Nonlinear dynamics of a negative stiffness oscillator: experimental identification and model updating

Systems exhibiting a negative stiffness region are often used as vibration isolators, due to their enhanced damping properties. The device tested in this paper is part of a damping system and it acts like an asymmetric double-well Duffing oscillator, with two stable and one unstable equilibrium positions. The range of motion can either be bounded around one stable position (in-well oscillations) or include all the three positions (cross-well oscillations). Depending on the input amplitude, the oscillator can exhibit linear and nonlinear dynamics, and chaotic motion as well. Due to its asymmetrical design, the two linearized systems associated to small-amplitude oscillations around one stable equilibrium position are different. In this work, the dynamical behavior of the system is first investigated in the case of linear and nonlinear in-well oscillations and then in the case of cross-well oscillations with chaotic motion. To accomplish this task, the device is mounted on a shaking table and it is driven through several excitation levels with both harmonic and random inputs. An experimental bifurcation tracking analysis is also carried out to understand the possible response scenarios. Afterwards, the nonlinear identification is performed using nonlinear subspace algorithms to extract the restoring force of the system. Eventually, the physically-based model of the device is updated to match the identified characteristics via genetic algorithms.