Dynamic Stability and Bifurcation in Nonconservative Mechanics (eBook)

Davide Bigoni, Oleg Kirillov (Herausgeber)

eBook Download: PDF

2018 | 1st ed. 2019
VII, 190 Seiten
Springer International Publishing (Verlag)
978-3-319-93722-9 (ISBN)

Infos

The book offers a unified view on classical results and recent advances in the dynamics of nonconservative systems. The theoretical fundamentals are presented systematically and include: Lagrangian and Hamiltonian formalism, non-holonomic constraints, Lyapunov stability theory, Krein theory of spectra of Hamiltonian systems and modes of negative and positive energy, anomalous Doppler effect, reversible systems, sensitivity analysis of non-self-adjoint operators, dissipation-induced instabilities, local and global instabilities. They are applied to engineering situations such as the coupled mode flutter of wings, flags and pipes, flutter in granular materials, piezoelectric mechanical metamaterials, wave dynamics of infinitely long structures, radiative damping, stability of high-speed trains, experimental realization of follower forces, soft-robot locomotion, wave energy converters, friction-induced instabilities, brake squeal, non-holonomic sailing, dynamics of moving continua, and stability of bicycles and walking robots. 

The book responds to a demand in the modern theory of nonconservative systems coming from the growing number of scientific and engineering disciplines including physics, fluid and solids mechanics, fluid-structure interactions, and modern multidisciplinary research areas such as biomechanics, micro- and nanomechanics, optomechanics, robotics, and material science. It is targeted at both young and experienced researchers and engineers working in fields associated with the dynamics of structures and materials. The book will help to get a comprehensive and systematic knowledge on the stability, bifurcations and dynamics of nonconservative systems and establish links between approaches and methods developed in different areas of mechanics and physics and modern applied mathematics.

Inhalt

Preface 6
Contents 8
Flutter from Friction in Solids and Structures 9
1 Introduction 9
2 Flutter for Structural Systems 12
2.1 The Ziegler Double Pendulum 12
2.2 The Standard Case as a Reference: The Dead Load H on the Double Pendulum 17
2.3 The Follower Force P on the Double Pendulum 20
2.4 Surprising Effects Related to the Viscosity: The Ziegler Paradox 25
2.5 The Deformation of an Elastic Rod: The Euler's Elastica 27
2.6 Constitutive Equation and Dynamics 33
2.7 The Beck and Pflüger Rods 36
2.8 Self-adjointness, an Exclusion Condition for Flutter 42
2.9 Beyond the Linearized Solution: Limit Cycle Behaviour 43
2.10 Follower Forces from Coulomb Friction 45
2.11 Self-oscillating Systems 47
3 Flutter in Frictional Solids 48
3.1 Contact with Coulomb Friction Versus Nonassociative Elastoplasticity 51
3.2 The Rate Equations of Nonassociative Elastoplasticity for Frictional Solids 54
3.3 The Propagation of Incremental Plane Waves 56
3.4 Strain Localization into Planar Bands 58
3.5 The Analysis of the Acoustic Tensor and Flutter Instability 61
4 Concluding Remarks on Flutter Instability in Structures and Solids 64
References 67
Dissipation Induced Instabilities of Structures Coupled to a Flow 70
1 Dynamics and Instabilities of Structures Coupled to a Flow 71
1.1 Cross-Flow Instabilities 71
1.2 Dynamic Instability by Negative Flow-Induced Damping 75
1.3 Wing Instabilities Due to Mode Coupling 77
1.4 Axial Flow Problems 80
2 Damping Induced Instabilities of Structures Coupled to a Flow 89
2.1 Damping Induced Instabilities of Wings 90
2.2 The Fluid-Conveying Pipe Model System 91
2.3 Conclusion 99
3 Applications in Energy Harvesting 100
3.1 Energy Converters 100
3.2 Models of Energy Harvesting Systems Based on Flow-Induced Vibrations 101
3.3 Conclusion 107
References 109
Some Surprising Conservative and Nonconservative Moments in the Dynamics of Rods and Rigid Bodies 110
1 Introduction 110
2 Background on Euler Angles and Bases 112
2.1 The Euler and Dual Euler Bases 114
2.2 Vector Representations 115
3 Lagrange's Equations of Motion and the Newton–Euler Equations of Motion 116
3.1 A Force FA Acting at a Material Point XA 118
3.2 Ideal Integrable Constraints 119
3.3 Potential Energies 120
3.4 A Canonical Form, Equilibria, and Linearization 120
4 Simple Conservative Moments 122
4.1 A Simple Representation for a Conservative Moment 123
4.2 Ziegler's Example Revisited 123
4.3 Torsional Springs 124
5 The Case of a Fixed Axis of Rotation 124
6 The Lagrange Top 125
6.1 Kinematical Considerations 125
6.2 Constraints and Constraint Forces 126
6.3 Kinetic and Potential Energies 127
6.4 The Equations of Motion 127
6.5 Equilibria and Linearized Equations of Motion 129
6.6 Solving for the Reaction Force 130
7 The Satellite Dynamics Problem 131
References 133
Classical Results and Modern Approaches to Nonconservative Stability 135
1 Introduction 135
1.1 ``It was Greenhill who Started the Trouble... 135
1.2 Greenhill's Shaft as a Non-self-adjoint Problem 137
1.3 From Follower Torques to Follower Forces 142
2 Reversible and Circulatory Systems 145
2.1 Zubov-Zhuravlev Decomposition of Non-potential Force Fields 146
2.2 Circulatory Forces in Rotor Dynamics 150
2.3 Stability Criteria for Circulatory Systems 152
2.4 Geometrical Interpretation for m=2 Degrees of Freedom 154
2.5 Approximating Flutter Cone by Perturbation of Eigenvalues 155
3 Perturbing Circulatory Systems 158
3.1 Shieh–Masur Shaft with Dissipative Forces 158
3.2 A Circulatory System Perturbed by Dissipative Forces 161
4 Krein Signature and Stability of Hamiltonian Systems 166
4.1 Canonical and Hamiltonian Equations 170
4.2 Krein Signature of Eigenvalues 171
4.3 Krein Collision or Linear Hamiltonian-Hopf Bifurcation 172
5 Dissipation-Induced Instabilities of Hamiltonian Systems 174
5.1 The Kelvin-Tait-Chetaev Theorem 174
5.2 Secular Instability of the Maclaurin Spheroids 174
6 Stability in the Presence of Potential, Circulatory, Gyroscopic and Dissipative Forces 182
6.1 Rotating Shaft by SM1968 182
6.2 Two-Mass-Skate (TMS) Model of a Bicycle 187
References 193

Produkt-Details

• Erscheint lt. Verlag: 9.7.2018
• Reihe/Serie: CISM International Centre for Mechanical Sciences
• Reihe/Serie: CISM International Centre for Mechanical Sciences
• Zusatzinfo: VII, 190 p. 77 illus., 59 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: fluid-structure interactions • Flutter instability • Friction-Induced Vibrations • Non-conservative Systems • Structural Stability
• ISBN-10: 3-319-93722-7 / 3319937227
• ISBN-13: 978-3-319-93722-9 / 9783319937229