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This book offers a comprehensive and accessible introduction to the mathematical theory of stationary Variational-Hemivariational Inequalities (VHIs), a rapidly growing area of research with significant applications in science and engineering. Unlike traditional approaches that rely heavily on abstract inclusion results for pseudomonotone operators, this work presents a more user-friendly method grounded in basic Functional Analysis. VHIs include variational inequalities and hemivariational inequalities as special cases. The book systematically categorizes and names different VHIs, making it easier for readers to understand the specific problems being addressed. Designed for graduate students and researchers in mathematics, physical sciences, and engineering, this monograph not only provides a concise review of essential materials in Sobolev spaces, convex analysis, and nonsmooth analysis but also delves into applications in contact and fluid mechanics. Through detailed explanations and practical examples, the book bridges the gap between theory and practice, making the complex subject of VHIs more approachable. By focusing on the well-posedness of various forms of VHIs and extending the analysis to include mixed VHIs for the Stokes and Navier-Stokes equations, this book serves as an essential resource for anyone interested in the modeling, analysis, numerical solutions, and real-world applications of VHIs.

This book, the eighth of 15 related monographs, discusses a product-cubic dynamical system possessing a product-cubic vector field and a crossing-univariate quadratic vector field. It presents equilibrium singularity and bifurcation dynamics, and. the saddle-source (sink) examined is the appearing bifurcations for saddle and source (sink). The double-inflection saddle equilibriums are the appearing bifurcations of the saddle and center, and also the appearing bifurcations of the network of saddles and centers. The infinite-equilibriums for the switching bifurcations featured in this volume include: Parabola-source (sink) infinite-equilibriums, Inflection-source (sink) infinite-equilibriums, Hyperbolic (circular) sink-to source infinite-equilibriums, Hyperbolic (circular) lower-to-upper saddle infinite-equilibriums.

This book is the first of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of self-variables and are discussed as the first part of the book. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-dimensional cubic systems are for the first time to be presented. Third-order source and sink flows are presented, and the third-order parabola flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order source and sink flows, and the second-order saddle flows with the first and third-order parabola flows, and the inflection flows. The appearing bifurcations in such cubic systems includes saddle flows and third-order source (sink) flows, inflection flows and third-order up (down)-parabola flows.

This book is the tenth of 15 related monographs, discusses product-cubic nonlinear systems with two crossing-linear and self-quadratic products vector fields and the dynamic behaviors and singularity are presented through the first integral manifolds. The equilibrium and flow singularity and bifurcations discussed in this volume are for the appearing and switching bifurcations. The double-saddle equilibriums described are the appearing bifurcations for saddle source and saddle-sink, and for a network of saddles, sink and source. The infinite-equilibriums for the switching bifurcations are also presented, specifically: · Inflection-saddle infinite-equilibriums, · Hyperbolic (hyperbolic-secant)-sink and source infinite-equilibriums · Up-down and down-up saddle infinite-equilibriums, · Inflection-source (sink) infinite-equilibriums.

This unique, first of its kind, book offers an integrated treatment of the atomistic-continuum behaviours of single and interacting microdefects under elasto-static loading. These microdefects may take the form of nanocracks, microcracks, microvoids, inclusions, and inhomogeneities. Professor Meguid elucidates the subject matter using novel treatment that offers a fresh look at molecular and continuum mechanics, imperfections in solids, the Griffith crack, modes of failure and diagnostics at varied length scales, LEFM and multiscale modeling of interacting microdefects. Providing a range of perspectives from theory and applications, this book is ideal for college seniors, graduate students, practicing and research engineers interested in failure analysis, diagnostics and prevention.

This book, the sixth of 15 related monographs, discusses singularity and networks of equilibriums and 1-diemsnional flows in product quadratic and cubic systems. The author explains how, in the networks, equilibriums have source, sink and saddles with counter-clockwise and clockwise centers and positive and negative saddles, and the 1-dimensional flows includes source and sink flows, parabola flows with hyperbolic and hyperbolic-secant flows. He further describes how the singular equilibriums are saddle-source (sink) and parabola-saddles for the appearing bifurcations, and the 1-dimensional singular flows are the hyperbolic-to-hyperbolic-secant flows and inflection source (sink) flows for 1-dimensional flow appearing bifurcations, and the switching bifurcations are based on the infinite-equilibriums, including inflection-source (sink), parabola-source (sink), up-down and down-up upper-saddle (lower-saddle), up-down (down-up) sink-to-source and source-to-sink, hyperbolic and hyperbolic-secant saddles. The diagonal-inflection upper-saddle and lower-saddle infinite-equilibriums are for the double switching bifurcations. The networks of hyperbolic flows with connected saddle, source and center are presented, and the networks of the hyperbolic flows with paralleled saddle and center are also illustrated. Readers will learn new concepts, theory, phenomena, and analysis techniques. Product-quadratic and product cubic systems Self-linear and crossing-quadratic product vector fields Self-quadratic and crossing-linear product vector fields Hybrid networks of equilibriums and 1-dimensional flows Up-down and down-up saddle infinite-equilibriums Up-down and down-up sink-to-source infinite-equilibriums Inflection-source (sink) Infinite-equilibriums Diagonal inflection saddle infinite-equilibriums Infinite-equilibrium switching bifurcations

