their limitations and applicability.
There are eight chapters in the book, with the first four containing more fundamental material on nonlinear vibrations and control. These could form the basis of a postgraduate or senior undergraduate level course. At the end of these chapters there are some problems for the enthusiastic reader/student. This reviewer found these chapters to be very well written, and refreshingly devoid of jargon which is found in many textbooks on nonlinear vibrations. Any engineer or researcher who has not had exposure to nonlinear vibrations or structural control would find these chapters to be a very useful introduction to the subject. They complement existing textbooks on the subject and give some very good explanations of the methods used to solve such problems and the phenomena that nonlinear systems exhibit. Such simple and clear explanations are rarely found in other text books.
Chapters five through to eight discuss more advanced topics and will be much more challenging for the novice in structural dynamics. Following chapter five, which is devoted to the analysis of linear and nonlinear multi-degree-of-freedom systems, the final part of the book, comprising chapters six through to eight are entirely devoted to the analysis and control of nonlinear distributed parameter structural elements. These contain detailed treatment of one-dimensional symmetric structural elements such as beams, the detailed analysis of asymmetric structures such as cables, and finally the treatment of plates and shells. Some of this work is very new and has only just been published as journal papers.
The authors should be congratulated for writing a very good book. It would be a useful text for the practicing engineer and researcher to have on their shelf as a reference book. It could, perhaps, also be used by a lecturer who wishes to introduce some nonlinear vibrations and control into their course.
Professor Michael J Brennan
Institute of Sound and Vibration Research
University of Southampton, UK
Book Review
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Jens Blauert and Ning Xiang |
Springer-Verlag Berlin Heidelberg |
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The aim of this book is to provide the materials for an introductory course in engineering acoustics at the university level. There are 14 main chapters, each based on a two-hour lecture, dealing with a well-defined topic.
Chapter 1 briefly introduces some basic terms and concepts such as auditory event, sound and acoustics, sound pressure, particle velocity and impedance. It also explains some basic mathematical calculations such as db addition and double-logarithmic plots.
Chapter 2 explains mechanic and acoustic oscillations. Following a systematic discussion on basic elements of linear, oscillating, mechanic systems, parallel mechanic oscillators, and free and forced oscillations of parallel mechanic oscillators, basic elements of linear, oscillating, acoustic systems are explained, with the Helmholtz resonator as an example. Chapter 3 first introduces electro-mechanic analogy and electro-acoustic analogy; and then discusses rules for deriving analogous electric circuits, as well as circuit fidelity, impedance fidelity and duality, followed by examples of electric analogies of mechanic and acoustic oscillators.
Chapter 4, entitled ‘electro-mechanic and electro-acoustic transduction’, demonstrates the possibility of coupling electrical and mechanical domains. The coupling of electro-acoustic transducers to the sound field and pressure and pressure-gradient receivers are also discussed, as well as directional characteristics and absolute calibration of transducers.
Chapters 5 and 6 respectively deal with magnetic-field and electric-field transducers. The former includes magneto-dynamic sound emitters and receivers, electromagnetic sound emitters and receivers, and magneto-strictive sound emitters and receivers. The latter includes piezoelectric sound emitters and receivers, electro-strictive sound emitters and receivers, and dielectric sound emitters and receivers.
While the previous chapters focus on vibration, Chapter 7 presents wave equations in fluids, including one-dimensional wave equation, and three-dimensional wave equation in Cartesian coordinates. The principles of impedance tube are also introduced. In Chapter 8 sound propagation in ducts with varied diameter along the length is discussed, including continuous variation of the cross area such as conical horn or exponential horn, and step-like mutations of the cross area such as stepped ducts.
Chapter 9 presents basic solutions to the wave equation in spherical coordinates, especially considering spherical harmonics of 0th and 1st order and the sound sources that emit them. Line arrays and directional equivalence of sound emitters and receivers are also discussed. In Chapter 10 area radiators, especially piston membranes, are examined, considering both far field and near field radiation. Diffraction and scattering from the membranes are also briefly discussed.
Chapter 11 deals with sound dissipation, reflection, refraction and absorption, including dissipation during sound propagation in air, sound propagation in porous media, reflection and refraction where a wave hits the boundary between two media, and wall impedance. Basic mechanism of porous absorbers and resonance absorbers are also briefly introduced.
