Thomsen Vibrations and Stability

Advanced Theory, Analysis, and Tools
2. Auflage 2003
ISBN: 978-3-662-10793-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 404 Seiten, Web PDF

Reihe: Engineering (R0)

Lucidly uniting classical and modern topics of advanced vibration analysis, this text provides students with a background in elementary vibrations, especially 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 levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. Readers gain analytical skills with simple models, learn to recognize nonlinear phenomena, and employ advanced tools such as perturbation analysis and bifurcation analysis. Enriching theory with relevant examples from real systems, this book meets the increasing interest in non-linear dynamics in engineering, applied mathematics, and physics. This edition includes a new chapter on the useful effects of fast vibrations and many new exercise problems.

Zielgruppe

Graduate

Autoren/Hrsg.

Thomsen, Jon Juel

Inhaltsverzeichnis

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.2Formulas 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.