This book is the seventh of 15 related monographs, concerns nonlinear dynamics and singularity of cubic dynamical systems possessing a product-cubic vector field and a self-univariate quadratic vector field. The equilibrium singularity and bifurcation dynamics are discussed. The saddle-source (sink) is the appearing bifurcations for saddle and source (sink). The double-saddle equilibriums are the appearing bifurcations of the saddle-source and saddle-sink, and also the appearing bifurcations of the network of saddles, sink and source. The infinite-equilibriums for the switching bifurcations include: • inflection-saddle infinite-equilibriums, • hyperbolic-source (sink) infinite-equilibriums, • up-down (down-up) saddle infinite-equilibriums, • inflection-source (sink) infinite-equilibriums.

This book is the eleventh of 15 related monographs on Cubic Systems, examines self-linear and crossing-quadratic product systems. It discusses the equilibrium and flow singularity and bifurcations, The double-inflection saddles featured in this volume are the appearing bifurcations for two connected parabola-saddles, and also for saddles and centers. The parabola saddles are for the appearing bifurcations of saddle and center. The inflection-source and sink flows are the appearing bifurcations for connected hyperbolic and hyperbolic-secant flows. Networks of higher-order equilibriums and flows are presented. For the network switching, the inflection-sink and source infinite-equilibriums exist, and parabola-source and sink infinite-equilibriums are obtained. The equilibrium networks with connected hyperbolic and hyperbolic-secant flows are discussed. The inflection-source and sink infinite-equilibriums are for the switching bifurcation of two equilibrium networks.

This third of three volumes presents papers from the third series of NODYCON to be held in June of 2023. The conference papers reflect a broad coverage of topics in nonlinear dynamics, both traditionally placed in established streams of research as well as they stand as newly explored and emerging venues of research. These include• Multi-scale dynamics: multiple time/space scales, large system dynamics• Experimental dynamics: benchmark experiments, experimental methods,instrumentation techniques, measurements in harsh environments, experimentalvalidation of nonlinear models• Reduced-order modeling: center manifold reduction, nonlinear normal modes, normalforms• Systems with time and/or space delays• Nonlinear interactions in multi-dof systems: parametric vibrations, multiple external andautoparametric resonances.• Computational techniques: efficient algorithms, use ofsymbolic manipulators, integrationof symbolic manipulation and numerical methods, use of parallel processors.• Nonlinear system identification: parametric/nonparametric identification, data-drivenidentification• Multibody dynamics: rigid and flexible multibody system dynamics, impact and contactmechanics, tire modeling, railroad vehicle dynamics, biomechanics applications,computational multibody dynamics• Fluid/structure interaction• Nonlinear wave propagation in discrete and continuous media

This book, the third of 15 related monographs, presents systematically a theory of self-independent cubic nonlinear systems. Here, at least one vector field is self-cubic, and the other vector field can be constant, self-linear, self-quadratic, or self-cubic. For constant vector fields in this book, the dynamical systems possess 1-dimensional flows, such as source, sink and saddle flows, plus third-order source and sink flows. For self-linear and self-cubic systems discussed, the dynamical systems possess source, sink and saddle equilibriums, saddle-source and saddle-sink, third-order sink and source (i.e, (3rd SI:SI)-sink and (3rdSO:SO)-source) and third-order source (i.e., (3rd SO:SI)-saddle, (3rd SI, SO)-saddle). For self-quadratic and self-cubic systems, in addition to the first and third-order sink, source and saddles plus saddle-source and saddle-sink, there are (3:2)-saddle-sink and (3:2) saddle-source and double-saddles. For the two self-cubic systems, (3:3)-source, sink and saddles exist. Finally, the author describes that homoclinic orbits without centers can be formed, and the corresponding homoclinic networks of source, sink and saddles exists. Readers will learn new concepts, theory, phenomena, and analytic techniques, including Constant and crossing-cubic systems Crossing-linear and crossing-cubic systems Crossing-quadratic and crossing-cubic systems Crossing-cubic and crossing-cubic systems Appearing and switching bifurcations Third-order centers and saddles Parabola-saddles and inflection-saddles Homoclinic-orbit network with centers Appearing bifurcations

This book, the fifth of 15 related monographs, presents systematically a theory of product-cubic nonlinear systems with constant and single-variable linear vector fields. The product-cubic vector field is a product of linear and quadratic different univariate functions. The hyperbolic and hyperbolic-secant flows with directrix flows in the cubic product system with a constant vector field are discussed first, and the cubic product systems with self-linear and crossing-linear vector fields are discussed. The inflection-source (sink) infinite equilibriums are presented for the switching bifurcations of a connected hyperbolic flow and saddle with hyperbolic-secant flow and source (sink) for the connected the separated hyperbolic and hyperbolic-secant flows. The inflection-sink and source infinite-equilibriums with parabola-saddles are presented for the switching bifurcations of a separated hyperbolic flow and saddle with a hyperbolic-secant flow and center. Readers learn new concepts, theory, phenomena, and analysis techniques, such as Constant and product-cubic systems, Linear-univariate and product-cubic systems, Hyperbolic and hyperbolic-secant flows, Connected hyperbolic and hyperbolic-secant flows, Separated hyperbolic and hyperbolic-secant flows, Inflection-source (sink) Infinite-equilibriums and Infinite-equilibrium switching bifurcations.

