THE EFFECT OF DAMPING ON THE STEADY STATE AND BASIN BIFURCATION PATTERNS OF A NONLINEAR MECHANICAL OSCILLATOR

Abstract

This paper examines the role of damping on both the steady state and basin behavior of a periodically driven damped oscillator with the ability to escape from a potential well. We examine the effect of damping on both the qualitative and quantitative resonance response of the system. Particular attention is paid to how the damping scales the main steady state bifurcations; saddle-nodes, period-doubling flips, cascades to chaos, boundary crises, etc. We also investigate how the damping level effects the main homoclinic and heteroclinic basin bifurcations that may result in a rapid erosion and stratification of the basin of attraction and hence a loss of engineering integrity of the system.