Increased damping of irregular resonators.
It is shown that fractal drums and jagged geometry resonators may be more damped than ordinary Euclidean systems. Several damping mechanisms are examined and studied by numerical calculations. The results depend on the dissipation mechanisms but globally they increase with localization, frequency, and the irregularity of the resonator. The increased dissipation is due to the uneven spatial distribution of the vibrational amplitude in two different ways. First, it is related to the partial confinement of the vibrational modes. Secondly, increased dissipation may be due to singularities in the amplitude distribution. This is the case when a few points exist where the vibration is pinned to zero inducing local logarithmic singularities. This last effect can be spectacular: a single defect can dominate the surface damping by viscous forces of a square drum.
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Institut für Theoretische Physik III, Universität Giessen, D-35392 Giessen, Germany.
Sapoval
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