Extreme stiffness systems due to negative stiffness elements

Yun-Che Wang, R. S. Lakes

Research output: Contribution to journalArticle

68 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)40-50
Number of pages11
JournalAmerican Journal of Physics
Volume72
Issue number1
DOIs
Publication statusPublished - 2004 Jan

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stiffness
composite materials
metastable state
infinity
frequency response
phase transformations
physical properties
diamonds
tubes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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Extreme stiffness systems due to negative stiffness elements. / Wang, Yun-Che; Lakes, R. S.

In: American Journal of Physics, Vol. 72, No. 1, 01.2004, p. 40-50.

Research output: Contribution to journalArticle

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