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Table of Contents
Intro
Preface
Acknowledgments
Contents
Electromechanical Systems and Nonlinear Dynamics of RNIS
A Tutorial on the Simplification of Electromechanical Dynamic Models
1 Introduction
2 Electromechanical System
3 Reduced-Order Dynamic System
4 Dimensionless Formulation
5 Results and Discussion
6 Conclusion
References
Cardiorespiratory System as the System with Limited Power
1 Introduction
2 The Mathematical Model of Direct and Feedback Interactions
3 Numerical Simulations Results for the Heart Beats 75 beats/min
4 The Cardiorespiratory System Regimes for Different Heart Rates
5 Conclusions
References
Slow Oscillations in Systems with Inertial Vibration Exciters
1 Introduction
2 An Analysis of Studies on the Dynamics of Vibration Machines with Unbalanced Drive
3 Investigation of Vibration machine's Drive Oscillations During Passing Through the Resonance Zone
3.1 Formulation of the Problem and Equations of Motion of Vibration Machine
3.2 The Slow Motion Equations of Rotors of Electric Motor and Vibration Exciter in the Zone of the Sommerfeld Effect
3.3 Equations of Rapid Motions of the Rotors of Electric Motor and Vibration Exciter and Their Analysis
3.4 Equations of Fast Motions of a Vibration machine's Drive
3.5 Computer Simulation of Oscillations in Drives of Vibration Machines in the Resonance Zone
4 Results and Discussion
5 Conclusions
References
Bifurcations "Cycle-Chaos-Hyperchaos" in Some Nonideal Electroelastic Systems
1 Introduction
2 Mathematical Model of System "piezoceramic Transducer-LC-Generator"
3 Research Methodology and Numerical Results
References
Nonlinear Dynamics of Self and Parametrically Excited Systems with Non-ideal Energy Source
1 Introduction
2 Model of the Structure
3 Two Degrees of Freedom Model with Non-ideal Energy Source
3.1 Analytical Solutions
3.2 Stability Analysis
4 Numerical Analysis of Regular Oscillations
5 Chaotic Oscillations of Nonlinear Two Degrees of Freedom System with Non-ideal Energy Source
6 Conclusions
References
A Study of the Sommerfeld Effect in a Rotor Machine Foundation Model with 4 DOF
1 Introduction
2 Physical Model
3 Mathematical Model
4 Torque Relationships
5 Numerical Simulations
6 Discussion
7 Conclusions
References
Three Kinds of Sommerfeld Effect in Rotor Dynamics
1 Introduction
2 Types of Sommerfeld Effect
3 The Sommerfeld Effect of First Kind Due to Lateral Vibrations
3.1 Modal Analysis
3.2 Interfacing the Non-ideal Drive
3.3 Transient Analysis
4 Sommerfeld Effect of First Kind Due to Torsional Vibrations
4.1 Equations of Motion
4.2 Numerical Simulation Results
5 The Sommerfeld Effect of Second Kind
5.1 Flexible Asymmetric Rotor Shaft with Rigid Supports
5.2 Equations of Motion of the System
Preface
Acknowledgments
Contents
Electromechanical Systems and Nonlinear Dynamics of RNIS
A Tutorial on the Simplification of Electromechanical Dynamic Models
1 Introduction
2 Electromechanical System
3 Reduced-Order Dynamic System
4 Dimensionless Formulation
5 Results and Discussion
6 Conclusion
References
Cardiorespiratory System as the System with Limited Power
1 Introduction
2 The Mathematical Model of Direct and Feedback Interactions
3 Numerical Simulations Results for the Heart Beats 75 beats/min
4 The Cardiorespiratory System Regimes for Different Heart Rates
5 Conclusions
References
Slow Oscillations in Systems with Inertial Vibration Exciters
1 Introduction
2 An Analysis of Studies on the Dynamics of Vibration Machines with Unbalanced Drive
3 Investigation of Vibration machine's Drive Oscillations During Passing Through the Resonance Zone
3.1 Formulation of the Problem and Equations of Motion of Vibration Machine
3.2 The Slow Motion Equations of Rotors of Electric Motor and Vibration Exciter in the Zone of the Sommerfeld Effect
3.3 Equations of Rapid Motions of the Rotors of Electric Motor and Vibration Exciter and Their Analysis
3.4 Equations of Fast Motions of a Vibration machine's Drive
3.5 Computer Simulation of Oscillations in Drives of Vibration Machines in the Resonance Zone
4 Results and Discussion
5 Conclusions
References
Bifurcations "Cycle-Chaos-Hyperchaos" in Some Nonideal Electroelastic Systems
1 Introduction
2 Mathematical Model of System "piezoceramic Transducer-LC-Generator"
3 Research Methodology and Numerical Results
References
Nonlinear Dynamics of Self and Parametrically Excited Systems with Non-ideal Energy Source
1 Introduction
2 Model of the Structure
3 Two Degrees of Freedom Model with Non-ideal Energy Source
3.1 Analytical Solutions
3.2 Stability Analysis
4 Numerical Analysis of Regular Oscillations
5 Chaotic Oscillations of Nonlinear Two Degrees of Freedom System with Non-ideal Energy Source
6 Conclusions
References
A Study of the Sommerfeld Effect in a Rotor Machine Foundation Model with 4 DOF
1 Introduction
2 Physical Model
3 Mathematical Model
4 Torque Relationships
5 Numerical Simulations
6 Discussion
7 Conclusions
References
Three Kinds of Sommerfeld Effect in Rotor Dynamics
1 Introduction
2 Types of Sommerfeld Effect
3 The Sommerfeld Effect of First Kind Due to Lateral Vibrations
3.1 Modal Analysis
3.2 Interfacing the Non-ideal Drive
3.3 Transient Analysis
4 Sommerfeld Effect of First Kind Due to Torsional Vibrations
4.1 Equations of Motion
4.2 Numerical Simulation Results
5 The Sommerfeld Effect of Second Kind
5.1 Flexible Asymmetric Rotor Shaft with Rigid Supports
5.2 Equations of Motion of the System