This book collects the edited and reviewed contribution presented in the 10th iTi conference in Bertinoro, covering fundamental and applied aspects in turbulence. In the spirit of the iTi conference, the book is produced after the conference so that the authors had the opportunity to incorporate comments and discussions raised during the meeting. The iTi has become an established biannual conference on turbulence research with 80 to 100 participants and places value on creating an environment to stimulate discussions and personal contacts in the beautiful town of Bertinoro in Northern Italy close to Bologna, continuing a tradition that has started in Bad Zwischenahn/Germany with the first edition of the conference in 2003. The content-related focus areas of the conference are the interdisciplinary aspects of turbulence, defining the abbreviation iTi—interdisciplinary turbulence initiative. iTi attracts scientist from the engineering, physics, and mathematics communities.

This book provides readers with up-to-date advances in applied and interdisciplinary engineering science and technologies related to nonlinear dynamics, vibration, control, robotics, and their engineering applications, developed in the most recent years. All the contributed chapters come from active scholars in the area, which cover advanced theory and methods, innovative technologies, benchmark experimental validations and engineering practices. Readers would benefit from this state-of-the-art collection of applied nonlinear dynamics, in-depth vibration engineering theory, cutting-edge control methods and technologies and definitely find stimulating ideas for their on-going R&D work. This book is intended for graduate students, research staff, and scholars in academics and also provides useful hand-up guidance for professionals and engineers in practical engineering missions.

This book provides an innovative approach to learning dynamics of particles and rigid bodies, emphasizing a consistent problem-solving framework designed to help students understand the subject while building and reinforcing the mathematical tools needed to bridge the gap between physical intuition and quantitative results. The theoretical developments are supported by an extensive set of MATLAB codes that give the reader powerful tools for exploring and visualizing basic concepts. The book is aimed at engineering students at the sophomore level who have a background in calculus, linear algebra, and differential equations. Uses clear and consistent derivations of the basic concepts of dynamics and provides an extensive set of MATLAB codes Embraces direct vector notation from the start and presents a consistent numerical framework for solving nonlinear differential equations Simplifies one of the most difficult aspects of dynamics—relative motion—using a novel approach to kinematics

This textbook provides the fundamentals of aeroelasticity, with particular attention to problems of interest to aeronautical engineering. The mathematical methods and tools applicable to the modern modeling of general aeroelastic problems are presented, discussed, and applied to fixed-wing aircraft configurations. It is composed of ten chapters divided into two parts: (I) aeroelastic modeling and analysis and (ii) mathematical tools. The six chapters that compose the first part start from the historical background of the discipline, then present the methods for coupling structural dynamics and unsteady aerodynamics for the aeroelastic modeling of the typical wing section, and then extend them to applications for twisted, tapered, swept finite-wing configurations. In this context, particular attention is paid to the presentation, interpretation, and discussion of the available unsteady sectional aerodynamic theories, both in the time and frequency domain, providing a broad scenario of the formulations that can be used for conventional and non-conventional aerodynamic/aeroelastic applications. For a modern view of aeroelasticity, a significant portion of the textbook deals with illustration and discussion of three-dimensional aerodynamic theories and computational methods for the determination of unsteady aerodynamic loads over lifting bodies in incompressible and compressible flows, as well as to the introduction and explanation of methodologies for the identification of reduced-order, state-space aerodynamic/aeroelastic operators suitable for stability (flutter) analysis and control purposes. A chapter is dedicated to the theories and approaches for aeroservoelastic modeling. In the second part of the textbook, additional chapters provide theoretical insights on topics that enrich the multidisciplinary knowledge related to widely applied methods and models for the analysis and solution of aeroelastic problems. The book serves as a reference tool for master's degree students in aeronautical/aerospace engineering, as well as researchers in the field of aeroelasticity.

This second of three volumes presents papers from the third series of NODYCON to be held in June of 2023. The conference papers reflect a broad coverage of topics in nonlinear dynamics, both traditionally placed in established streams of research as well as they stand as newly explored and emerging venues of research. These include• Multi-scale dynamics: multiple time/space scales, large system dynamics• Experimental dynamics: benchmark experiments, experimental methods,instrumentation techniques, measurements in harsh environments, experimentalvalidation of nonlinear models• Reduced-order modeling: center manifold reduction, nonlinear normal modes, normalforms• Systems with time and/or space delays• Nonlinear interactions in multi-dof systems: parametric vibrations, multiple external andautoparametric resonances.• Computational techniques: efficient algorithms, use ofsymbolic manipulators, integrationof symbolic manipulation and numerical methods, use of parallel processors.• Nonlinear system identification: parametric/nonparametric identification, data-drivenidentification• Multibody dynamics: rigid and flexible multibody system dynamics, impact and contactmechanics, tire modeling, railroad vehicle dynamics, biomechanics applications,computational multibody dynamics• Fluid/structure interaction• Nonlinear wave propagation in discrete and continuous media

