Analytical Methods in Nonlinear Oscillations Approaches and Applications /
This book covers both classical and modern analytical methods in nonlinear systems. A wide range of applications from fundamental research to engineering problems are addressed. The book contains seven chapters, each with miscellaneous problems and their detailed solutions. More than 100 practice pr...
| Κύριοι συγγραφείς: | , , |
|---|---|
| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Dordrecht :
Springer Netherlands : Imprint: Springer,
2019.
|
| Έκδοση: | 1st ed. 2019. |
| Σειρά: | Solid Mechanics and Its Applications,
252 |
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- Chapter I: Introduction
- Why Nonlinear Oscillations?
- Brief Review of Nonlinear Oscillations History
- Overview of the Book
- Nonlinear Dynamical Systems
- Conservative Oscillatory Systems
- Non-Conservative Oscillatory Systems
- Parametrically Excited Vibration
- Resonance in Nonlinear Systems
- Chapter II: Classical Methods
- Nonlinear Differential Equations
- Perturbation Methods
- Parametric Excitation and Hill's Equation
- Practice Problems
- Chapter III: Energy Balance Methods
- Part I Approach
- Fundamentals of the Energy Balance Method
- Modified Energy Balance Method: Galerkin Approach
- Modified Energy Balance Method: Least Square Method
- Hamiltonian Approach
- Modified Hamiltonian Approach
- Rational Energy Balance Method
- Part II Applications
- Generalized Duffing Equation
- Nonlinear Dynamic Buckling of an Elastic Column
- Vibrations of Cracked Rectangular Plate
- Relativistic Oscillator
- Plasma Physics Equation
- Nonlinear Oscillator with Discontinuity
- Nonlinear Oscillator with Fractional-Power Restoring Force
- Generalized Conservative Oscillatory Systems (Type 1)
- Generalized Conservative Oscillatory Systems (Type 2)
- Duffing Harmonic Oscillator
- Helmholtz Duffing Oscillator
- Autonomous Conservative Oscillatory System
- Nonlinear Oscillation of Rigid Bar on Semi-Circular Surface
- Nonlinear Oscillations of Centrifugal Governor Systems
- Nonlinear Lateral Sloshing in Partially-Filled Elliptical Tankers
- Nonlinear Oscillations of Elevator Cable in in a Drum Drive Elevator
- Chapter IV: Residual Methods
- Part I Approach
- Basic Idea
- Frequency Amplitude Formulation
- Max-Min Approach
- Part II Applications
- Generalized Duffing Equation
- Generalized Conservative Oscillatory Systems (Type 1)
- Generalized Conservative Oscillatory Systems (Type 2)
- Nonlinear Oscillator with Fractional Power
- Nonlinear Oscillation of a Mass Attached to a Stretched Elastic Wire
- Nonlinear Schrödinger Equation
- A Rigid Frame Rotates at a Fixed Rate
- Conservative Lienard Type Equation
- Part III Practice Problems
- Chapter V: Semi-Inverse and Variational Methods
- Semi-Inverse and Variational Approaches
- Part I Approach
- Variational Principle.-Semi-Inverse Method
- Variational Approach.-Hamiltonian Approach
- Relationship between Hamiltonian and Variational Approaches
- Part II Applications
- Generalized Duffing Equation
- Elastic Force with Rational Characteristic Equation
- Elastic Force with Non-integer Fractional Characteristic Equation
- Higher-Order Hamiltonian Approach to Duffing Equations
- Hamiltonian Approach to Rational and Irrational Oscillator
- Hamiltonian Approach to Nonlinear Oscillator with Discontinuity
- Nonlinear Oscillator with Quintic Nonlinearity
- Nonlinear Schrodinger's Equation
- Thomas-Fermi Equation
- Heat Conduction Equation
- Lane-Edmen Type Equation
- Dynamic Analysis of Centrifugal Governor System
- Duffing Harmonic Equation
- Part III Practice Problems
- Chapter VI: Ingegral Based Methods
- Part I Approaches
- Adomian Decomposition Method
- Variational Iteration Method
- Homotopy Analysis Method
- Part II Applications
- Volterra-Integro Differential Equations
- Nonlinear Schrödinger Equations
- Van der Pol Equation
- Korteweg-de Vries Equation
- Part III Practice Problems
- Chapter VII:Nonlinearities in Nano and Micro Systems
- Duffing Equation in NEMS and MEMS
- Parametric and Self-Excited Oscillations
- Nonlinear Coupled Oscillators
- Other Types of Nonlinearities
- Part III Practice Problems.
