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Nonlinear Second Order Elliptic Equations
by Mingxin Wang Peter Y. PangThis book focuses on the following three topics in the theory of boundary value problems of nonlinear second order elliptic partial differential equations and systems: (i) eigenvalue problem, (ii) upper and lower solutions method, (iii) topological degree method, and deals with the existence of solutions, more specifically non-constant positive solutions, as well as the uniqueness, stability and asymptotic behavior of such solutions.While not all-encompassing, these topics represent major approaches to the theory of partial differential equations and systems, and should be of significant interest to graduate students and researchers. Two appendices have been included to provide a good gauge of the prerequisites for this book and make it reasonably self-contained.A notable strength of the book is that it contains a large number of substantial examples. Exercises for the reader are also included. Therefore, this book is suitable as a textbook for graduate students who havealready had an introductory course on PDE and some familiarity with functional analysis and nonlinear functional analysis, and as a reference for researchers.
Nonlinear Solid Mechanics For Finite Element Analysis: Statics
by Javier Bonet Antonio J. Gil Richard D. WoodDesigning engineering components that make optimal use of materials requires consideration of the nonlinear static and dynamic characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, which requires an understanding of both the theoretical background and associated computer solution techniques. By presenting both the nonlinear solid mechanics and the associated finite element techniques together, the authors provide, in the first of two books in this series, a complete, clear, and unified treatment of the static aspects of nonlinear solid mechanics. Alongside a range of worked examples and exercises are user instructions, program descriptions, and examples for the FLagSHyP MATLAB computer implementation, for which the source code is available online. While this book is designed to complement postgraduate courses, it is also relevant to those in industry requiring an appreciation of the way their computer simulation programs work.
Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability
by Davide BigoniThis book covers solid mechanics for non-linear elastic and elastoplastic materials, describing the behaviour of ductile material subject to extreme mechanical loading and its eventual failure. The book highlights constitutive features to describe the behaviour of frictional materials such as geological media. On the basis of this theory, including large strain and inelastic behaviours, bifurcation and instability are developed with a special focus on the modelling of the emergence of local instabilities such as shear band formation and flutter of a continuum. The former is regarded as a precursor of fracture, while the latter is typical of granular materials. The treatment is complemented with qualitative experiments, illustrations from everyday life and simple examples taken from structural mechanics.
Nonlinear Sound Waves in Solids (Advances in Acoustics)
by Xiaozhou LiuThis book highlights the fundamental principles and analytical methods of nonlinear acoustics in solids, with a focus on the theories and applications of nonlinear acoustics in ultrasonic non-destructive testing and metamaterials. The text is designed to provide readers with a deep understanding of how nonlinear acoustic phenomena manifest in various material contexts, from crystalline structures to complex composites. Suitable for readers in the fields of acoustics, materials science, and engineering, this book can advance the development of nonlinear acoustics theory and promote its applications in non-destructive testing, materials sciences, and related areas.
Nonlinear Stochastic Systems with Incomplete Information
by Huisheng Shu Zidong Wang Bo ShenNonlinear Stochastic Processes addresses the frequently-encountered problem of incomplete information. The causes of this problem considered here include: missing measurements; sensor delays and saturation; quantization effects; and signal sampling. Divided into three parts, the text begins with a focus on H filtering and control problems associated with general classes of nonlinear stochastic discrete-time systems. Filtering problems are considered in the second part, and in the third the theory and techniques previously developed are applied to the solution of issues arising in complex networks with the design of sampled-data-based controllers and filters. Among its highlights, the text provides: * a unified framework for filtering and control problems in complex communication networks with limited bandwidth; * new concepts such as random sensor and signal saturations for more realistic modeling; and * demonstration of the use of techniques such as the Hamilton-Jacobi-Isaacs, difference linear matrix, and parameter-dependent matrix inequalities and sums of squares to handle the computational challenges inherent in these systems. The collection of recent research results presented in Nonlinear Stochastic Processes will be of interest to academic researchers in control and signal processing. Graduate students working with communication networks with lossy information and control of stochastic systems will also benefit from reading the book.
