Numerical simulation for designing tuned liquid dampers to damp out double-pendulum oscillations

Abstract

This paper presents a simplified dynamic analytical model based on the Lagrangian formalism to describe the annular sloshing damper behavior used to damp out free oscillations of a double-pendulum system. A simulation program using this model has been developed with the mathematical software MATLAB®. This simulation method is applied to design dampers for the mass and coil suspensions of the French watt balance experiment. The motion of each suspension is equivalent to a double-pendulum motion having two main natural frequencies for each configuration considered. The shape of the damper used is a ring composed of one or two concentric annular channels partially filled with a liquid (water for instance). The depth of the liquid must be adjusted in each channel in order to tune the resonance frequency of the liquid to a natural frequency of the suspension. Two corrective parameters determined experimentally have been added to our model in order to yield results in fair agreement with experiment. The numerical simulation based on our analytical model has provided useful information for designing annular sloshing dampers as efficient as possible for the experiment concerned. Furthermore, this method can be used to study any pendulous load system behavior and to design appropriate sloshing dampers.