Formulation of a hysteretic restoring force model. Application to vibration isolation

This article focuses on the formulation of a hysteretic model used as an isolator restoring force model. The proposed model is based on operator governing input and output functions that depend on the deflection and the restoring force of the isolator. First, the mathematical formulation is demonstrated, then the hysteretic model proposed is applied to isolators having different types of behavior. The model parameters are sought using the experimental force-deflection loop of each of the isolators studied. Next, the transient response of a flexible structure mounted on an all-metal isolator is predicted by coupling the first order differential equation of the restoring force and the second order differential equations of the structure's motion. The experimental investigation validates the proposed hysteretic model applied to the all-metal mount.