Energy-based theory of autoresonance phenomena: Application to Duffing-like systems

Departamento de Electrónica e Ingeniería Electromecánica Escuela de Ingenierías Industriales, Universidad de Extremadura Apartado Postal 382, E-06071, Badajoz, Spain

Received: 21 April 2004
Accepted: 7 February 2005

Abstract

A general energy-based theory of autoresonance (self-sustained resonance) in low-dimensional nonautonomous systems is presented. The equations that together govern the autoresonance solutions and excitations are derived with the aid of a variational principle concerning the power functional. These equations provide a feedback autoresonance-controlling mechanism. The theory is applied to Duffing-like systems to obtain exact analytical expressions for autoresonance excitations and solutions which explain all the phenomenological and approximate results arising from a previous (adiabatic) approach to autoresonance phenomena in such systems. The theory is also applied to obtain new, general, and exact properties concerning autoresonance phenomena in a broad class of dissipative and Hamiltonian systems, including (as a particular case) Duffing-like systems.