This book is the thirteenth of 15 related monographs on Cubic Dynamical Systems, discusses self- and product-cubic systems with a crossing-linear and self-quadratic products vector field. Equilibrium series with flow singularity are presented and the corresponding switching bifurcations are discussed through up-down saddles, third-order concave-source (sink), and up-down-to-down-up saddles infinite-equilibriums. The author discusses how equilibrium networks with paralleled hyperbolic and hyperbolic-secant flows exist in such cubic systems, and the corresponding switching bifurcations obtained through the inflection-source and sink infinite-equilibriums. In such cubic systems, the appearing bifurcations are: saddle-source (sink) hyperbolic-to-hyperbolic-secant flows double-saddle third-order saddle, sink and source third-order saddle-source (sink)

The 2nd International Conference of Mechanical System Dynamics (ICMSD2023) is devoted to “Technology Innovations by Understanding Mechanical Dynamics”, with 18 sessions to promote research in dynamic theories on complex structures, multidisciplinary integration, and advanced technologies for applications. It is held on September 1–5 in Peking University, Beijing, China. The conference is expected to provide a platform for academic researchers and engineers in the field of mechanical system dynamics to exchange scientific and technical ideas.

This volume gathers the latest advances, innovations and applications in the field of cable dynamics and aerodynamics, as presented by leading researchers and engineers at the 3rd International Symposium on Dynamics and Aerodynamics of Cables (ISDAC), held in Rome, Italy on June 15-17, 2023. The contributions encompass topics such as nonlinear cable dynamics, cable structures and moving cables, cable aging, fatigue, degradation and failure mechanisms, laboratory testing of cable dynamics and aerodynamics, computational models for cable dynamics and fluid-structure interaction, cable vibration control, cable driven parallel manipulators, monitoring of cable performance, environmental and anthropic loads on cable structures. The contributions, which were selected through a rigorous international peer-review process, share exciting ideas that will spur novel research directions and foster new multidisciplinary collaborations.

Das Ziel dieses Buches ist die Charakterisierung und Beschreibung des Ausbreitungsverhaltens geführter Ultraschallwellen (GUW) in Faserverbund-Metall-Laminaten (FML). Sie gliedert sich in drei experimentelle Untersuchungen. Im ersten Experiment wird das Phasenverhältnis der Schwingungen an Strukturober – und -unterseite als Maß für die Ähnlichkeit zu den für isotrope Materialien hergeleiteten Lamb-Wellen untersucht. Dazu erfolgt die Entwicklung eines Verfahrens zum Phasenwinkelvergleich, welches auf der Continuous Wavelet Transformation sowie der Short-Time Fourier-Transformation beruht. Damit kann anhand simulierter Zeitsignalverläufe in verschiedenen Strukturen gezeigt werden, dass sich auch in FML die geführten Wellen wie klassische Lamb-Wellen ausbilden. Auch in einer experimentellen Untersuchung an einem FML kann die Beobachtungen für gleichphasige Schwingungen bestätigt und für Schwingungen mit Phasenversatz geschlussfolgert werden. Im anschließenden Experiment wird die Frage adressiert, wie sich das Wellenausbreitungsverhalten im Inneren von FML verhält. Dazu werden auf piezoelektrischem Polyvinylidenfluorid (PVDF)-basierende Foliensensoren gewählt, die sich aufgrund ihrer geringen Abmaße und ihrer geringen akustischen Impedanz gut für die möglichst rückwirkungsarme Integration in flache Strukturen aus Faserverbundkunststoff (FVK) eignen. Die erwartete Wirkweise der PVDF-Foliensensoren unter GUW-Erfassung wird erklärt. Anschließend erfolgt die experimentelle Untersuchung des FML, in deren Rahmen die Wellenmoden identifiziert werden sowie eine Abschätzung des Verschiebungsfeldverlaufes entlang der Strukturhöhe gegeben wird. Die Ergebnisse liefern einen experimentellen Hinweis auf die Modenkopplung im gewählten Laminataufbau. Das dritte und letzte Experiment liefert den konkreten Anwendungsfall der Schadensdetektion und -charakterisierung in FML. Dazu werden im Rahmen einer Parameterstudie ein Referenzlaminat sowie zwei Laminate mit künstlichen Delaminationen bei ansonsten übereinstimmendem Laminataufbau gefertigt. Ziel ist zum einen die Untersuchung, inwiefern sich eine unterschiedliche relative Höhenlage eines Schadens im Wellenfeld der FML zeigt. Zum anderen soll geprüft werden, inwiefern sich Schadensinformationen über einen integrierten Sensor erfassen lassen. Flächige Vergleichsmessungen an den Plattenoberflächen über ein Laser-Doppler-Vibrometer dienen der Abschätzung der über die integrierten PVDF-Foliensensoren und unterstützen die Auswertung. Es kann gezeigt werden, dass anhand des horizontalen Scherwellenmoden zusätzliche Schadensinformation über den integrierten Sensor gewonnen werden kann. Über Wellenausbreitungsszenarien gelingt es das Auftreten einiger Wellenpakete in den Sensorzeitsignalen über Modenkonversion zu erklären. Es erfolgt eine Zusammenfassung der Ergebnisse sowie ein Ausblick auf mögliche Folgearbeiten zu jedem Experiment.

