Resonant damping of flexible structures

Abstract eng:
Structural vibrations are often dominated by resonant response, and increased efficiency in the damping of these vibrations can often be attained by using the resonant properties of these modes. A typical example is the ’tuned mass absorber’. The principle of tuning a resonant mass has been known for nearly a hundred years, but has found increased use in recent years in connection with the development of slender flexible structures. The traditional design procedure for tuned mass absorbers is based on characteristics of the frequency response curves for a single-degree-of-freedom system equipped with a resonant mass with suitable damping. Recently, it has been demonstrated that this procedure can be reinterpreted in a more precise and general format as the special property of equal damping of the two modes generated by introduction of the resonant mass. In the present paper the basic principle of resonant absorbers is presented in concise form and generalized in two ways. First the principle of resonant absorbers is extended to more general implementations in terms of sensors and actuators, recording the motion and imposing appropriate forces, respectively. A general design procedure is developed for resonant displacement and acceleration feedback, respectively, based on a combination of ’equal modal damping’ and approximately equal response amplitudes of the two modes. This leads to explicit design formulae for the parameters of the damping system. The optimal calibration leads to a plateau of near-equal amplification in a frequency interval around the original natural frequency. In flexible structures the introduction of the damping device leads to a change of the original vibration modes of the structure. Generally speaking, the damping device should be controlled by the motion of the mode to be controlled. This means that the single-degree-of-freedom model should be modified to account for the fact that only part of the local motion should be included in controlling the behavior of the damper. A procedure is developed, in which an approximate representation of the effect of higher modes is subtracted from the direct response. Examples demonstrate that the explicit calibration procedure for resonant damping of flexible structures is very effective, introducing high, nearly-equal damping in a frequency interval around the original resonance frequency.

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