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Table of Contents
Preface; Contents; 1 Introduction; References; 2 Linear Oscillator and a Non-ideal Energy Source; 2.1 Simple Degree of Freedom Oscillator Coupled with a Non-ideal #x83;; 2.1.1 Analytical Solving Procedure; 2.1.2 Steady-State Solution and Sommerfeld Effect; 2.1.3 Model Analogy and Numerical Simulation; 2.1.4 Stability Analysis; 2.2 Oscillator with Variable Mass Excited with Non-ideal Source; 2.2.1 Model of the System with Variable Mass; 2.2.2 Model of the System with Constant Mass; 2.2.3 Comparison of the Systems with Constant and Variable Mass.
2.3 Oscillator with Clearance Coupled with a Non-ideal Source2.3.1 Model of the System; 2.3.2 Transient Motion of the System; 2.3.3 Steady-State Motion of the System; 2.3.4 Chaotic Motion; 2.3.5 Chaos Control; 2.4 Conclusion; References; 3 Nonlinear Oscillator and a Non-ideal Energy Source; 3.1 Nonlinear Oscillator Coupled with a Non-ideal Motor #x83;; 3.1.1 Nonlinear Motor Torque Property; 3.1.2 Solution Procedure in General; 3.1.3 Steady-State Motion and Its Stability; 3.1.4 Characteristic Points on the Steady State Curves; 3.1.5 Suppression of the Sommerfeld Effect; 3.1.6 Conclusion.
3.2 Pure Nonlinear Oscillator and the Motor with Nonlinear Torque3.2.1 Approximate Solution Procedure; 3.2.2 Steady-State Motion and Its Properties; 3.2.3 Characteristic Points; 3.2.4 Suppression of the Sommerfeld Effect; 3.2.5 Numerical Examples; 3.3 Pure Strong Nonlinear Oscillator and a Non-ideal Energy Source; 3.3.1 Model of the System; 3.3.2 Analytical Solving Procedure; 3.3.3 Resonant Case and the Averaging Solution Procedure; 3.3.4 Suppression of the Sommerfeld Effect; 3.3.5 Numerical Examples of Non-ideal Driven Pure Nonlinear Oscillators; 3.3.6 Conclusion.
3.4 Stable Duffing Oscillator and a Non-ideal Energy Source3.4.1 Asymptotic Solving Method; 3.4.2 Stability of the Steady State Solution and Sommerfeld Effect; 3.4.3 Numerical Simulation and Chaotic Behavior; 3.4.4 Chaos Control; 3.4.5 Conclusion; 3.5 Bistable Duffing Oscillator Coupled with a Non-ideal Source; 3.5.1 Semi-trivial Solutions and Quenching of Amplitude; 3.5.2 Non-trivial Solutions and Their Stability; 3.5.3 Conclusion; References; 4 Two Degree-of-Freedom Oscillator Coupled to a Non-ideal Source ; 4.1 Model of the System; 4.2 Analytical Solution; 4.2.1 Steady-State Motion.
4.2.2 Stability Analysis4.3 Special Cases; 4.3.1 Resonance Frequencies in Orthogonal Directions Are Equal; 4.3.2 Resonance Frequency in One Direction Is Half of the Resonance frequency in Other Direction; 4.4 Numerical Simulation; 4.5 Conclusions; References; 5 Dynamics of Polymer Sheets Cutting Mechanism; 5.1 Structural Synthesis of the Cutting Mechanism; 5.1.1 Comparison of the Simple, Eccentric and Two Slider-Crank mechanisms; 5.2 Kinematics of the Cutting Mechanism; 5.3 Dynamic Analysis of the Mechanism with Rigid Support; 5.3.1 Mathematical Model of the Mechanism.
2.3 Oscillator with Clearance Coupled with a Non-ideal Source2.3.1 Model of the System; 2.3.2 Transient Motion of the System; 2.3.3 Steady-State Motion of the System; 2.3.4 Chaotic Motion; 2.3.5 Chaos Control; 2.4 Conclusion; References; 3 Nonlinear Oscillator and a Non-ideal Energy Source; 3.1 Nonlinear Oscillator Coupled with a Non-ideal Motor #x83;; 3.1.1 Nonlinear Motor Torque Property; 3.1.2 Solution Procedure in General; 3.1.3 Steady-State Motion and Its Stability; 3.1.4 Characteristic Points on the Steady State Curves; 3.1.5 Suppression of the Sommerfeld Effect; 3.1.6 Conclusion.
3.2 Pure Nonlinear Oscillator and the Motor with Nonlinear Torque3.2.1 Approximate Solution Procedure; 3.2.2 Steady-State Motion and Its Properties; 3.2.3 Characteristic Points; 3.2.4 Suppression of the Sommerfeld Effect; 3.2.5 Numerical Examples; 3.3 Pure Strong Nonlinear Oscillator and a Non-ideal Energy Source; 3.3.1 Model of the System; 3.3.2 Analytical Solving Procedure; 3.3.3 Resonant Case and the Averaging Solution Procedure; 3.3.4 Suppression of the Sommerfeld Effect; 3.3.5 Numerical Examples of Non-ideal Driven Pure Nonlinear Oscillators; 3.3.6 Conclusion.
3.4 Stable Duffing Oscillator and a Non-ideal Energy Source3.4.1 Asymptotic Solving Method; 3.4.2 Stability of the Steady State Solution and Sommerfeld Effect; 3.4.3 Numerical Simulation and Chaotic Behavior; 3.4.4 Chaos Control; 3.4.5 Conclusion; 3.5 Bistable Duffing Oscillator Coupled with a Non-ideal Source; 3.5.1 Semi-trivial Solutions and Quenching of Amplitude; 3.5.2 Non-trivial Solutions and Their Stability; 3.5.3 Conclusion; References; 4 Two Degree-of-Freedom Oscillator Coupled to a Non-ideal Source ; 4.1 Model of the System; 4.2 Analytical Solution; 4.2.1 Steady-State Motion.
4.2.2 Stability Analysis4.3 Special Cases; 4.3.1 Resonance Frequencies in Orthogonal Directions Are Equal; 4.3.2 Resonance Frequency in One Direction Is Half of the Resonance frequency in Other Direction; 4.4 Numerical Simulation; 4.5 Conclusions; References; 5 Dynamics of Polymer Sheets Cutting Mechanism; 5.1 Structural Synthesis of the Cutting Mechanism; 5.1.1 Comparison of the Simple, Eccentric and Two Slider-Crank mechanisms; 5.2 Kinematics of the Cutting Mechanism; 5.3 Dynamic Analysis of the Mechanism with Rigid Support; 5.3.1 Mathematical Model of the Mechanism.