This book presents recent research in the field of piezoelectric vibration energy harvesting in which intentionally designed nonlinearities as well as inherently present are widely considered. It provides an overview of the state-of-the-art, with a sharp classification into linear and nonlinear devices, and recalls the fundamentals of piezoelectricity and magnetostatics. A detailed treatment of linear and nonlinear mathematical modeling of piezoelectric harvesters is then developed to provide the reader with a wide range of modeling possibilities. Theoretical, computational, and experimental approaches to modeling the magnetic interaction are also provided. Several cases of innovative piezoelectric harvester designs based on magnetic interaction as a frequency up-conversion mechanism (FuC) are developed. Improvements of the magnetic FuC are proposed, in combination with indirect impacts as well as the manipulation of magnetic forces with novelty methods. Novel studies on the magnetic interaction itself and its implications for the dynamic behavior of the harvester are also summarized. The book provides an integrated view of theoretical, computational, and experimental research in this field, as such it can be useful for researchers interested in linear and nonlinear piezoelectric energy harvesting, for graduate courses on smart structures and devices, microsystems, and for designers.

This book, the 14th of 15 related monographs on Cubic Dynamical Systems, discusses crossing and product cubic systems with a self-linear and crossing-quadratic product vector field. Dr. Luo discusses singular equilibrium series with inflection-source (sink) flows that are switched with parabola-source (sink) infinite-equilibriums. He further describes networks of simple equilibriums with connected hyperbolic flows are obtained, which are switched with inflection-source (sink) and parabola-saddle infinite-equilibriums, and nonlinear dynamics and singularity for such crossing and product cubic systems. In such cubic systems, the appearing bifurcations are: double-inflection saddles, inflection-source (sink) flows, parabola-saddles (saddle-center), third-order parabola-saddles, third-order saddles (centers), third-order saddle-source (sink).

This book is the ninth of 15 related monographs, discusses a two product-cubic dynamical system possessing different product-cubic structures and the equilibrium and flow singularity and bifurcations for appearing and switching bifurcations. The appearing bifurcations herein are parabola-saddles, saddle-sources (sinks), hyperbolic-to-hyperbolic-secant flows, and inflection-source (sink) flows. The switching bifurcations for saddle-source (sink) with hyperbolic-to-hyperbolic-secant flows and parabola-saddles with inflection-source (sink) flows are based on the parabola-source (sink), parabola-saddles, inflection-saddles infinite-equilibriums. The switching bifurcations for the network of the simple equilibriums with hyperbolic flows are parabola-saddles and inflection-source (sink) on the inflection-source and sink infinite-equilibriums. Readers will learn new concepts, theory, phenomena, and analysis techniques. · Two-different product-cubic systems · Hybrid networks of higher-order equilibriums and flows · Hybrid series of simple equilibriums and hyperbolic flows · Higher-singular equilibrium appearing bifurcations · Higher-order singular flow appearing bifurcations · Parabola-source (sink) infinite-equilibriums · Parabola-saddle infinite-equilibriums · Inflection-saddle infinite-equilibriums · Inflection-source (sink) infinite-equilibriums · Infinite-equilibrium switching bifurcations.

This book provides a systematic introduction to the dynamical behaviors of discontinuous dynamical systems and system synchronization. The first part of the book presents the theory of flow switching in discontinuous dynamical systems as well as the switching dynamics in such discontinuous systems. The second part presents a theory for interaction discontinuities between distinct dynamical systems, from which partial and complete chaotic synchronizations in such systems are studied analytically and experimentally.

This book presents the dynamics of spinning bodies, the most confusing topic in Classical Mechanics, using both Lagrangian and Hamiltonian formulations. Choosing the variational problem as a sole starting point, it treats the rigid body as a system of particles with holonomic constraints within the standard methods of classical mechanics, eliminating the need for additional postulates. All basic quantities, equations, and integrals of motion are derived systematically. The rotation matrix, central to the formalism, is the main focus. The reader should find this approach more simple, transparent, and convincing than the traditional presentations. Chapter 2 covers the theory, while subsequent chapters apply the formalism to motions under external forces. Issues of integrability and many cases of solutions in elementary functions are presented. This book is suitable for undergraduate and graduate students familiar with classical mechanics.

This volume aims to present the latest advancements in experimental, analytical, and numerical methodologies aimed at exploring the nonlinear dynamics of diverse systems across varying length and time scales. It delves into the following topics:Methodologies for nonlinear dynamic analysis (harmonic balance, asymptotic techniques, enhanced time integration)Data-driven dynamics, machine learning techniquesExploration of bifurcations and nonsmooth systemsNonlinear phenomena in mechanical systems and structuresExperimental dynamics, system identification, and monitoring techniquesFluid-structure interactionDynamics of multibody systemsTurning processes, rotating systems, and systems with time delays

Dedicated to Professor S. Leela in recognition of her significant contribution to the field of nonlinear dynamics and differential equations, this text consists of 38 papers contributed by experts from 15 countries, together with a survey of Professor Leela's work. The first group of papers examines stability, the second process controls, and the third section contains papers on various topics, including solutions for new classes of systems of equations and boundary problems, and proofs of basic theorems. Many of the featured problems are associated with the ideas and methods proposed and developed by Professor Leela.

