Nutation Damper Undergoing a Coupled Motion

Abstract

A novel numerical model is proposed to simulate liquid sloshing in a rectangular nutation damper (i.e. a tuned liquid damper) undergoing a coupled horizontal and rotational motion. Shallow water theory is used consistently to derive the governing equations of motion so that the model is applicable to large sloshing involving a hydraulic jump. It can also accommodate exposure of part of the damper’s floor to air by using a somewhat improved boundary shear approximation. A simple finite difference approach – the Lax scheme – is found to solve the equations of motion surprisingly well. Numerical predictions are checked against limited experimental data for a purely horizontal motion. Good agreement is generally observed. Furthermore, to demonstrate the model’s broader scope, the effect of a rotation is also considered in conjunction with a horizontal motion. The rotation is shown to significantly enhance the damper’s energy dissipation and, hence, its attenuation capability. For convenient practical application, an equivalent singledegree-of-freedom oscillator model is presented to characterize a nutation damper’s behavior for a coupled motion. The equivalent parameters of the model are determined so that the dissipated energy “best” fits a numerical counterpart. Their effect is investigated for different lengths, depths, and vibration levels of the damper. While the motivation of this investigation is to control the wind-induced galloping of overhead power lines, the proposed approach is applicable more generally to any excitation that induces low frequency vibrations.