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Vibrations and Stability [electronic resource] : Advanced Theory, Analysis, and Tools /
This book ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It provides students with a background in elementary vibrations, with tools necessary for understanding and analyzing more complex dynamical phenomena that can be encountered in engineering and scientific practice. It progresses steadily from linear vibration theory over various levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. It trains the student to analyze simple models, recognize nonlinear phenomena and work with advanced tools such as perturbation analysis and bifurcation analysis. Explainig theory in terms of relevant examples from real systems, this book is user- friendly and meets the increasing interest in non-linear dynamics in mechanical/structural engineering and applied mathematics and physics. The new revised and updated edition includes a new chapter on useful effects of fast vibrations and many new exercise problems.
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| Main Authors: | , |
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| Format: | Texto biblioteca |
| Language: | eng |
| Published: |
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,
2003
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| Subjects: | Engineering., Dynamics., Ergodic theory., Applied mathematics., Engineering mathematics., Statistical physics., Dynamical systems., Structural mechanics., Vibration., Mechanical engineering., Mechanical Engineering., Vibration, Dynamical Systems, Control., Structural Mechanics., Statistical Physics, Dynamical Systems and Complexity., Applications of Mathematics., Dynamical Systems and Ergodic Theory., |
| Online Access: | http://dx.doi.org/10.1007/978-3-662-10793-5 |
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Engineering. Dynamics. Ergodic theory. Applied mathematics. Engineering mathematics. Statistical physics. Dynamical systems. Structural mechanics. Vibration. Mechanical engineering. Engineering. Mechanical Engineering. Vibration, Dynamical Systems, Control. Structural Mechanics. Statistical Physics, Dynamical Systems and Complexity. Applications of Mathematics. Dynamical Systems and Ergodic Theory. Engineering. Dynamics. Ergodic theory. Applied mathematics. Engineering mathematics. Statistical physics. Dynamical systems. Structural mechanics. Vibration. Mechanical engineering. Engineering. Mechanical Engineering. Vibration, Dynamical Systems, Control. Structural Mechanics. Statistical Physics, Dynamical Systems and Complexity. Applications of Mathematics. Dynamical Systems and Ergodic Theory. |
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Engineering. Dynamics. Ergodic theory. Applied mathematics. Engineering mathematics. Statistical physics. Dynamical systems. Structural mechanics. Vibration. Mechanical engineering. Engineering. Mechanical Engineering. Vibration, Dynamical Systems, Control. Structural Mechanics. Statistical Physics, Dynamical Systems and Complexity. Applications of Mathematics. Dynamical Systems and Ergodic Theory. Engineering. Dynamics. Ergodic theory. Applied mathematics. Engineering mathematics. Statistical physics. Dynamical systems. Structural mechanics. Vibration. Mechanical engineering. Engineering. Mechanical Engineering. Vibration, Dynamical Systems, Control. Structural Mechanics. Statistical Physics, Dynamical Systems and Complexity. Applications of Mathematics. Dynamical Systems and Ergodic Theory. Thomsen, Jon Juel. author. SpringerLink (Online service) Vibrations and Stability [electronic resource] : Advanced Theory, Analysis, and Tools / |
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This book ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It provides students with a background in elementary vibrations, with tools necessary for understanding and analyzing more complex dynamical phenomena that can be encountered in engineering and scientific practice. It progresses steadily from linear vibration theory over various levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. It trains the student to analyze simple models, recognize nonlinear phenomena and work with advanced tools such as perturbation analysis and bifurcation analysis. Explainig theory in terms of relevant examples from real systems, this book is user- friendly and meets the increasing interest in non-linear dynamics in mechanical/structural engineering and applied mathematics and physics. The new revised and updated edition includes a new chapter on useful effects of fast vibrations and many new exercise problems. |
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Texto |
| topic_facet |
Engineering. Dynamics. Ergodic theory. Applied mathematics. Engineering mathematics. Statistical physics. Dynamical systems. Structural mechanics. Vibration. Mechanical engineering. Engineering. Mechanical Engineering. Vibration, Dynamical Systems, Control. Structural Mechanics. Statistical Physics, Dynamical Systems and Complexity. Applications of Mathematics. Dynamical Systems and Ergodic Theory. |
| author |
Thomsen, Jon Juel. author. SpringerLink (Online service) |
| author_facet |
Thomsen, Jon Juel. author. SpringerLink (Online service) |
| author_sort |
Thomsen, Jon Juel. author. |
| title |
Vibrations and Stability [electronic resource] : Advanced Theory, Analysis, and Tools / |
| title_short |
Vibrations and Stability [electronic resource] : Advanced Theory, Analysis, and Tools / |
| title_full |
Vibrations and Stability [electronic resource] : Advanced Theory, Analysis, and Tools / |
| title_fullStr |
Vibrations and Stability [electronic resource] : Advanced Theory, Analysis, and Tools / |
