Hyper-Damping Behavior of Stiff and Stable Oscillators with Embedded Statically Unstable Stiffness Elements

A novel concept of a nonlinear oscillator is proposed, based on a bistable element, which operates around an unstable equilibrium point. Contrary to the Quasi-Zero Stiffness oscillators, a totally different redistribution of the stiffness elements is followed, so that any level required static stiffness for the entire system can be maintained. This oscillator is designed to present the same overall (static) stiffness around the system equilibrium point, the same mass and to use the same damping element as a reference classical linear SDOF oscillator. Once such an oscillator is optimally designed, it is shown to exhibit an extraordinary apparent damping ratio, which is several orders of magnitude higher than that of the original SDOF system, especially in cases where the original damping of the SDOF system is extremely low. This damping behavior is not a result of a novel additional extraordinary energy dissipation mechanism, but a result of the phase difference between the positive and the negative stiffness elastic forces; this is in turn a consequence of the proper redistribution of the stiffness and the damping elements. This fact ensures that an adequate level of elastic forces exists throughout the entire frequency range, able to counteract the inertial and the external excitation forces. Consequently, a resonance phenomenon, which is inherent in the original linear SDOF system, cannot emerge in the proposed oscillator.