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This volume introduces new approaches to modeling strongly nonlinear behaviour of structural mechanical units: beams, plates and shells or composite systems. The text draws on bifurcation theory and chaos, emphasizing control and stability of objects and systems.
Book Synopsis Chaos in Structural Mechanics by : Jan Awrejcewicz
Download or read book Chaos in Structural Mechanics written by Jan Awrejcewicz and published by Springer Science & Business Media. This book was released on 2009-11-11 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces new approaches to modeling strongly nonlinear behaviour of structural mechanical units: beams, plates and shells or composite systems. The text draws on bifurcation theory and chaos, emphasizing control and stability of objects and systems.
Book Synopsis Stress, Stability, and Chaos in Structural Engineering by : Mohammed S. El Naschie
Download or read book Stress, Stability, and Chaos in Structural Engineering written by Mohammed S. El Naschie and published by . This book was released on 1992 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stress, stability and chaos in structural engineering : an energy approach by : Mohammed S. El Naschie
Download or read book Stress, stability and chaos in structural engineering : an energy approach written by Mohammed S. El Naschie and published by . This book was released on 1989 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt:
For the many different deterministic non-linear dynamic systems (physical, mechanical, technical, chemical, ecological, economic, and civil and structural engineering), the discovery of irregular vibrations in addition to periodic and almost periodic vibrations is one of the most significant achievements of modern science. An in-depth study of the theory and application of non-linear science will certainly change one's perception of numerous non-linear phenomena and laws considerably, together with its great effects on many areas of application. As the important subject matter of non-linear science, bifurcation theory, singularity theory and chaos theory have developed rapidly in the past two or three decades. They are now advancing vigorously in their applications to mathematics, physics, mechanics and many technical areas worldwide, and they will be the main subjects of our concern. This book is concerned with applications of the methods of dynamic systems and subharmonic bifurcation theory in the study of non-linear dynamics in engineering. It has grown out of the class notes for graduate courses on bifurcation theory, chaos and application theory of non-linear dynamic systems, supplemented with our latest results of scientific research and materials from literature in this field. The bifurcation and chaotic vibration of deterministic non-linear dynamic systems are studied from the viewpoint of non-linear vibration.
Book Synopsis Bifurcation and Chaos in Engineering by : Yushu Chen
Download or read book Bifurcation and Chaos in Engineering written by Yushu Chen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the many different deterministic non-linear dynamic systems (physical, mechanical, technical, chemical, ecological, economic, and civil and structural engineering), the discovery of irregular vibrations in addition to periodic and almost periodic vibrations is one of the most significant achievements of modern science. An in-depth study of the theory and application of non-linear science will certainly change one's perception of numerous non-linear phenomena and laws considerably, together with its great effects on many areas of application. As the important subject matter of non-linear science, bifurcation theory, singularity theory and chaos theory have developed rapidly in the past two or three decades. They are now advancing vigorously in their applications to mathematics, physics, mechanics and many technical areas worldwide, and they will be the main subjects of our concern. This book is concerned with applications of the methods of dynamic systems and subharmonic bifurcation theory in the study of non-linear dynamics in engineering. It has grown out of the class notes for graduate courses on bifurcation theory, chaos and application theory of non-linear dynamic systems, supplemented with our latest results of scientific research and materials from literature in this field. The bifurcation and chaotic vibration of deterministic non-linear dynamic systems are studied from the viewpoint of non-linear vibration.
Computational structural mechanics (CSM) and computational fluid dynamics (CFD) have emerged in the last two decades as new disciplines combining structural mechanics and fluid dynamics with approximation theory, numerical analysis and computer science. Their use has transformed much of theoretical mechanics and abstract science into practical and essential tools for a multitude of technological developments which affect many facets of our life. This collection of over 40 papers provides an authoritative documentation of major advances in both CSM and CFD, helping to identify future directions of development in these rapidly changing fields. Key areas covered are fluid structure interaction and aeroelasticity, CFD technology and reacting flows, micromechanics, stability and eigenproblems, probabilistic methods and chaotic dynamics, perturbation and spectral methods, element technology (finite volume, finite elements and boundary elements), adaptive methods, parallel processing machines and applications, and visualization, mesh generation and artificial intelligence interfaces.
