Forced Harmonic Vibration of an Asymmetric Duffing Oscillator

Abstract

Two nonlinear asymmetric systems are described in this chapter. The first is a pure cubic nonlinear oscillator with a constant and a harmonic force acting on it, associated with a vibration isolator. The second is a hanging cable which the asymmetry is caused by gravity. Both of these systems have a single-well potential. The equations of motion can be written in such a way that they include a quadratic and cubic nonlinearity, and only a harmonic forcing term. Different analytical and numerical approaches are used to study and illustrate the rich dynamics of the systems. © 2011 John Wiley & Sons, Ltd. All rights reserved.