Nonlinear Stochastic Systems with Network-Induced Phenomena
by Zidong Wang Huijun Gao Jun HuThis monograph introduces methods for handling filtering and control problems in nonlinear stochastic systems arising from network-induced phenomena consequent on limited communication capacity. Such phenomena include communication delay, packet dropout, signal quantization or saturation, randomly occurring nonlinearities and randomly occurring uncertainties. The text is self-contained, beginning with an introduction to nonlinear stochastic systems, network-induced phenomena and filtering and control, moving through a collection of the latest research results which focuses on the three aspects of: · the state-of-the-art of nonlinear filtering and control; · recent advances in recursive filtering and sliding mode control; and · their potential for application in networked control systems, and concluding with some ideas for future research work. New concepts such as the randomly occurring uncertainty and the probability-constrained performance index are proposed to make the network models as realistic as possible. The power of combinations of such recent tools as the completing-the-square and sums-of-squares techniques, HamiltonJacobiIsaacs matrix inequalities, difference linear matrix inequalities and parameter-dependent matrix inequalities is exploited in treating the mathematical and computational challenges arising from nonlinearity and stochasticity. Nonlinear Stochastic Systems with Network-Induced Phenomena establishes a unified framework of control and filtering which will be of value to academic researchers in bringing structure to problems associated with an important class of networked system and offering new means of solving them. The significance of the new concepts, models and methods presented for practical control engineering and signal processing will also make it a valuable reference for engineers dealing with nonlinear control and filtering problems.
Nonlinear Structural Dynamics and Damping (Mechanisms and Machine Science #69)
by Juan Carlos JaureguiThis book compiles recent research in the field of nonlinear dynamics, vibrations and damping applied to engineering structures. It addresses the modeling of nonlinear vibrations in beams, frames and complex mechanical systems, as well as the modeling of damping systems and viscoelastic materials applied to structural dynamics. The book includes several chapters related to solution techniques and signal analysis techniques. Last but not least, it deals with the identification of nonlinear responses applied to condition monitoring systems.
Nonlinear Structural Mechanics
by Walter LacarbonaraThis book reviews the theoretical framework of nonlinear mechanics, covering computational methods, applications, parametric investigations of nonlinear phenomena and mechanical interpretation towards design. Builds skills via increasing levels of complexity.
Nonlinear Structures & Systems, Vol. 1: Proceedings of the 42nd IMAC, A Conference and Exposition on Structural Dynamics 2024 (Conference Proceedings of the Society for Experimental Mechanics Series)
by Matthew R. W. Brake Ludovic Renson Paolo Tiso Robert J. KuetherNonlinear Structures & Systems, Volume 1: Proceedings of the 42nd IMAC, A Conference and Exposition on Structural Dynamics, 2024, the first volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Experimental Nonlinear Dynamics Jointed Structures: Identification, Mechanics, Dynamics Nonlinear Damping Nonlinear Modeling and Simulation Nonlinear Reduced-Order Modeling Nonlinearity and System Identification
Nonlinear Structures & Systems, Volume 1: Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics 2020 (Conference Proceedings of the Society for Experimental Mechanics Series)
by Gaetan Kerschen Matthew R. W. Brake Ludovic RensonNonlinear Structures & Systems, Volume 1: Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020, the first volume of eight from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on:Nonlinear Reduced-order ModelingJointed Structures: Identification, Mechanics, DynamicsExperimental Nonlinear DynamicsNonlinear Model & Modal InteractionsNonlinear DampingNonlinear Modeling & SimulationNonlinearity & System Identification
Nonlinear Structures & Systems, Volume 1: Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics 2021 (Conference Proceedings of the Society for Experimental Mechanics Series)
by Gaetan Kerschen Matthew R. W. Brake Ludovic Renson<p>Nonlinear Structures & Systems, Volume 1: Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics, 2021, the first volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on:<p> <p>• Nonlinear Reduced-order Modeling<p> <p>• Jointed Structures: Identification, Mechanics, Dynamics<p> <p>• Experimental Nonlinear Dynamics<p> <p>• Nonlinear Model & Modal Interactions<p> <p>• Nonlinear Damping<p> <p>• Nonlinear Modeling & Simulation<p> <p>• Nonlinearity & System Identification<p>
Nonlinear Structures & Systems, Volume 1: Proceedings of the 41st IMAC, A Conference and Exposition on Structural Dynamics 2023 (Conference Proceedings of the Society for Experimental Mechanics Series)
by Matthew R. W. Brake Ludovic Renson Paolo Tiso Robert J. KuetherNonlinear Structures & Systems, Volume 1: Proceedings of the 41st IMAC, A Conference and Exposition on Structural Dynamics, 2023, the first volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on:Experimental Nonlinear DynamicsJointed Structures: Identification, Mechanics, DynamicsNonlinear DampingNonlinear Modeling and SimulationNonlinear Reduced-Order ModelingNonlinearity and System Identification
Nonlinear Structures and Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics 2019
by Gaetan Kerschen Ludovic Renson Brake, M. R. W.Nonlinear Structures & Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics, 2019, the first volume of eight from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Nonlinear Reduced-order Modeling Jointed Structures: Identification, Mechanics, Dynamics Experimental Nonlinear Dynamics Nonlinear Model & Modal Interactions Nonlinear Damping Nonlinear Modeling & Simulation Nonlinearity & System Identification.