Book Synopsis Computational Structural Mechanics & Fluid Dynamics by : A.K. Noor
Download or read book Computational Structural Mechanics & Fluid Dynamics written by A.K. Noor and published by Elsevier. This book was released on 2013-10-22 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational structural mechanics (CSM) and computational fluid dynamics (CFD) have emerged in the last two decades as new disciplines combining structural mechanics and fluid dynamics with approximation theory, numerical analysis and computer science. Their use has transformed much of theoretical mechanics and abstract science into practical and essential tools for a multitude of technological developments which affect many facets of our life. This collection of over 40 papers provides an authoritative documentation of major advances in both CSM and CFD, helping to identify future directions of development in these rapidly changing fields. Key areas covered are fluid structure interaction and aeroelasticity, CFD technology and reacting flows, micromechanics, stability and eigenproblems, probabilistic methods and chaotic dynamics, perturbation and spectral methods, element technology (finite volume, finite elements and boundary elements), adaptive methods, parallel processing machines and applications, and visualization, mesh generation and artificial intelligence interfaces.
This book provides a collection of research papers on one of the topics where the applications of chaos have been more fruitful: controlling chaos. Here, new theoretical ideas, as experimental implementations of controlling chaos, are included, while the applications contained in this volume can be referred to turbulent magnetized plasmas, chaotic neural networks, modeling city traffic and models of interest in celestial mechanics. Recent Progress in Controlling Chaos will provide an overview of the recent progress in this field, which will be very useful for students and researchers. The authors of these research works are prominent in their areas of specialization, and they offer an excellent state-of-the-art of this field and its most recent developments and progress.
Book Synopsis Recent Progress in Controlling Chaos by : Miguel Angel Fern ndez Sanju n
Download or read book Recent Progress in Controlling Chaos written by Miguel Angel Fern ndez Sanju n and published by World Scientific. This book was released on 2010 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a collection of research papers on one of the topics where the applications of chaos have been more fruitful: controlling chaos. Here, new theoretical ideas, as experimental implementations of controlling chaos, are included, while the applications contained in this volume can be referred to turbulent magnetized plasmas, chaotic neural networks, modeling city traffic and models of interest in celestial mechanics. Recent Progress in Controlling Chaos will provide an overview of the recent progress in this field, which will be very useful for students and researchers. The authors of these research works are prominent in their areas of specialization, and they offer an excellent state-of-the-art of this field and its most recent developments and progress.
This book is a collection of recent reprints and new material on fundamentally nonlinear problems in structural systems which demonstrate localized responses to continuous inputs. It has two intended audiences. For mathematicians and physicists it should provide useful new insights into a classical yet rapidly developing area of application of the rich subject of dynamical systems theory. For workers in structural and solid mechanics it introduces a new methodology for dealing with structural localization and the related topic of the generation of solitary waves. Applications range from classical problems such as the buckling of cylindrical shells, twisted rods and pipelines, to the folding of geological strata, the failure of sandwich structures and the propagation of solitary waves in suspended beam systems.
Book Synopsis Localization And Solitary Waves In Solid Mechanics by : Alan R Champneys
Download or read book Localization And Solitary Waves In Solid Mechanics written by Alan R Champneys and published by World Scientific. This book was released on 1999-11-30 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of recent reprints and new material on fundamentally nonlinear problems in structural systems which demonstrate localized responses to continuous inputs. It has two intended audiences. For mathematicians and physicists it should provide useful new insights into a classical yet rapidly developing area of application of the rich subject of dynamical systems theory. For workers in structural and solid mechanics it introduces a new methodology for dealing with structural localization and the related topic of the generation of solitary waves. Applications range from classical problems such as the buckling of cylindrical shells, twisted rods and pipelines, to the folding of geological strata, the failure of sandwich structures and the propagation of solitary waves in suspended beam systems.
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz
Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
This book presents the latest results related to shells characterize and design shells, plates, membranes and other thin-walled structures, a multidisciplinary approach from macro- to nanoscale is required which involves the classical disciplines of mechanical/civil/materials engineering (design, analysis, and properties) and physics/biology/medicine among others. The book contains contributions of a meeting of specialists (mechanical engineers, mathematicians, physicists and others) in such areas as classical and non-classical shell theories. New trends with respect to applications in mechanical, civil and aero-space engineering, as well as in new branches like medicine and biology are presented which demand improvements of the theoretical foundations of these theories and a deeper understanding of the material behavior used in such structures.
Book Synopsis Shell and Membrane Theories in Mechanics and Biology by : Holm Altenbach
Download or read book Shell and Membrane Theories in Mechanics and Biology written by Holm Altenbach and published by Springer. This book was released on 2014-09-09 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the latest results related to shells characterize and design shells, plates, membranes and other thin-walled structures, a multidisciplinary approach from macro- to nanoscale is required which involves the classical disciplines of mechanical/civil/materials engineering (design, analysis, and properties) and physics/biology/medicine among others. The book contains contributions of a meeting of specialists (mechanical engineers, mathematicians, physicists and others) in such areas as classical and non-classical shell theories. New trends with respect to applications in mechanical, civil and aero-space engineering, as well as in new branches like medicine and biology are presented which demand improvements of the theoretical foundations of these theories and a deeper understanding of the material behavior used in such structures.
