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LINEAR and NONLINEAR INSTABILITIES in MECHANICAL SYSTEMS An in-depth insight into nonlinear analysis and control As mechanical systems become lighter, faster, and more flexible, various nonlinear instability phenomena can occur in practical systems. The fundamental knowledge of nonlinear analysis and control is essential to engineers for analysing and controlling nonlinear instability phenomena. This book bridges the gap between the mathematical expressions of nonlinear dynamics and the corresponding practical phenomena. Linear and Nonlinear Instabilities in Mechanical Systems: Analysis,…mehr
LINEAR and NONLINEAR INSTABILITIES in MECHANICAL SYSTEMS An in-depth insight into nonlinear analysis and control As mechanical systems become lighter, faster, and more flexible, various nonlinear instability phenomena can occur in practical systems. The fundamental knowledge of nonlinear analysis and control is essential to engineers for analysing and controlling nonlinear instability phenomena. This book bridges the gap between the mathematical expressions of nonlinear dynamics and the corresponding practical phenomena. Linear and Nonlinear Instabilities in Mechanical Systems: Analysis, Control and Application provides a detailed and informed insight into the fundamental methods for analysis and control for nonlinear instabilities from the practical point of view. Key features: * Refers to the behaviours of practical mechanical systems such as aircraft, railway vehicle, robot manipulator, micro/nano sensor * Enhances the rigorous and practical understanding of mathematical methods from an engineering point of view * The theoretical results obtained by nonlinear analysis are interpreted by using accompanying videos on the real nonlinear behaviors of nonlinear mechanical systems Linear and Nonlinear Instabilities in Mechanical Systems is an essential textbook for students on engineering courses, and can also be used for self-study or reference by engineers.
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Autorenporträt
HIROSHI YABUNO is Professor of Mechanical Engineering at University of Tsukuba in Japan. In 1990, he attained his Ph.D. in Engineering from Keio University, Japan and was appointed Professor at Keio University. He was a Visiting Scholar at the Virginia Polytechnic Institute and State University in 1997 and, in 2002 and 2008, he was a Visiting Professor at the University of Rome "La Sapienza". He was also Chair of Working Party II (Dynamical Systems and Mechatronics) of IUTAM. He is an associate editor of international journals including Journal of Computational and Nonlinear Dynamics (ASME), Nonlinear Dynamics, Journal of Vibration and Control, and International Journal of Dynamics in Various Mechanical Systems and Control. His research interests include analysis and control of nonlinear dynamics and positive utilization of the nonlinear instability phenomena to mechanical systems in particular, micro/nano resonators.
Inhaltsangabe
Preface 1
References 8
1 Equilibrium States and their Stability 11
1.1 Equilibrium states 11
1.1.1 Spring-mass system 12
1.1.2 Magnetically levitated system 16
1.1.3 Simple pendulum 20
1.2 Work and potential energy 23
1.3 Stability of the equilibrium state in conservative systems 27
1.4 Stability of mechanical systems 29
1.4.1 Stability of spring-mass system 29
1.4.2 Stability of magnetically levitated system 31
1.4.3 Pendulum 32
1.4.4 Stabilization control of magnetically levitated system 32
References 34
2 Linear Dynamical Systems 35
2.1 Vector field and phase space 35
2.2 Stability of equilibrium states 40
2.3 Linearization and local stability 41
2.4 Eigenvalues of linear operators and phase portraits in a single-degree-offreedom system 44
2.4.1 Description of the solution by matrix exponential function 44
2.4.2 Case with distinct eigenvalues 45
2.4.3 Case with repeated eigenvalues 49
2.4.4 Case with complex eigenvalues 54
2.5 Invariant subspaces 60
2.6 Change of stability due to the variation of system parameters 61
References 67
3 Dynamic Instability of Two-Degree-of-Freedom-Systems 69
3.1 Positional forces and velocity-dependent forces 69
3.2 Total energy and its time-variation 71
3.2.1 Kinetic energy 71
3.2.2 Potential energy due to conservative force FK 72
3.2.3 Effect of velocity dependent damping force FD 76
3.2.4 Effect of circulatory force FN 78
3.2.5 Effect of gyroscopic force FG 81
References 83
4 Modal Analysis of Systems Subject to Conservative and Circulatory Forces 85
4.1 Decomposition of the matrix M 86
4.2 Characteristic equation and modal vector 89
4.3 Modal analysis in case without circulatory force 90
4.4 Modal analysis in case with circulatory force 97
4.4.1 Case study 1: _i are real 100
4.4.2 Case study 2: _i are complex 103
4.5 Synchronous and nonsynchronous motions in a fluid-conveying pipe (video) 114
References 115
5 Static Instability and Practical Examples 117
5.1 Two-link model for a slender straight elastic rod subject to compressive forces 117
5.1.1 Static instability due to compressive forces 117
5.1.2 Effect of a spring attached in the longitudinal direction 122
5.2 Spring-mass-damper models in MEMS 125
5.2.1 Comb-type MEMS actuator devices 125
5.2.2 Cantilever-type MEMS switch 129
References 131
6 Dynamic Instability and Practical Examples 135
6.1 Self-excited oscillation of belt-driven mass-spring-damper system 135
6.2 Flutter of wing 139
6.2.1 Static destabilization in case when the mass center is located in front of the elastic center 145
6.2.2 Static and dynamic destabilization in case when the mass center is located behind the elastic center 146
6.3 Hunting motion in a railway vehicle 149
6.4 Dynamic instability in Jeffcott rotor due to internal damping 161
6.4.1 Fundamental rotor dynamics 161
6.4.2 Effects of the centrifugal force and the Coriolis force on static stability 166
6.4.3 Effect of external damping 170
6.4.4 Dynamics instability due to internal damping 174
6.5 Dynamic instability in fluid-conveying pipe due to follower force 178
References 180
7 Local Bifurcations 183
7.1 Nonlinear analysis of a two-link-model subjected