This book provides an overview of computational methods based on peridynamics and nonlocal operators and their application to challenging numerical problems which are difficult to deal with traditional methods such as the finite element method, material failure being “only” one of them. The authors have also developed a higher-order nonlocal operator approaches capable of solving higher-order partial differential equations on arbitrary domains in higher-dimensional space with ease. This book is of interest to those in academia and industry.

Engineering Mechanics helps you learn what can often be a challenging subject more efficiently and effectively. It covers the basic principles of mechanics in an example-driven format that emphasizes critical thinking. Clear explanations are accompanied by engineering examples and practice problems. Compelling photorealistic art, free-body diagrams and a robust photograph program are integrated within the examples and throughout the reading to help you see the topics in action. The 6th Edition features 30% new or updated problems. New examples and topics keep pace with the state of the engineering field. As you read and explore concepts, new thought-provoking questions to consider help you better understand and relate to the material.

Machine learning (ML) approaches have been extensively and successfully employed in various areas, like in economics, medical predictions, face recognition, credit card fraud detection, and spam filtering. There is clearly also the potential that ML techniques developed in Engineering and the Sciences will drastically increase the possibilities of analysis and accelerate the design to analysis time. With the use of ML techniques, coupled to conventional methods like finite element and digital twin technologies, new avenues of modeling and simulation can be opened but the potential of these ML techniques needs to still be fully harvested, with the methods developed and enhanced. The objective of this book is to provide an overview of ML in Engineering and the Sciences presenting fundamental theoretical ingredients with a focus on the next generation of computer modeling in Engineering and the Sciences in which the exciting aspects of machine learning are incorporated. The book is of value to any researcher and practitioner interested in research or applications of ML in the areas of scientific modeling and computer aided engineering.

This book provides the essence of aerodynamics, fluid mechanics, experimental methods, gas dynamics, high enthalpy gas dynamics, helicopter aerodynamics, heat transfer, and thermodynamics, describing the underlying principles of these subjects before list

This updated and enriched new edition maintains its complementarity principle in which the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, whereas translations and reflections, impact oscillators, and hyperbolic Clifford's algebras, give rise to the essentially nonlinear “quasi-impact” methodology based on the idea of non-smooth temporal substitutions. In the years since “Nonlinear Dynamics: Between Linear and Impact Limits,” the previous edition of this book, was published, due to a widening area of applications, a deeper insight into the matter has emerged leading to the rudimentary algebraic view on the very existence of the complementary smooth and non-smooth base systems as those associated with two different signs of the algebraic equation j2 =± 1. This edition further includes an overview of applications found in the literature after the publication of first edition, and new physical examples illustrating both theoretical statements and constructive analytical tools.

This revised and updated edition expands on its explanations of methods used to analyze waves in solid materials, such as the waves created by earthquakes and the ultrasonic waves used to detect flaws in materials and for medical diagnoses. In addition to the traditional methods used to analyze steady-state and transient waves in elastic materials, the book contains introductions to advanced areas that no other single text covers. These topics include the use of finite elements to solve wave problems, the Cagniard-de Hoop method, the four-pole technique for analyzing waves in layered media, and the growth and decay of shock and acceleration waves. The authors explain the theory of linear elasticity through the displacement equations of motion, methods used to analyze steady-state and transient waves in layered media, and include an appendix on functions of a complex variable. Originally developed for a graduate course for which no suitable text existed, the new edition retains its classroom-tested treatment of the theories of linear elasticity and complex variables for students needing background in those subjects.

This book presents the research results of advanced vibration control technology, based on two types of typical equipment in industrial engineering of China: power equipment and vibration-sensitive equipment. The main contents of this book include optimized active control strategy research, semi-active control research that can track and equivalently achieve active control effects, refined analysis of active control based on finite element method, research on the impact of vibration isolator layout on vibration isolation performance, passive and active control research based on system freedom decoupling and load decoupling, realized passive and active control research using quasi-zero stiffness system based on positive and negative stiffness, intelligent sensors optimization deployment of plane and space structure, and related key technology application cases in engineering applications. This book provides useful references for engineers and researchers in industrial engineering and technical support for practitioners in the development of China's high-end industry.

Dynamic Behavior of Materials, Volume 1 of the Proceedings of the 2021 SEM Annual Conference & Exposition on Experimental and Applied Mechanics, the first volume of six 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 Experimental Mechanics, including papers on: Hybrid Experimental-Analytical Techniques Industrial Applications Quantitative Visualization of Dynamic Events Novel Testing Techniques Shock and Blast Synchrotron Applications and Advanced Imaging

This textbook summarizes the course of engineering mechanics, designed for one or two semesters, at the undergraduate or graduate level for a range of academic majors. The book covers all the main components of the discipline including: Theoretical Mechanics, Theory of Mechanisms and Machines, Resistance of Materials, Machine Parts and Design Basic; and Interchangeability, Standardization, and Technical Measurements. It can also be used by students of other technical areas in to achieve competence in each of the listed disciplines. The concise presentation facilitates concentration on the most important elements of the concepts presented while also outlining the current state of mechanics, demonstrating engineering applications using various computer packages (MathCad, CosmosWorks, Inkscape, AutoCad), and updating data on engineering materials. Examples of both simple and complex engineering calculations are given at the end of each chapter along with self-assessment questions.

