Transition to chaos and escape phenomenon in two degrees of freedom oscillator with a kinematic excitation

TL;DR

This paper investigates how a two-degree-of-freedom nonlinear oscillator, modeled as a quartercar, transitions to chaos or escape under harmonic excitation, using Melnikov analysis and numerical simulations.

Contribution

It derives the Melnikov criterion for chaos and escape in a nonlinear quartercar model with harmonic excitation, confirmed by numerical and recurrence analysis.

Findings

Melnikov criterion predicts transition to chaos and escape.

Numerical simulations confirm analytical estimations.

Recurrence analysis provides insight into transient vibrations.

Abstract

We study the dynamics of a two-degrees-of-freedom (two DOF) nonlinear oscillator representing a quartercar model excited by a road roughness profile. Modelling the road profile by means of a harmonic function we derive the Melnikov criterion for a system transition to chaos or escape. The analytically obtained estimations are confirmed by numerical simulations. To analyze the transient vibrations we used recurrences.