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Vibrations and stability : advanced theory, analysis, and tools

Author: Jon Juel Thomsen
Publisher: Berlin ; New York : Springer, 2003.
Edition/Format:   Print book : English : 2nd edView all editions and formats

An ideal text for students that ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It trains the student to analyze simple models, recognize  Read more...


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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Jon Juel Thomsen
ISBN: 3540401407 9783540401407 9783642072727 3642072720
OCLC Number: 52547705
Description: xxi, 404 pages : illustrations ; 24 cm
Contents: 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.
Responsibility: Jon Juel Thomsen.
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From the reviews of the second edition:"Vibrations and stability ... attracted a vast amount of attention of a multitude of researchers in the past and present and will remain highly topical in the Read more...

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