Author | Esmailzadeh, Ebrahim. author. Author. http://id.loc.gov/vocabulary/relators/aut |
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Title | Analytical Methods in Nonlinear Oscillations [electronic resource] : Approaches and Applications / by Ebrahim Esmailzadeh, Davood Younesian, Hassan Askari |
Imprint | Dordrecht : Springer Netherlands : Imprint: Springer, 2019 |
Edition | 1st ed. 2019 |
Connect to | https://doi.org/10.1007/978-94-024-1542-1 |
Descript | XV, 286 p. 56 illus., 41 illus. in color. online resource |
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