AN OSCILLATOR WITH CUBIC AND PIECEWISE-LINEAR SPRINGS

A system consisting of a mass attached to a nonlinear spring with negative linear stiffness and cubic nonlinearity, (i.e., a spring obeying Duffing's equation with negative linear stiffness) and a linear spring at a certain offset distance is studied. Melnikov's method is applied to determine the existence of homoclinic points for the Poincare map, and preserved resonant orbits and boundaries for these are given in the parameter space. This system is then compared to the system consisting of only the nonlinear spring with regard to the existence of parameter regimes where chaotic motion is possible. It is shown that if the linear spring is of appropriate stiffness the chaotic motion for a given set of parameter values occurring for the system consisting of only the nonlinear spring is replaced by periodic motion and the mechanism of this phenomenon is explained.