Dynamics of Machines with Variable Mass

Description

Designed to be a complete and integrated text on the dynamic properties of machines, mechanisms, and rotors with variable mass, this book presents new results from investigations based on the general dynamics of systems with variable parameters. The book considers both weak and strong nonlinear vibrations of these systems, and chaotic phenomena are also discussed. The conservation laws and adiabatic invariants for systems with variable mass are formulated and the stability and instability conditions of motion are defined. Cover Half Title Series Title Title Page Copyright Page Dedication Table of Contents Introduction to the Series Preface 1: Machines with Variable Mass 1.0 Introduction 1.1 Mechanisms with Variable Mass 1.2 Rotors with Variable Mass 1.3 Comments and References 2: General Principles of Dynamics of Systems with Variable Mass 2.0 Introduction 2.1 Dynamics of Particles with Variable Mass 2.2 Dynamics of a System of Particles with Variable Mass 2.3 Dynamics of Bodies with Variable Mass 2.4 Mathematical Models of Mechanisms and Rotors with Variable Parameters 2.5 Comments and References 3: Vibrations in Machines with Small Nonlinearities and with Parameters Which Vary with Time 3.0 Introduction 3.1 Free Vibrations of One-Degree-of-Freedom Mechanisms with Time Variable Parameters 3.2 Vibrations of Wagon-Measuring Mechanisms 3.3 Free Vibrations of Single Mass Systems with Two-Degrees-of-Freedom 3.4 Vibrations of Rotors with Variable Mass 3.5 Forced Vibrations of a Single Mass System with Two-Degrees-of-Freedom 3.6 Comments and References 4: Vibrations of Machines with Time Variable Parameters and Strong Nonlinearity 4.0 Introduction 4.1 Vibrations of One-Degree-of-Freedom Oscillators with Time Variable Parameters 4.2 Vibrations of a System with a Complex Deflection Function and Strong Quasi-Cubic Nonlinearity 4.3 Vibrations of a Centrifuge with Variable Mass 4.4 Cubic Nonlinear Systems with Slowly Varying Parameters and Complex Deflection Functions 4.5 Vibrations of a Rotor with a Winding Band 4.6 Comments and References 5: Chaos in Systems with Time Variable Parameters 5.0 Introduction 5.1 Melnikov’s Criteria for Chaos Applied to Systems with Time Variable Parameters 5.2 Chaos in One-Degree-of-Freedom Systems with Variable Mass 5.3 Dynamic Behaviour of a Lifting Crane Mechanism 5.4 Chaos in Rotors with Variable Mass 5.5 Comments and References 6: Conservation Laws and Adiabatic Invariants for Systems with Variable Mass 6.0 Introduction 6.1 Conservation Laws of Nonconservative Lagrange Systems 6.2 Conservation Laws of Systems with Variable Mass Under the Influence of a Central Force 6.3 Conservation Laws for Purely Nonconservative Systems 6.4 Conservation Laws for Vibrating Machines with Variable Mass 6.5 Conservation Laws for Sieve Vibrations 6.6 Adiabatic Invariants for Dynamic Systems with One-Degree-of-Freedom 6.7 Adiabatic Invariants of Quasi-Pure-Cubic Oscillators 6.8 Adiabatic Invariants of Dynamic Systems with Two-Degrees-of-Freedom 6.9 Adiabatic Invariants for Strongly Nonlinear Dynamic Systems Described by a Complex Function 6.10 Comments and References 7: Stability of Motion of Machines with Variable Mass 7.0 Introduction 7.1 The Lyapunov Function. General Criteria of Sylvester 7.2 The Lyapunov Direct Method 7.3 The Influence of the Impact Force on the Stability of Motion for Mechanisms with One-Degree-of-Freedom and Variable Mass 7.4 Stability of Rotation of a Rotor with Time-Dependent Parameters 7.5 Stability of Rotation of a Symmetrical Rotor with Variable Mass Supported on Bearings with Clearance 7.6 The Stability of a Clamped-Free Rotor with Variable Mass in the Case of Radial Rubbing 7.7 Comments and References References Index