Nonlinear Structures and Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics 2019 (Conference Proceedings of the Society for Experimental Mechanics Series)
by Gaetan Kerschen M. R. W. Brake Ludovic RensonNonlinear Structures & Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics, 2019, the first volume of eight from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Nonlinear Reduced-order Modeling Jointed Structures: Identification, Mechanics, Dynamics Experimental Nonlinear Dynamics Nonlinear Model & Modal Interactions Nonlinear Damping Nonlinear Modeling & Simulation Nonlinearity & System Identification
Nonlinear Super-Resolution Nano-Optics and Applications
by Jingsong WeiThis book covers many advances in the subjects of nano-optics and nano photonics. The author describes the principle and technical schematics of common methods for breaking through the optical diffraction limit and focuses on realizing optical super-resolution with nonlinear effects of thin film materials. The applications of nonlinear optical super-resolution effects in nano-data storage, nanolithography, and nano-imaging are also presented. This book is useful to graduate students majoring in optics and nano science and also serves as a reference book for academic researchers, engineers, technical professionals in the fields of super-resolution optics and laser techniques, nano-optics and nano photonics, nano-data storage, nano imaging, micro/nanofabrication and nanolithography and nonlinear optics.
Nonlinear System Identification: From Classical Approaches to Neural Networks, Fuzzy Models, and Gaussian Processes
by Oliver NellesThis book provides engineers and scientists in academia and industry with a thorough understanding of the underlying principles of nonlinear system identification. It equips them to apply the models and methods discussed to real problems with confidence, while also making them aware of potential difficulties that may arise in practice. Moreover, the book is self-contained, requiring only a basic grasp of matrix algebra, signals and systems, and statistics. Accordingly, it can also serve as an introduction to linear system identification, and provides a practical overview of the major optimization methods used in engineering. The focus is on gaining an intuitive understanding of the subject and the practical application of the techniques discussed. The book is not written in a theorem/proof style; instead, the mathematics is kept to a minimum, and the ideas covered are illustrated with numerous figures, examples, and real-world applications. In the past, nonlinear system identification was a field characterized by a variety of ad-hoc approaches, each applicable only to a very limited class of systems. With the advent of neural networks, fuzzy models, Gaussian process models, and modern structure optimization techniques, a much broader class of systems can now be handled. Although one major aspect of nonlinear systems is that virtually every one is unique, tools have since been developed that allow each approach to be applied to a wide variety of systems.
Nonlinear Systems
by Nathan van de Wouw Erjen Lefeber Ines Lopez ArteagaThis treatment of modern topics relatedto the control of nonlinear systems is a collection of contributionscelebrating the work of Professor Henk Nijmeijer and honoring his 60thbirthday. It addresses several topics that have been the core of ProfessorNijmeijer's work, namely: the control of nonlinear systems, geometric controltheory, synchronization, coordinated control, convergent systems and thecontrol of underactuated systems. The book presents recent advances in theseareas, contributed by leading international researchers in systems and control. In addition to the theoretical questions treated in the text, particularattention is paid to a number of applications including (mobile) robotics,marine vehicles, neural dynamics and mechanical systems generally. This volume providesa broad picture of the analysis and control of nonlinear systems for scientistsand engineers with an interest in the interdisciplinary field of systems andcontrol theory. The reader will benefit from the expert participants' ideas on importantopen problems with contributions that represent the state of the art innonlinear control.
