Damping of flexural vibrations in thin plates using one and two dimensional acoustic black hole effect

The reduction of flexural vibration in thin plates is examined using the acoustic black hole effect associated with nearly zero reflection of quasi-plane waves from a lightly damped wedge or tapered hole where the profile varies according to a power-law. The flexural wave propagation can be determined through the application of geometrical acoustics approximation or exact analytical solutions. For a plate of thickness of power-law profile, the wave slows down and grows in amplitude. In the ideal case of no truncation of the quadratic (or higher) profile, the phase speed asymptotically decreases to zero and the wave never reaches the end. Manufactured plates always have a truncation, leading to relatively high reflection coefficients, however, the application of small damping layers leads to substantial decreases in the reflection coefficients and thus large reductions in mobility amplitudes. This paper contains the results of numerical models and experimental measurements of point mobility for structural plates incorporating tapered holes for validation. A rectangular plate with a 1D wedge on one end is examined, in addition to a circular plate with a quadratic profile in the centre. In both cases, the measurements show significant reductions in resonant peaks of mobility, in good agreement to numerical predictions.