Abstract
This paper describes as to fundamental theoretical study on the method of conversion of restoring force characteristics into an equivalent model. First, in a general nonlinear hysteretic force-deflection relation, the relation between vibrational characteristics (damping capacity and natural frequency) and geometric shape of the hysteresis curves are investigated. Next, the geometrical conditions for equivalent restoring force model in which have naturally vibrational characteristics for the hysteresis systems are considered. From these results, it is found that natural frequency of the hysteresis systems are determined by the total amount of ascending and decending branch of the hysteresis loops. This fact shows to equal the potential energy with hysteresis curves that natural frequencies are the same each other. The other side, damping capacity of the hysteresis systems is closely related to the energy dissipated in a single cycle, that is to say geometrically, to the area surrunded by the hysteresis curves. From the facts discribed above, we may determine the geometrical conditions for a equivalent restoring force model.
