Interaction of a simple linear structure and a ball-type vibration absorber for harmonic and random loads

Abstract

Abstract Ball-type tuned mass absorbers are attractive for use in lightweight and slender designs because they combine multi-directional action with compact dimensions. However, their main disadvantage is the limited ability to adjust the damping level to a prescribed value, making them susceptible to undesirable effects arising from their non-linear nature. A 2D and 3D mathematical models of a ball-type absorber coupled to a simple linear elastic structure are presented, which show the effectiveness of such a damper for harmonic and random excitation. To prevent the occurrence of auto-parametric resonance conditions for safety reasons, the structure and damping equipment must be designed based on system parameters and the characteristics of possible excitation. The paper presents the dependence of the damped structure’s response on damper parameters for each type of resonant behaviour, the origin and nature of longitudinal and spatial response, and the influence of resonant conditions on the behaviour of the damped structure. The work is complemented by a simplified analysis of the response to random excitation, with examples of typical auto-parametric response patterns and possible applications in practical engineering.