Damping of flexural vibrations in circular plates with tapered central holes

Abstract

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 = 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 ≥ 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.

Acoustic black holes: recent developments in the theory and applications

“…Other important structures that have been investigated at Loughborough were rectangular plates with tapered indentations (pits) of power-law profile drilled inside the plates [27][28][29][30]. In black holes for flexural waves.…”

“…Theoretical and experimental investigations have been carried out for a specific case of circular indentations of power-law profile drilled in the centre of a circular plate [27,28]. The advantage of this geometrical configuration is that it facilitates theoretical calculations of the frequency response functions.…”

“…11. Steel (a) and composite (b) plates containing slots of power-law profile [27] Following the idea first proposed in [4], experimental investigations into damping of flexural vibrations in turbofan blades with trailing edges tapered according to a power-law profile have been carried out in the papers [32,33]. Obviously, wedges of power-law profile fit naturally with a fan blade geometry (see Fig.…”

Effect of geometrical and material imperfections on damping flexural vibrations in plates with attached wedges of power law profile

“…In the papers [13][14][15], the numerical modelling and experimental measurements of point mobilities in rectangular plates with attached power-law wedges and in circular plates with central tapered holes have been carried out. The results show that substantial damping of resonant peaks takes place in rectangular plates with attached wedges, whereas in circular plates with central tapered holes damping is not as large, which was expected since there was no focusing in this case.…”

Damped Vibrations of Rectangular Plate of Variable Thickness Resting on Elastic Foundation: A Spline Technique

“…In reality all the vibrations are damped vibration, as free vibrations are ideal and can't be practically possible, so no vibration can be thought of being in existence without damping. In a series of papers, recently DJO'Boy [3] have analyzed the damping of flexural vibration and Alisjahbana and Wangsadinata [4] discussed the realistic vibrational problem incorporating dynamic analysis of rigid roadway pavement under moving traffic loads. In the demand of modern science, a study dealing with damped vibrations of homogeneous isotropic rectangular plate of linearly varying thickness along one direction and resting on elastic foundation is presented employing classical plate theory.…”