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Deterministic Chaos in One Dimensional Continuous Systems

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Description: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: BeamsPlatesPanelsShells Introduction to Fractal Dynamics: Cantor Set and Cantor DustKoch Snowflake1D MapsSharkovsky's TheoremJulia SetMandelbrot's Set Introduction to Chaos and Wavelets: Routes to ChaosQuantifying Chaotic Dynamics Simple Chaotic Models: IntroductionAutonomous SystemsNon-Autonomous Systems Discrete and Continuous Dissipative Systems: IntroductionLinear FrictionNonlinear FrictionHysteretic FrictionImpact DampingDamping in Continuous 1D Systems Euler-Bernoulli Beams: IntroductionPlanar BeamsLinear Planar Beams and Stationary Temperature FieldsCurvilinear Planar Beams and Stationary Temperature and Electrical FieldsBeams with Elasto-Plastic DeformationsMulti-Layer Beams Timoshenko and Sheremetev-Pelekh Beams: The Timoshenko BeamsThe Sheremetev-Pelekh BeamsConcluding Remarks Panels: Infinite Length PanelsCylindrical Panels of Infinite Length Plates and Shells: Plates with Initial ImperfectionsFlexible Axially-Symmetric ShellsReadership: Post-graduate and doctoral students, applied mathematicians, physicists, mechanical and civil engineers.Bifurcation;Chaos;Structural Members;PDEs and ODEs;Lyapunov Exponents;WaveletsKey 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 scalesContainWe have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Deterministic Chaos in One Dimensional Continuous Systems. To get started finding Deterministic Chaos in One Dimensional Continuous Systems, you are right to find our website which has a comprehensive collection of manuals listed.
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ISBN: 9814719714

Description: 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: BeamsPlatesPanelsShells Introduction to Fractal Dynamics: Cantor Set and Cantor DustKoch Snowflake1D MapsSharkovsky's TheoremJulia SetMandelbrot's Set Introduction to Chaos and Wavelets: Routes to ChaosQuantifying Chaotic Dynamics Simple Chaotic Models: IntroductionAutonomous SystemsNon-Autonomous Systems Discrete and Continuous Dissipative Systems: IntroductionLinear FrictionNonlinear FrictionHysteretic FrictionImpact DampingDamping in Continuous 1D Systems Euler-Bernoulli Beams: IntroductionPlanar BeamsLinear Planar Beams and Stationary Temperature FieldsCurvilinear Planar Beams and Stationary Temperature and Electrical FieldsBeams with Elasto-Plastic DeformationsMulti-Layer Beams Timoshenko and Sheremetev-Pelekh Beams: The Timoshenko BeamsThe Sheremetev-Pelekh BeamsConcluding Remarks Panels: Infinite Length PanelsCylindrical Panels of Infinite Length Plates and Shells: Plates with Initial ImperfectionsFlexible Axially-Symmetric ShellsReadership: Post-graduate and doctoral students, applied mathematicians, physicists, mechanical and civil engineers.Bifurcation;Chaos;Structural Members;PDEs and ODEs;Lyapunov Exponents;WaveletsKey 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 scalesContainWe have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Deterministic Chaos in One Dimensional Continuous Systems. To get started finding Deterministic Chaos in One Dimensional Continuous Systems, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Deterministic Chaos in One Dimensional Continuous Systems

Deterministic Chaos in One Dimensional Continuous Systems

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