Vibrations and Stability: Advanced Theory, Analysis, and Tools (Hardcover, 2)

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.