Vibrations of a mass-spring system using a granular-material damper

摘要

The control of vibrations of a mass-spring system with a damper made of granular material is modeled, numerically simulated and experimentally verified. The damper consists of a hermetically closed flexible sleeve filled with granular material. Pumping air out of or into the sleeve increases or decreases the under-pressure, which increases or decreases the compression of the granules, causing the system to become more or less rigid. This, in turn, increases or decreases the energy dissipation, which provides the damping control mechanism of the system's vibrations. The spring is assumed to be nonlinear and once the coils are fully compressed it becomes essentially rigid. The changes to the damping characteristics of the damper caused by the rearrangement and compacting of the granules are described by a 'damage-like' variable- the granules rearrangement function. The model consists of a nonlinear ordinary differential equation for the mass-spring-damper system and a differential inclusion for the granules rearrangement function. A numerical algorithm for the problem is presented and simulations of the system behavior depicted. In particular, the changes in the oscillations of the system as the grain rearrangement progresses are shown. Then, the predictions of a version of the model are compared to experimental results that are presented briefly. The numerical results are fully supported by the experiments. It is concluded that a granular material damper may be an easy to implement and cost effective way to dampen vibrations of a mechanical system.