dynamic systems

harmonic balance

equations motion

time integration

van der pol

normal modes

lyapunov exponent

probability density

Facta Universitatis

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.

SIMPLIFIED HAMILTONIAN-BASED FREQUENCY-AMPLITUDE FORMULATION FOR NONLINEAR VIBRATION SYSTEMS