Negative Stiffness Elements Research Articles

Stable extremely-high-damping discrete viscoelastic systems due to negative stiffness elements

Systems with negative stiffness constituents can have extreme material properties greatly exceeding those of either constituent. We show that a discrete system with a viscoelastic damping element and a negative stiffness element can be made with overall viscoelastic damping orders of magnitude higher than that of any constituent, or of the system with all elements of positive stiffness. The product of stiffness and damping, important for vibration damping, is also enhanced by orders of magnitude. We show this system is unconditionally stable in the high damping regime. The singularity in damping can be made arbitrarily close to the stability boundary.

Extreme stiffness systems due to negative stiffness elements

When an elastic object is pressed, we expect it to resist by exerting a restoring force. A reversal of this force corresponds to negative stiffness. If we combine elements with positive and negative stiffness in a composite, it is possible to achieve stiffness greater than (or less than) that of any of the constituents. This behavior violates established bounds that tacitly assume that each phase has positive stiffness. Extreme composite behavior has been experimentally demonstrated in a lumped system using a buckled tube to achieve negative stiffness and in a composite material in the vicinity of a phase transformation of one of the constituents. In the context of a composite system, extreme refers to a physical property greater than either constituent. We consider a simple spring model with pre-load to achieve negative stiffness. When suitably tuned to balance positive and negative stiffness, the system shows a critical equilibrium point giving rise to extreme overall stiffness. A stability analysis of a viscous damped system containing negative stiffness springs reveals that the system is stable when tuned for high compliance, but metastable when tuned for high stiffness. The metastability of the extreme system is analogous to that of diamond. The frequency response of the viscous damped system shows that the overall stiffness increases with frequency and goes to infinity when one constituent has a suitable negative stiffness.