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A multi-harmonic generalized energy balance method for studying autonomous oscillations of nonlinear conservative systems
, Praveen Krishna I R, Narayanaa B Nidhish
Published in Academic Press
2018
Volume: 422
   
Pages: 526 - 541
Abstract
The Harmonic Balance Method (HBM) is a frequency-domain based approximation approach used for obtaining the steady state periodic behavior of forced dynamical systems. Intrinsically these systems are non-autonomous and the method offers many computational advantages over time-domain methods when the fundamental period of oscillation is known (generally fixed as the forcing period itself or a corresponding sub-harmonic if such behavior is expected). In the current study, a modified approach, based on He's Energy Balance Method (EBM), is applied to obtain the periodic solutions of conservative systems. It is shown that by this approach, periodic solutions of conservative systems on iso-energy manifolds in the phase space can be obtained very efficiently. The energy level provides the additional constraint on the HBM formulation, which enables the determination of the period of the solutions. The method is applied to the linear harmonic oscillator, a couple of nonlinear oscillators, the elastic pendulum and the Henon-Heiles system. The approach is used to trace the bifurcations of the periodic solutions of the last two, being 2 degree-of-freedom systems demonstrating very rich dynamical behavior. In the process, the advantages offered by the current formulation of the energy balance is brought out. A harmonic perturbation approach is used to evaluate the stability of the solutions for the bifurcation diagram. © 2018 Elsevier Ltd
About the journal
JournalJournal of Sound and Vibration
PublisherAcademic Press
ISSN0022460X
Open AccessNo
Concepts (20)
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    Bifurcation (mathematics)
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    Degrees of freedom (mechanics)
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    Dynamical systems
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    Dynamics
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    Energy balance
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    Frequency domain analysis
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    Galerkin methods
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    Harmonic analysis
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    Oscillators (electronic)
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    Oscillators (mechanical)
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    Pendulums
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    Computational advantages
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    ELASTIC PENDULUM
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    ENERGY BALANCE METHOD (EBM)
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    HARMONIC BALANCE
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    Harmonic balance method
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    HENON-HEILES SYSTEMS
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    LINEAR HARMONIC OSCILLATOR
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    STEADY STATE PERIODIC BEHAVIORS
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    Time domain analysis