Volume I: Fundamental Concepts and Methods; Applications to Single Degree-Of-Freedom Systems Volume II: Advanced Concepts and Applications to Multi-Degree-Of-Freedom Systems
Volume I: Fundamental Concepts and Methods; Applications to Single Degree-Of-Freedom Systems Volume II: Advanced Concepts and Applications to Multi-Degree-Of-Freedom Systems
The first volume addresses the fundamental concepts used in the treatment of single-degree-of-freedom systems. Subjects covered include the mathematical model of the system, stability of motion, and the principal approximate analytical methods used to describe both harmonic and non-harmonic oscillat
The first volume addresses the fundamental concepts used in the treatment of single-degree-of-freedom systems. Subjects covered include the mathematical model of the system, stability of motion, and the principal approximate analytical methods used to describe both harmonic and non-harmonic oscillat
1/Normal Oscillations in Autonomous Conservative Systems.- 2/Normal Oscillations of Elastic Nonlinear Continuous Systems.- 3/Free Oscillations with Arbitrary Initial Conditions.- 4/Harmonic Solution in Nonautonomous Systems and Its Local Stability.- 4.1. The Ritz method and variational coupled Hill's equations.- 4.2. The first order unstable regions by the perturbation procedure based on the Floquet theory.- 4.3. The first order unstable regions by the asymptotic and averaging method.- 4.4. First order unstable regions of harmonic solution in a two- degree-of-freedom system - theoretical and computer simulation analysis.- 4.5. Harmonic plus constant term solution - systems with quadratic nonlinearity.- 5/Principal Resonances.- 6/Principal Resonances - Examples of Theoretical and Computer Simulation Analysis.- 6.1. Two-degree-of-freedom systems - problem of coupling of normal coordinates.- 6.2. Three-degree-of-freedom systems - the single nonlinear mode method.- 6.3. Homogeneous system with two-degrees-of-freedom.- 7/Secondary Resonances (Periodic and Almost-Periodic).- 8/Internal Resonances.- 9/Parametric Resonances.- References.
1/Normal Oscillations in Autonomous Conservative Systems.- 2/Normal Oscillations of Elastic Nonlinear Continuous Systems.- 3/Free Oscillations with Arbitrary Initial Conditions.- 4/Harmonic Solution in Nonautonomous Systems and Its Local Stability.- 4.1. The Ritz method and variational coupled Hill's equations.- 4.2. The first order unstable regions by the perturbation procedure based on the Floquet theory.- 4.3. The first order unstable regions by the asymptotic and averaging method.- 4.4. First order unstable regions of harmonic solution in a two- degree-of-freedom system - theoretical and computer simulation analysis.- 4.5. Harmonic plus constant term solution - systems with quadratic nonlinearity.- 5/Principal Resonances.- 6/Principal Resonances - Examples of Theoretical and Computer Simulation Analysis.- 6.1. Two-degree-of-freedom systems - problem of coupling of normal coordinates.- 6.2. Three-degree-of-freedom systems - the single nonlinear mode method.- 6.3. Homogeneous system with two-degrees-of-freedom.- 7/Secondary Resonances (Periodic and Almost-Periodic).- 8/Internal Resonances.- 9/Parametric Resonances.- References.
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