SIMPLIFIED HAMILTONIAN-BASED FREQUENCY-AMPLITUDE FORMULATION FOR NONLINEAR VIBRATION SYSTEMS
Hongjin Ma
Abstract
The Hamiltonian-based frequency formulation has been hailed as an unprecedented success for it gives a straightforward insight into a complex nonlinear vibration system with simple calculation. This paper gives a systematical analysis of the formulation, and two simplified formulations are suggested. The cubic-quintic Duffing oscillator is used as an example to show extremely simple calculation and remarkable accuracy. It can be used as a paradigm for many other applications, and the one-step solving process has cleaned up the road of the nonlinear vibration theory.
Topics & Concepts
Duffing equationNonlinear systemVibrationHamiltonian (control theory)Quintic functionSimple (philosophy)Hamiltonian systemAmplitudeControl theory (sociology)Classical mechanicsMathematicsPhysicsComputer scienceMathematical analysisAcousticsMathematical optimizationQuantum mechanicsArtificial intelligenceEpistemologyPhilosophyControl (management)Vibration and Dynamic AnalysisMagnetic Bearings and Levitation DynamicsDynamics and Control of Mechanical Systems