Chapter 12 presents concepts and methods in room acoustics. Image source method and ray tracing are introduced and some basic room acoustic phenomena are discussed based on impulse responses, such as flutter echoes. With diffuse sound field theories, some commonly used room acoustics concepts are introduced, including reverberation time, measurement of spatially averaged absorption and the critical radius.
Chapter 13 deals with isolation of airborne and structure-borne sounds, including sound propagation in solids, radiation of airborne sound by bending waves, and sound transmission loss of single-leaf and double-leaf walls. The measurement of sound isolation and correspondingly, the weighted sound reduction index, is explained. Finally isolation of vibrations and floor impact sound are discussed briefly.
Chapter 14 covers noise reduction in indoor and outdoor environments. Brief discussion is given in terms of noise reduction at the source, along the indoor or outdoor propagation paths, and at the receiver’s end.
A number of appendices are given in Chapter 15, including well-designed exercise for each chapter, a list of symbols, notations and units, some numerical details, and a list of supplementary textbooks for self-study, although no research papers are listed.
The book is relevant to a range of engineers, from electro-acoustics to building acoustics. A notable feature of this book is that each chapter is relatively short but covers a range of key concepts and equations which are clearly explained. As indicated in the Preface of the book, under the guidance of an academic teacher, this book is sufficient as the sole textbook for the subject. Some chapters may contain slightly more materials than a two-hour lecture, but this gives the teacher some flexibility to adjust. For the purpose of self-study, the reader should use this book in parallel with further materials. The book is not only useful as a textbook, but would also useful as a handbook for professional engineers and researchers. It is assumed that the reader will have a basic knowledge of mathematics.
Professor Jian Kang
School of Architecture
University of Sheffield, UK
Book Review
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Pijush K. Kundu and Ira M. Cohen |
Fluid Mechanics with Multimedia DVD, 4th Edition |
904 pp., USD 109.95 (hardbound) |
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After twenty five years of teaching thermal fluid sciences it was intriguing and refreshing to find myself reviewing an established general text in Fluid Mechanics that I was not too familiar with. To find that this is a comprehensive and very well written book was even more welcome. It covers the classical topics of fluid flow: Kinematics, Conservation Laws, Vorticity Dynamics, Irrotational Flow, Gravitational Waves, Viscous flow and Boundary Layers, which are all treated rigorously. However, one of the greatest assets of the book is that it includes chapters with good coverage on the basics of numerical solution techniques, stability theory and the fundamental characteristics of turbulence combined with an interesting selection of application topics such as Aerodynamics, Biofluid Dynamics and Geophysical Fluid Dynamics. In a substantial book of over 800 pages it attempts to provide a complete overview of the subject of fluid mechanics from fundamentals to how it can be used. However, the potential reader needs to be warned; this is a not a text book for a complete newcomer to the subject. It has a rigorous mathematical approach and makes no apology for it; Chapter 2 is on Cartesian Tensors for example. It would suit a graduate engineering student who has a need to attain a greater depth than normally found in undergraduate engineering courses or an applied physics or mathematical graduate who is approaching fluid mechanics for the first time.
A welcome addition to the 4th edition is the inclusion of the wonderful Multimedia Fluid Mechanics DVD, 2nd edition by Homsey et al which has been significantly extended from the first edition. Unfortunately the DVD is a standalone addition to the text and is not well integrated into the book chapters. With a 4th edition one expects a steady development in the content, corrections to errors and improvements in explanations but with the essential benefits of previous editions maintained. This has certainly been achieved and the new chapter on Biofluid Mechanics makes an uncommon and useful addition which may widen the book’s attraction.
The book has a dated approach to presentation compared to modern teaching texts but beyond that this is a book of substance and worthy of a place on the book shelf of any academic, engineer or applied scientist who has a need or desire to see the broader picture at a more rigorous level.