This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations. Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler–Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic–plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels. The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering. Contents:Bifurcational and Chaotic Dynamics of Simple Structural Members:BeamsPlatesPanelsShellsIntroduction to Fractal Dynamics:Cantor Set and Cantor DustKoch Snowflake1D MapsSharkovsky's TheoremJulia SetMandelbrot's SetIntroduction to Chaos and Wavelets:Routes to ChaosQuantifying Chaotic DynamicsSimple Chaotic Models:IntroductionAutonomous SystemsNon-Autonomous SystemsDiscrete and Continuous Dissipative Systems:IntroductionLinear FrictionNonlinear FrictionHysteretic FrictionImpact DampingDamping in Continuous 1D SystemsEuler-Bernoulli Beams:IntroductionPlanar BeamsLinear Planar Beams and Stationary Temperature FieldsCurvilinear Planar Beams and Stationary Temperature and Electrical FieldsBeams with Elasto-Plastic DeformationsMulti-Layer BeamsTimoshenko and Sheremetev-Pelekh Beams:The Timoshenko BeamsThe Sheremetev-Pelekh BeamsConcluding RemarksPanels:Infinite Length PanelsCylindrical Panels of Infinite LengthPlates and Shells:Plates with Initial ImperfectionsFlexible Axially-Symmetric Shells Readership: Post-graduate and doctoral students, applied mathematicians, physicists, mechanical and civil engineers. Key Features:Includes fascinating and rich dynamics exhibited by simple structural members and by the solution properties of the governing 1D non-linear PDEs, suitable for applied mathematicians and physicistsCovers a wide variety of the studied PDEs, their validated reduction to ODEs, classical and non-classical methods of analysis, influence of various boundary conditions and control parameters, as well as the illustrative presentation of the obtained results in the form of colour 2D and 3D figures and vibration type charts and scalesContains originally discovered, illustrated and discussed novel and/or modified classical scenarios of transition from regular to chaotic dynamics exhibited by 1D structural members, showing a way to control chaotic and bifurcational dynamics, with directions to study other dynamical systems modeled by chains of nonlinear oscillators
Book Synopsis Deterministic Chaos in One-Dimensional Continuous Systems by : Jan Awrejcewicz
Download or read book Deterministic Chaos in One-Dimensional Continuous Systems written by Jan Awrejcewicz and published by World Scientific. This book was released on 2016-03-14 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations. Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler–Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic–plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels. The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering. Contents:Bifurcational and Chaotic Dynamics of Simple Structural Members:BeamsPlatesPanelsShellsIntroduction to Fractal Dynamics:Cantor Set and Cantor DustKoch Snowflake1D MapsSharkovsky's TheoremJulia SetMandelbrot's SetIntroduction to Chaos and Wavelets:Routes to ChaosQuantifying Chaotic DynamicsSimple Chaotic Models:IntroductionAutonomous SystemsNon-Autonomous SystemsDiscrete and Continuous Dissipative Systems:IntroductionLinear FrictionNonlinear FrictionHysteretic FrictionImpact DampingDamping in Continuous 1D SystemsEuler-Bernoulli Beams:IntroductionPlanar BeamsLinear Planar Beams and Stationary Temperature FieldsCurvilinear Planar Beams and Stationary Temperature and Electrical FieldsBeams with Elasto-Plastic DeformationsMulti-Layer BeamsTimoshenko and Sheremetev-Pelekh Beams:The Timoshenko BeamsThe Sheremetev-Pelekh BeamsConcluding RemarksPanels:Infinite Length PanelsCylindrical Panels of Infinite LengthPlates and Shells:Plates with Initial ImperfectionsFlexible Axially-Symmetric Shells Readership: Post-graduate and doctoral students, applied mathematicians, physicists, mechanical and civil engineers. Key Features:Includes fascinating and rich dynamics exhibited by simple structural members and by the solution properties of the governing 1D non-linear PDEs, suitable for applied mathematicians and physicistsCovers a wide variety of the studied PDEs, their validated reduction to ODEs, classical and non-classical methods of analysis, influence of various boundary conditions and control parameters, as well as the illustrative presentation of the obtained results in the form of colour 2D and 3D figures and vibration type charts and scalesContains originally discovered, illustrated and discussed novel and/or modified classical scenarios of transition from regular to chaotic dynamics exhibited by 1D structural members, showing a way to control chaotic and bifurcational dynamics, with directions to study other dynamical systems modeled by chains of nonlinear oscillators