| title_full_unstemmed |
Vibrations and Stability [electronic resource] : Advanced Theory, Analysis, and Tools / |
| title_sort |
vibrations and stability [electronic resource] : advanced theory, analysis, and tools / |
| publisher |
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, |
| publishDate |
2003 |
| url |
http://dx.doi.org/10.1007/978-3-662-10793-5 |
| work_keys_str_mv |
AT thomsenjonjuelauthor vibrationsandstabilityelectronicresourceadvancedtheoryanalysisandtools AT springerlinkonlineservice vibrationsandstabilityelectronicresourceadvancedtheoryanalysisandtools |
| _version_ |
1756263615743131648 |
| spelling |
KOHA-OAI-TEST:1726352018-07-30T22:50:05ZVibrations and Stability [electronic resource] : Advanced Theory, Analysis, and Tools / Thomsen, Jon Juel. author. SpringerLink (Online service) textBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,2003.engThis book ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It provides students with a background in elementary vibrations, with tools necessary for understanding and analyzing more complex dynamical phenomena that can be encountered in engineering and scientific practice. It progresses steadily from linear vibration theory over various levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. It trains the student to analyze simple models, recognize nonlinear phenomena and work with advanced tools such as perturbation analysis and bifurcation analysis. Explainig theory in terms of relevant examples from real systems, this book is user- friendly and meets the increasing interest in non-linear dynamics in mechanical/structural engineering and applied mathematics and physics. The new revised and updated edition includes a new chapter on useful effects of fast vibrations and many new exercise problems.1 Vibration Basics -- 2 Eigenvalue Problems of Vibrations And Stability -- 3 Nonlinear Vibrations: Classical Local Theory -- 4 Nonlinear Multiple-DOF Systems: Local Analysis -- 5 Bifurcations -- 6 Chaotic Vibrations -- 7 Special Effects of High-Frequency Excitation -- Appendix A — Performing Numerical Simulations -- A.1 Solving Differential Equations -- A.2 Computing Chaos-Related Quantities -- A.3 Interfacing with the ODE-Solver -- A.4 Locating Software on the Internet -- Appendix B — Major Exercises -- B.1 Tension Control of Rotating Shafts -- B.1.1 Mathematical Model -- B.1.2 Eigenvalue Problem, Natural Frequencies and Mode Shapes -- B.1.3 Discretisations, Choice of Control Law -- B.1.5 Quantitative Analysis of the Controlled System -- B.1.6 Using a Dither Signal for Open-Loop Control -- B.1.7 Numerical Analysis of the Controlled System -- B.1.8 Conclusions -- B.2 Vibrations of a Spring-Tensioned Beam -- B.2.1 Mathematical Model -- B.2.2 Eigenvalue Problem, Natural Frequencies and Mode Shapes -- B.2.3 Discrete Models -- B.2.4 Local Bifurcation Analysis for the Unloaded System -- B.2.5 Quantitative Analysis of the Loaded System -- B.2.6 Numerical Analysis -- B.2.7 Conclusions -- B.3 Dynamics of a Microbeam -- B.3.1 System Description -- B.3.2 Mathematical Model -- B.3.3 Eigenvalue Problem, Natural Frequencies and Mode Shapes -- B.3.4 Discrete Models, Mode Shape Expansion -- B.3.5 Local Bifurcation Analysis for the Statically Loaded System -- B.3.6 Quantitative Analysis of the Loaded System -- B.3.7 Numerical Analysis -- B.3.8 Conclusions -- Appendix C — Mathematical Formulas -- C.1 Formulas Typically Used in Perturbation analysis -- C.1.1 Complex Numbers -- C.1.2 Powers of Two-Term Sums -- C.1.3 Dirac’s Delta Function (?) -- C.1.4 Averaging Integrals -- C.1.5 Fourier Series of a Periodic Function -- C.2 Formulas for Stability Analysis -- C.2.1 The Routh-Hurwitz Criterion -- C.2.2 Mathieu’s Equation:Stability of the Zero-Solution -- Appendix D — Vibration Modes and Frequencies for Structural Elements -- D.1 Rods -- D.1.1 Longitudinal Vibrations -- D.1.2 Torsional Vibrations -- D.2 Beams -- D.2.1 Bernoulli-Euler Theory -- D.2.2 Timoshenko Theory -- D.3 Rings -- D.3.1 In-Plane Bending -- D.3.2 Out-of-Plane Bending -- D.3.3 Extension -- D.4 Membranes -- D.4.1 Rectangular Membrane -- D.4.2 Circular Membrane -- D.5 Plates -- D.5.1 Rectangular Plate -- D.5.2 Circular Plate -- D.6 Other Structures -- Appendix E — Properties of Engineering Materials -- E.1 Friction and Thermal Expansion Coefficients -- E.2 Density and Elasticity Constants -- References.This book ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It provides students with a background in elementary vibrations, with tools necessary for understanding and analyzing more complex dynamical phenomena that can be encountered in engineering and scientific practice. It progresses steadily from linear vibration theory over various levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. It trains the student to analyze simple models, recognize nonlinear phenomena and work with advanced tools such as perturbation analysis and bifurcation analysis. Explainig theory in terms of relevant examples from real systems, this book is user- friendly and meets the increasing interest in non-linear dynamics in mechanical/structural engineering and applied mathematics and physics. The new revised and updated edition includes a new chapter on useful effects of fast vibrations and many new exercise problems.Engineering.Dynamics.Ergodic theory.Applied mathematics.Engineering mathematics.Statistical physics.Dynamical systems.Structural mechanics.Vibration.Mechanical engineering.Engineering.Mechanical Engineering.Vibration, Dynamical Systems, Control.Structural Mechanics.Statistical Physics, Dynamical Systems and Complexity.Applications of Mathematics.Dynamical Systems and Ergodic Theory.Springer eBookshttp://dx.doi.org/10.1007/978-3-662-10793-5URN:ISBN:9783662107935 |