Dr William Dempster
Department of Mechanical Engineering
University of Strathclyde
Glasgow, UK
Book Review
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M. A. Bernstein and W. A. Friedman |
Thinking About Equations: A practical Guide for Developing Mathematical Intuition in the Physical Sciences and Engineering |
258 pp., £40.50 (soft cover) |
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Mathematics is the natural language for the physical and engineering sciences. This has the consequence that all fundamental theories covering these areas are formulated in terms of mathematics equations which at some point have to be solved. However, a major difficulty arising in both the pure and applied sciences is that few of these equations can have their exact solutions expressed by means of a finite number of the elementary functions. One way to resolve this difficulty is to construct schemes for the calculation of numerical approximations to the solutions. In general, these methods are not fully satisfactory since systems having multi-parameters may lead to a vast amount of computation and the resulting numerics may not give clear insight into the dynamics.
Often special exact solutions to our equations may be found. In spite of the fact that for particular equations, the special solutions may be very relevant for explaining the phenomena under investigation, what is often required by the scientist is deeper understanding of both the physical system and the underlying mathematical structure given either by the theory or the mathematical model based on this theory. A way to make progress on these issues is to derive “valid” mathematical approximations to the unknown solutions. However, a major (maybe) problem is to determine, for a particular case, what is a valid mathematical approximation procedure. Techniques in this area include Taylor series expansions, perturbation methods, eigen-function expansion of solutions, and asymptotic representations. Together, all of these techniques comprise a large portion of applied mathematics.
There does exists a broad set of other techniques and mathematical related methodologies such that their application leads to either great simplification in the equations being studied and/or provide increased insight and understanding of the equations and their solutions. These general procedures include the use of dimensional analysis, the construction of physical scales and the associated dimensionless variables and parameters, the application of symmetry arguments, and appropriate graphic displays. This current book under review deals with each of these issues and much more.
The two authors are seasoned professionals in several areas of applied science and engineering, and bring to this book knowledge and background information that may be applied to a broad spectrum of equations which arise in the sciences and engineering. The book is arranged in eight chapters, each dealing with two to three concepts. One of the outstanding features is that each chapter gives examples and the details for obtaining the desired solution and/or some other related issues. (More on this later.) While few references are listed, at the end of each chapter, the authors always seem to come up with the one or two citations that contain the essence of the concepts and examples presented in that chapter.
In summary, the eight chapters cover the following topics: equations representing physical quantities and the use of dimensional checks to assess the correctness of these equations; pitfalls that a careless application of mathematical theorems can cause; limiting and special cases of equations; graphic solutions and the use of symmetry; estimation and approximation applied to equations and other more general situations; dimensional analysis and scaling; a variety of techniques that may be used to generalize elementary mathematical results; and a collection of several interesting and instructive examples.
I really enjoyed reading this book and, in fact, worked out in detail a number of the exercises given at each chapter’s end. From my perspective, as one who has a broad background in applied mathematics and modeling, this book has several strengths. First, and most important, the contents of the book demonstrate that in the process of trying to obtain either exact or approximate solutions to equations, pitfalls are everywhere! This knowledge will be of value to all who engage in this activity and the authors provide excellent suggestions for the avoidance of the most elementary cases. Second, sprinkled throughout the book are nuggets of great wisdom, each of which should be incorporated into the intuition of scientists and engineers who require solutions to equations. Two examples of this are:
(pp. 18) “Proper application of a theorem does not necessarily require one to prove it, or even to understand all the logical steps in the proof. What is essential … is that all of the conditions are understood. When all of the conditions of a theorem are not satisfied, incorrect … answers can result …”
(pp. 188) “We generalize an equation by making changes to it that increase its range of applicability. The resulting generalized equation can then contain multiple special cases embedded within it, so it is usually more useful than the original version.”
The book contains some rather minor typos. The two that caught my attention are: i) pp. 71, line 8; the word “temperature” should be replaced with “pressure;” ii) pp. 176, in Eq. (6.66), the b3 should be b 3 .
It is not clear why most of the subject matter in Chapter 6 was not incorporated into Chapter 1. After the discussion on physical units and dimensional checks, it would then be natural to follow this with a treatment of dimensional analysis, scaling, and the construction of dimensionless variables and parameters. In all instances, the equations to be investigated should be fully dimensionless in both its variables and parameters. Scaling is the mechanism that allows this construction to be actualized.