Nonlinear Approaches in Engineering Applications: Design Engineering Problems examines the latest applications of nonlinear approaches in engineering and addresses a range of scientific problems. Chapters are authored by world-class scientists and researchers and focus on the application of nonlinear approaches in different disciplines of engineering and scientific applications, with a strong emphasis on application, physical meaning, and methodologies of the approaches. Topics covered are of high interest in engineering and physics, and an attempt has been made to expose engineers and researchers to a broad range of practical topics and approaches. This book is appropriate for researchers, students, and practicing engineers who are interested in the applications of engineering, physics, and mathematics in nonlinear approaches to solving engineering and science problems.

This first of three volumes includes papers from the second series of NODYCON, which was held virtually in February of 2021. The conference papers reflect a broad coverage of topics in nonlinear dynamics, ranging from traditional topics from established streams of research to those from relatively unexplored and emerging venues of research. These includeFluid-structure interactions Mechanical systems and structures Computational nonlinear dynamics Analytical techniques Bifurcation and dynamic instability Rotating systems Modal interactions and energy transferNonsmooth systems

This book offers up novel research which uses analytical approaches to explore nonlinear features exhibited by various dynamic processes. Relevant to disciplines across engineering and physics, the asymptotic method combined with the multiple scale method is shown to be an efficient and intuitive way to approach mechanics.Beginning with new material on the development of cutting-edge asymptotic methods and multiple scale methods, the book introduces this method in time domain and provides examples of vibrations of systems. Clearly written throughout, it uses innovative graphics to exemplify complex concepts such as nonlinear stationary and nonstationary processes, various resonances and jump pull-in phenomena. It also demonstrates the simplification of problems through using mathematical modelling, by employing the use of limiting phase trajectories to quantify nonlinear phenomena. Particularly relevant to structural mechanics, in rods, cables, beams, plates and shells, as well as mechanical objects commonly found in everyday devices such as mobile phones and cameras, the book shows how each system is modelled, and how it behaves under various conditions.It will be of interest to engineers and professionals in mechanical engineering and structural engineering, alongside those interested in vibrations and dynamics. It will also be useful to those studying engineering maths and physics.

This second of three volumes includes papers from the second series of NODYCON which was held virtually in February of 2021. The conference papers reflect a broad coverage of topics in nonlinear dynamics, ranging from traditional topics from established streams of research to those from relatively unexplored and emerging venues of research. These include· Nonlinear vibration control · Control of nonlinear systems and synchronization · Experimental dynamics · System identification and SHM · Multibody dynamics

This third of three volumes includes papers from the second series of NODYCON, which was held virtually in February of 2021. The conference papers reflect a broad coverage of topics in nonlinear dynamics, ranging from traditional topics from established streams of research to those from relatively unexplored and emerging venues of research. These include· Complex dynamics of COVID-19: modeling, prediction and control · Nonlinear phenomena in bio-systems and eco-systems · Energy harvesting · MEMS/NEMS · Multifunctional structures, materials and metamaterials · Nonlinear waves · Chaotic systems, stochasticity, and uncertainty

This book provides a lucid introduction to the theory of elasticity as applied to isotropic, specially orthotropic and laminated structures. With an application-oriented approach, the contents emphasize the need for rigorous analysis and illustrate its utility for a variety of problems. The simultaneous treatment of comparable isotropic and orthotropic problems enables one to easily visualize the changes in structural behaviour due to material orthotropy. Though intended as a textbook for graduate engineering study, this book is valuable as a self-study aid for practicing engineers as well.

This book is a compilation of scientific articles written by recognized researchers, and select students, participating in the Second Conference on the Study of Complex Systems and their Applications (EDIESCA 2021). EDIESCA 2021 arose from the need for academic and research groups that carry out this scientific research to disseminate their results internationally. The study and characterization of systems with non-linear and/or chaotic behavior has been of great interest to researchers around the world, for which many important results have been obtained with various applications. The dynamic study of chaotic oscillators of different models, such as Rössler, Lorenz, and Chua, has generated important advances in understanding of chemical reactions, meteorological behavior, design of electronic devices, and other applications. Topics at the event included applications for communications systems by masking techniques, financial behavior, networks analysis, nonlinear lasers, numerical modeling, electronic design, and other interesting topics in the area of complex systems. Additionally, there are results on numerical simulation and electronic designs to generate complex dynamic behaviors.

This book presents the latest accomplishments in Novikov/conformal gearing as well as high-conformal gearing. It is focused primarily on strength calculation of gear teeth and the manufacturing of gears for Novikov/conformal and high-conformal gearing along with a brief discussion of achievements in the modern theory of gearing. The modern theory of gearing is the foundation of all optimal designs of gears, gear-sets, and transmissions of all known designs, as well as, of all those to be developed in the future. As even a small improvement in efficiency on a single gear can represent a significant cost saving, given the millions of gears used in industry every year, this volume provides the design and manufacturing engineer in invaluable resource.

