Damping of flexural vibrations in circular plates with tapered central holes

The paper develops a numerical approach to the calculation of mobilities for a circular plate with a tapered central hole of power-law profile. The exact solution of the corresponding flexural wave equation that exists for m=2m=2 has been used in the process of the numerical solution of the corresponding boundary problem. Note that this value of m   belongs to the power-law range m≥2m≥2 associated with zero reflection of quasi-plane waves from a tapered hole in geometrical acoustics approximation. Two cases of added damping in the central hole area have been considered: a thin absorbing layer and a constrained layer. Cross and point mobilities have been calculated for both these cases. The obtained results for point and cross mobilities show a substantial suppression of resonant peaks (up to 17 dB), in comparison with the cases of a plate with an uncovered hole of the same power-law profile and of a reference circular plate of constant thickness covered or uncovered by a thin absorbing layer. Further theoretical and experimental research is needed to examine applications of the obtained numerical results to more practical situations, e.g. to rectangular plates or other structures with arbitrary locations of tapered holes.