Nonlinear Systems Stability Analysis: Lyapunov-Based Approach
by Seyed Kamaleddin NikraveshThe equations used to describe dynamic properties of physical systems are often nonlinear, and it is rarely possible to find their solutions. Although numerical solutions are impractical and graphical techniques are not useful for many types of systems, there are different theorems and methods that are useful regarding qualitative properties of nonlinear systems and their solutions—system stability being the most crucial property. Without stability, a system will not have value.Nonlinear Systems Stability Analysis: Lyapunov-Based Approach introduces advanced tools for stability analysis of nonlinear systems. It presents the most recent progress in stability analysis and provides a complete review of the dynamic systems stability analysis methods using Lyapunov approaches. The author discusses standard stability techniques, highlighting their shortcomings, and also describes recent developments in stability analysis that can improve applicability of the standard methods. The text covers mostly new topics such as stability of homogonous nonlinear systems and higher order Lyapunov functions derivatives for stability analysis. It also addresses special classes of nonlinear systems including time-delayed and fuzzy systems.Presenting new methods, this book provides a nearly complete set of methods for constructing Lyapunov functions in both autonomous and nonautonomous systems, touching on new topics that open up novel research possibilities. Gathering a body of research into one volume, this text offers information to help engineers design stable systems using practice-oriented methods and can be used for graduate courses in a range of engineering disciplines.
Nonlinear Systems and Optimization for the Chemical Engineer
by Guido Buzzi-Ferraris Flavio ManentiThis third book in a suite of four practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. The required software is provided by way of the freeware mathematical library BzzMath that is developed and maintained by the authors. The present volume focuses on optimization and nonlinear systems solution. The book describes numerical methods, innovative techniques and strategies that are all implemented in a well-established, freeware library. Each of these handy guides enables the reader to use and implement standard numerical tools for their work, explaining the theory behind the various functions and problem solvers, and showcasing applications in diverse scientific and engineering fields. Numerous examples, sample codes, programs and applications are proposed and discussed. The book teaches engineers and scientists how to use the latest and most powerful numerical methods for their daily work.
Nonlinear Theory of Electroelastic and Magnetoelastic Interactions
by Luis Dorfmann Ray W. OgdenThis book provides a unified theory on nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classic theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell's equations. They summarize relevant theories of continuum mechanics, required to account for the deformability of material and present a constitutive framework for the nonlinear magneto-and electroelastic interactions in a highly deformable material. The equations contained in the book formulate and solve a variety of representative boundary-value problems for both nonlinear magnetoelasticity and electroelasticity.
Nonlinear Ultrasonic and Vibro-Acoustical Techniques for Nondestructive Evaluation
by Tribikram KunduThis multi-contributed volume provides a practical, applications-focused introduction to nonlinear acoustical techniques for nondestructive evaluation. Compared to linear techniques, nonlinear acoustical/ultrasonic techniques are much more sensitive to micro-cracks and other types of small distributed damages. Most materials and structures exhibit nonlinear behavior due to the formation of dislocation and micro-cracks from fatigue or other types of repetitive loadings well before detectable macro-cracks are formed. Nondestructive evaluation (NDE) tools that have been developed based on nonlinear acoustical techniques are capable of providing early warnings about the possibility of structural failure before detectable macro-cracks are formed. This book presents the full range of nonlinear acoustical techniques used today for NDE. The expert chapters cover both theoretical and experimental aspects, but always with an eye towards applications. Unlike other titles currently available, which treat nonlinearity as a physics problem and focus on different analytical derivations, the present volume emphasizes NDE applications over detailed analytical derivations. The introductory chapter presents the fundamentals in a manner accessible to anyone with an undergraduate degree in Engineering or Physics and equips the reader with all of the necessary background to understand the remaining chapters. This self-contained volume will be a valuable reference to graduate students through practising researchers in Engineering, Materials Science, and Physics.Represents the first book on nonlinear acoustical techniques for NDE applicationsEmphasizes applications of nonlinear acoustical techniquesPresents the fundamental physics and mathematics behind nonlinear acoustical phenomenon in a simple, easily understood mannerCovers a variety of popular NDE techniques based on nonlinear acoustics in a single volume
Nonlinear Vibration and Dynamics of Smart Continuous Structures and Materials
by Majid GhadiriNonlinear Vibration and Dynamics of Smart Continuous Structures and Materials delves into intricate subjects concerning the analysis of nonlinear vibration issues in continuous structures. It covers general concepts and a history of nonlinear systems before evolving into kinetics and solution methods of continuous structures.Exploring the implementation of new types of materials in various sectors of automobile, aerospace, and structural engineering, the book provides applicable information on the behaviors of smart structures. The book provides a set of mathematical formulations to solve nonlinear static and dynamic behaviors of smart continuous structures by applying principles of elasticity.The book will interest academic researchers and graduate students studying structural engineering, mechanics of solids, and smart materials.