This course text provides a practical hands-on introduction to the essentials of kinetics, thermodynamics and microstructure modelling of materials. It provides concise practical descriptions of kinetics and microstructure modelling, condensing the essential information into an engaging and accessible text. Class tested by graduate students, the book includes worked examples throughout and is supplemented with phase diagram calculation software to aid learning. This book is ideal as a practical course for final year undergraduates and masters students in materials science and engineering, and is a core text for courses on thermodynamics, phase diagrams, kinetics and microstructure modelling.

Dynamic Behavior of Materials, Volume 1 of the Proceedings of the 2021 SEM Annual Conference & Exposition on Experimental and Applied Mechanics, the first volume of four 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 Experimental Mechanics, including papers on:Synchrotron Applications/Advanced Dynamic ImagingQuantitative Visualization of Dynamic EventsNovel Experimental TechniquesDynamic Behavior of GeomaterialsDynamic Failure & FragmentationDynamic Response of Low Impedance MaterialsHybrid Experimental/Computational StudiesShock and Blast LoadingAdvances in Material ModelingIndustrial Applications

This book is an essential guide to nonlinear dynamics and vibration control, detailing both the theory and the practical industrial applications within all aspects of engineering. Demonstrating how to improve efficiency through reducing unwanted vibration, it will aid both students and engineers in practically and safely improving flexible structures through control methods. Increasing demand for light-weight robotic systems and space applications has actuated the design and construction of more flexible structures. These flexible structures, involving numerous dynamic systems, experience unwanted vibrations, impacting accuracy, operating speed, safety and, importantly, efficiency. This book aids engineers in assuaging this issue through vibration control methods, including nonlinear dynamics. It covers topics such as dynamic modeling of nonlinear system, nonlinear oscillators, and modal analyses of multiple-mode system. It also looks at vibration control methods including linear control, nonlinear control, intelligent control, and command smoothers. These control methods are effective and reliable methods to counteract unwanted vibrations. The book is practically minded, using industrial applications throughout, such as bridge cranes, tower cranes, aerial cranes and liquid sloshing. It also discusses cable-suspension structures, light-weight links, and fluid motions which exhibit flexible-structure dynamics. The book will be of interest to students and engineers alike, in the field of mechatronics, mechanical systems and signal processing, nonlinear dynamics, vibration, and control engineering.

This book is a novel tutorial for research-oriented study of vibration mechanics. The book begins with twelve open problems from six case studies of vibration mechanics in order to guide readers in studying the entire book. Then, the book surveys both theories and methods of linear vibrations in an elementary course from a new perspective of aesthetics of science so as to assist readers to upgrade their way of learning. The successive chapters offer a theoretical frame of linear vibrations and waves, covering the models of vibration systems, the vibration analysis of discrete systems, the natural vibrations of one-dimensional structures, the natural vibrations of symmetric structures, and the waves and vibrations of one-dimensional structures. The chapters help readers solve the twelve open problems step by step during the research-oriented study.The book tries to arouse the interest of graduate students and professionals, who have learnt an elementary course of vibration mechanics of two credits, to conduct the research-oriented study and achieve a helical upgrade understanding to vibration mechanics.

This book presents recent improvements in peridynamic modeling of structures. It provides sufficient theory and numerical implementation helpful to both new and existing researchers in the field. The main focus of the book is on the non-ordinary state-based (NOSB) peridynamics (PD) and its applications for performing finite deformation. It presents the framework for modeling high stretch polymers, viscoelastic materials, thermoelasticity, plasticity, and creep. It provides a systematic derivation for dimensionally reduced structures such as axisymmetric structures and beams. Also, it presents a novel approach to impose boundary conditions without suffering from displacement kinks near the boundary. Furthermore, it presents refinements to bond-based PD model by including rotation kinematics for modeling isotropic and composite materials. Moreover, it presents a PD – FEM coupling framework in ANSYS based on principle for virtual work. Lastly, it presents an application of neural networks in the peridynamic (PINN) framework. Sample codes are provided for readers to develop hands-on experience on peridynamic modeling. Describes new developments in peridynamics and their applications in the presence of material and geometric nonlinearity; Describes an approach to seamlessly couple PD with FE; Introduces the use of the neural network in the PD framework to solve engineering problems;Provides theory and numerical examples for researchers and students to self-study and apply in their research (Codes are provided as supplementary material);Provides theoretical development and numerical examples suitable for graduate courses.

The theory of dynamic equations has many interesting applications in control theory, mathematical economics, mathematical biology, engineering and technology. In some cases, there exists uncertainty, ambiguity, or vague factors in such problems, and fuzzy theory and interval analysis are powerful tools for modeling these equations on time scales. The aim of this book is to present a systematic account of recent developments; describe the current state of the useful theory; show the essential unity achieved in the theory fuzzy dynamic equations, dynamic inclusions and optimal control problems on time scales; and initiate several new extensions to other types of fuzzy dynamic systems and dynamic inclusions. The material is presented in a highly readable, mathematically solid format. Many practical problems are illustrated, displaying a wide variety of solution techniques. The book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. Students in mathematical and physical sciences will find many sections of direct relevance.