Optimization of acoustic blackhole structure for the reduction of plate vibration

Abstract

Reduction of unwanted vibration is important in the design of structure. A new method has been suggested to reduce the vibration of structure by reduction of the wave reflection from the edge of which using acoustic black hole. When the thickness of structure decreases gradually, a flexural wave propagating to the edge slows down and does not reach the end of structure. Then, the wave energy is concentrated near the edge without reflection and this is called acoustic black hole (ABH) effect. In practice, it is not easy to make structure which has zero thickness and the truncated edge gives a high value of reflection coefficient. By covering the tapered wedge with small amounts of damping material, this high reflection coefficient can be reduced dramatically. Then, the ABH structure becomes very efficient vibration dampers for flexural vibrations. However, not many research has been conducted to give a guide to design effective acoustic black hole plate in practice. Then, the goal of this study is to design an effective ABH plate structure to attenuate vibration energy in the interested frequency range. To achieve this goal, the parameters which affect the acoustic black hole effect was studied theoretically and numerically using finite element method, and also be attempted to optimize by surrogate model using limited number of numerical results. In this work, the effect of ABH has been evaluated not only using the magnitude of resonance peaks of direct point mobility but also using mean-sqaure spatial average velocity in the interested frequency bands. To maximize acoustic black hole effect, optimization was largely divided into two parts. First, optimization of a tapered wedge was conducted. It is noticed that two thing are important to design optimized wedge profile. One is a smoothness of wedge profile at the point where the wedge meets the homogeneous plate. It can be expressed using a normalized wavenumber variation. The other one is the length of constant minimum thickness. Then, it is concluded that the optimized wedge profile of ABH plate has the normalized wavenumber from 0.45 to 0.55 as far as it has constant length of minimum thickness larger than 1/10 of length of wedge. It is obtained that the ABH plate which consist of optimized wedge profile has smaller vibration energy than one which consist of initial wedge profile. Second, optimization of a damping layer on the optimized tapered wedge was conducted. It is noticed that to dissipate the vibration energy concentrated at the end of tapered wedge the mass of damping layer is important. Then, optimized damping layer is when the mass of damping layer is between 10 g to 20 g. When ABH plate which consist of optimized wedge profile and optimized damping layer is compared with the ABH plate which consist of initial wedge profile and optimized damping layer for the initial wedge, it is concluded that optimized ABH plate has large attenuation of vibration energy in comparison to the initial ABH plate and simple plate. Therefore, ABH plate becomes much more efficient vibration dampers for flexural vibrations as far as it satisfy these design conditions which are the value of normalized wave number variation, length of minimum thickness in wedge, and mass of damping layer.