Forced harmonic vibration in a system with negative linear stiffness and linear viscous damping

Various aspects of the dynamical behaviour of a twin-well Duffing oscillator are investigated by the combined use of analytical and numerical tools. Non-linear periodic oscillations are discussed first, and the classical non-linear resonance is studied in detail by the method of multiple scales. Then, transition to a complex response is investigated by using bifurcation diagrams, basins of attractions, and stable and unstable invariant manifolds, by summarizing the regions of different dynamical response in a comprehensive behaviour chart. Analytical prediction of the transition to chaos via the Melnikov method is then presented. Finally, non-classical issues such as control of homoclinic bifurcation and chaos, and dynamical integrity are discussed in detail with the aim of highlighting the most important ideas and objectives.