Friction-Maintained Dynamic Stability

Abstract

Mechanical systems relying on Coulomb friction to maintain dynamic stability may suffer a dynamic instability if exposed to an initial displacement exceeding a system-specific threshold. In fluid systems, even small values of negative damping are sufficient to drive the dynamic instability with sufficiently large initial displacement. The Tainter gate failures at the Folsom dam in 1995 and at the Wachi dam in 1967 are two well-known failures. To aid in preventing a recurrence, the authors engaged in a decade long research program that provided evidence that both gates failed due to an essential dynamic instability mechanism that all Tainter-gates may possess. This paper presents measurements suggesting “friction-maintained dynamic stability” of a full-scale 50-ton Tainter gate. Accompanying gate model studies showed that the gate can fail when exposed to an initial displacement exceeding a threshold value. The present study should serve to alert gate designers, owners and operators that many Tainter gates which have not yet failed may, nonetheless, have a high susceptibility to failure if and when they are exposed to a sudden input of energy resulting in an initial displacement exceeding the gate-specific threshold displacement.