Who is the intended audience for this book? The authors “tried to target the level of the book so it is accessible to undergraduate students who have a background in basic calculus and familiarity with differential equations.” Other needed background topics include introductory physics, linear algebra and complex analysis. My long experience (over 40 years of teaching and research) suggest that even individuals who have this preparation will still have a rough time in using this book. While from my perspective the examples in the book are outstanding, the range of topics is so broad that it is unlikely that most professional scientists and engineers will have the background to fully appreciate the authors’ presentations. In particular, discussions are given on the following topics: Compton scattering, the random walk, ferromagnetism, van der Waals’ equation of state, first-and second-order phase transitions, the chemical potential and law of mass action, chaos, cosmology, and other subjects. The authors do give interesting details on each of these topics, but for anyone seeing these issues for the first time, it is not likely they will come away with any fundamental understating of the important issues.
In spite of what was just stated, this is an exciting and important book. Every library should have one or more copies in their collection. I would also recommend this book to be in the personal library holdings of each professional scientist and engineer who in their daily work come across mathematical equations for which some understanding of the nature of their solutions is required. I look forward, with great anticipation, to a second edition of this volume. Further, I will recommend this volume to my colleagues for use as a supplement to their current courses.
Professor Ronald E Mickens
Department of Physics
Clark Atlanta
Atlanta, USA
Book Reviews
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Smart Structures: Physical Behaviour, Mathematical Modelling and Applications |
194pp., £75.00 (hard cover) |
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The title of this book suggests it gives an overview of the huge research effort in the understanding, modelling and application of smart structures. In fact the contribution is not so wide ranging, and although the book gives a brief introduction to a range of smart materials, it really concentrates on piezoelectric materials and gives general analysis for strain actuators and sensors.
The first chapter motivates the area of smart structures well and provides a link to active materials. This chapter then introduces common active materials: piezoelectric are reviewed in detail including an understanding of the crystal structure and the constitutive laws; a physical understanding of shape memory alloys is given using the transition between the austenite and martensite phases; magnetostrictive and electrostrictive materials are overviewed briefly. Although the title implies a range of smart structures are covered, the remainder of the book is really concerned with piezoelectric materials. The first chapter concludes with an overview of four popular applications of smart structures, namely structural health monitoring, shape morphing, vibration control and energy harvesting.
Chapter 2 takes the constitutive model from chapter 1 and incorporates this model into a general analysis of structures containing piezoelectric material. Examples are given where detailed analysis of the electrical potential and mechanical strain are required, such as in the design of piezoelecric actuators using interdigitated electrodes.
Chapter 3 presents techniques to analyse systems with strain actuators and sensors. Most smart materials essentially work as an actuator through an induced strain mechanism, and the author summarises the physical processes for inducing this strain for a range of smart materials. The physical basis of concepts such as actuator strain and blocking force are explained. Various systems of beams with strain actuator patches on the surface are then modelled from first principles. Simple pin-force models are introduced, and their accuracy demonstrated when the actuator thickness is small relative to the beam thickness. The effect of the actuator length and position on the excitation of the lower modes is shown. The chapter also considers piezoelectric patches as sensors, including some discussion on signal conditioning, and gives a brief introduction to control issues, although the author only considers proportional and derivative control.
Chapter 4 combines piezoelectric material with other material to produce an active composite. The chapter concentrates on two major applications, namely the analysis of actuators with interdigitated electrodes based on either piezoelectric plates or fibres, and the introduction of piezoelectric layers into classical laminated composite shells. The final chapter gives a brief summary of three applications of piezoelectric materials for spacecraft: shape control of an antenna; vibration control of an optical payload; and an ultrasonic motor.
The book represents a good introduction to the modelling and analysis of structures with piezoelectric sensors and actuators. Of particular merit is the development of the models and analysis from first principles. However it is not exactly clear to the reviewer who the target audience is. The book contains suitable material for a senior undergraduate or masters level course to introduce smart structures, although the chapters do not have any problems for students to attempt, which a textbook would normally have. The book could be used as an introduction for new researchers in the field, although they would very quickly outgrow the book and would then have to move to other books and papers. Despite these reservations, this book represents a welcome addition for new and established researchers in the field, and will also find a place in courses teaching smart materials.
Professor Michael Friswell
School of Engineering
Swansea University, Singleton Park Swansea SA2 8PP, United Kingdom
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