Mechanics and FEM simulation of active vibration control in structural systems by using internal mass reconfiguration

Relative motion of different parts of a structure can affect its vibrations that may be amplified or attenuated. If such a motion is properly devised, it can lead to continuous attenuation of vibration and thus be used for eliminating vibration of the structure, as has been shown in previous works on an oscillating physical pendulum. In this thesis, the moving mass/structure interaction is investigated in order to devise a numerical tool for modeling such problems for arbitrary structures. The mass (or masses) motion patterns are synchronized such that a continuous attenuation of vibration is achieved. This is a novel technique for active vibration control especially for structures where the conventional stationary actuators are not practical. To analyze the dynamic response of such moving mass-structure systems, a ‘composite’ beam element is introduced that permits extending the conventional finite element formulation (and software) and explicitly identifying the Coriolis and centripetal inertia effects of the moving mass. A numerical procedure is then proposed in which these inertia effects are included in the finite element model as fictitious transversal and axial forces applied to the beam element currently being traversed by the moving mass. The proposed approach is verified by comparing the results with those available in the literature as well as exact solutions possible for the pendulum. Numerical simulations show that the periodic relative motion of the mass with a constant frequency normally tends to amplify vibration. In order to obtain a continuous attenuation, a proper synchronization method is required. It is demonstrated that such synchronization can be determined to be effective for vibration control of different structures. In particular, for structures which can be treated as uni-modal, like the pendulum, the method is quite effective with a relatively high vibration attenuation rate. For multi-modal structures, represented by beams and frames in this thesis, the vibration attenuation is less smooth and more complicated mass motion patterns and synchronization methods are needed. It is concluded that the effectiveness of such active vibration control depends on how distinct the vibration modes to be attenuated are in the frequency spectrum