Exact analytical investigation of Duffing oscillator vibration spectra under time-periodic oscillatory external force

Abstract

This work introduces an analytical technique for determining solutions to a highly nonlinear Duffing-harmonic oscillator model problem. The parametric solutions of Duffing oscillator vibrations for an undamped case are achieved analytically in terms of Adomian polynomials by implementing the straightforward approach of the Laplace Transformation, known as the Laplace Decomposition Procedure (LDP). Possible plots of both numerical and analytical results sketched for various parameters are also presented to support our discussion. These graphs demonstrate variations of position-time, speed-time, and speed-position for an undamped Duffing oscillator case. When analyzed in general, they can provide vibration pattern descriptions for a variety of physical and engineering system configurations. We also examine their physical structures and behavioral characteristics within the conceptual framework of chaotic formalism.