目次

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.