Nonlinear Vibration with Control
by David Wagg Simon NeildThis book provides a comprehensive discussion of nonlinear multi-modal structural vibration problems, and shows how vibration suppression can be applied to such systems by considering a sample set of relevant control techniques. It covers the basic principles of nonlinear vibrations that occur in flexible and/or adaptive structures, with an emphasis on engineering analysis and relevant control techniques. Understanding nonlinear vibrations is becoming increasingly important in a range of engineering applications, particularly in the design of flexible structures such as aircraft, satellites, bridges, and sports stadia. There is an increasing trend towards lighter structures, with increased slenderness, often made of new composite materials and requiring some form of deployment and/or active vibration control. There are also applications in the areas of robotics, mechatronics, micro electrical mechanical systems, non-destructive testing and related disciplines such as structural health monitoring. Two broader themes cut across these application areas: (i) vibration suppression - or active damping - and, (ii) adaptive structures and machines. In this expanded 2nd edition, revisions include: An additional section on passive vibration control, including nonlinear vibration mounts. A more in-depth description of semi-active control, including switching and continuous schemes for dampers and other semi-active systems. A complet e reworking of normal form analysis, which now includes new material on internal resonance, bifurcation of backbone curves and stability analysis of forced responses. Further analysis of the nonlinear dynamics of cables including internal resonance leading to whirling. Additional material on the vibration of systems with impact friction. The book is accessible to practitioners in the areas of application, as well as students and researchers working on related topics. In particular, the aim is to introduce the key concepts of nonlinear vibration to readers who have an understanding of linear vibration and/or linear control, but no specialist knowledge in nonlinear dynamics or nonlinear control.
Nonlinear Water Waves
by Adrian Constantin Joachim Escher Robin Stanley Stanley Johnson Gabriele Villariadrian ConstantinThis volumebrings together four lecture courses on modern aspects of water waves. Theintention, through the lectures, is to present quite a range of mathematicalideas, primarily to show what is possible and what, currently, is of particularinterest. Water wavesof large amplitude can only be fully understood in terms of nonlinear effects,linear theory being not adequate for their description. Taking advantage ofinsights from physical observation, experimental evidence and numericalsimulations, classical and modern mathematical approaches can be used to gaininsight into their dynamics. The book presents several avenues and offers awide range of material of current interest. Thelectures provide a useful source for those who want to begin to investigate howmathematics can be used to improve our understanding of water wave phenomena. In addition, some of the material can be used by those who are already familiarwith one branch of the study of water waves, to learn more about other areas.
Nonlinear Wave Dynamics of Materials and Structures (Advanced Structured Materials #122)
by Holm Altenbach Victor A. Eremeyev Alexey V. Porubov Igor S. PavlovThis book marks the 60th birthday of Prof. Vladimir Erofeev – a well-known specialist in the field of wave processes in solids, fluids, and structures. Featuring a collection of papers related to Prof. Erofeev’s contributions in the field, it presents articles on the current problems concerning the theory of nonlinear wave processes in generalized continua and structures. It also discusses a number of applications as well as various discrete and continuous dynamic models of structures and media and problems of nonlinear acoustic diagnostics.