Semi–active multimodal vibration absorber

This paper presents three types of semi-active vibration absorbers, which are designed to control the response and sound radiation of a thin plate at low audio frequencies. Semi-active control systems are used to tune the absorbers to the resonance frequencies of the first three flexural natural modes of the plate where they are mounted. The first configuration consists of three axial tune mass dampers, which are properly adjusted and distributed on the plate so that each of them controls one of the first three flexural modes of the plate. The second configuration consists of a single axial switching tune mass damper that can switch to different states characterised by discrete values of the suspension stiffness and mechanical damping. At each state the parameters are set to control one of the first three flexural modes of the plate. Finally the third configuration consists of a single three-axis tune mass damper whose mass oscillates axially and rotates around two cross axis. This device is also located and tuned to control the first three flexural modes of the plate. The simulation study shows that the three axial tune mass dampers reduce the flexural kinetic energy of the plate by about 17 dB around the first three resonance frequencies and about 8 dB around the fourth and fifth resonance frequencies. Thus large control effects are produced in the low frequency range between 30 and 150 Hz. The single axial switching tune mass damper produces about 14 dB reductions around the first three resonances and 3 dB and 7 dB around the fourth and fifth resonances respectively. Finally the single three-axis tune mass damper generates about 21 dB reductions around the first three resonance frequencies and about 9 dB reductions around the fourth resonance frequency. Thus the proposed single axial and single three-axis tune mass dampers produce comparatively similar results as the three axial tune mass dampers with the same total mass. In particular it is shown that the best location for the single three-axis tune mass damper should be chosen either in the centre or inner centre of the polygon defined by the border of the plate. The control performance of the single three-axis tune mass damper has also been compared with that produced by an active velocity feedback loop using an inertial electromagnetic actuator with equivalent proof mass. The simulation study shows that the activesystem outperforms the single three-axis tune mass damper only around the first resonance frequency, where it produces 7 dB larger reduction of the flexural kinetic energy. However this result is obtained with large feedback control gains and at the expenses of low frequency control spillover. When a smaller and more realistic control gain is implemented, the control effects become comparable to that of a single three-axis tune mass damper.