Vibrations and Stability 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 eng...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2003, 2003
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| Edition: | 2nd ed. 2003 |
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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
- 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
- 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