Acoustic black hole plates for vibration and sound radiation mitigation

Abstract

This thesis proposes an efficient, flexible and versatile 2D semi-analytical model for the vibration and sound radiation analyses of Acoustic Black Hole (ABH) plates. The proposed model, along with the associated wavelet-based solution procedure, is intended to overcome major technical difficulties which are specific to ABH structures: the non-uniform wavelength distribution and ABH-induced wave compressions at the high frequency range in a realistic structure of finite size. Under the general Rayleigh-Ritz framework, Daubechies wavelet (DW) scaling functions are used for expressing the transverse displacement of the ABH plates. The accuracy of the propose model is thoroughly validated using Finite Element simulations and experiments. Results show that the model allows an accurate prediction of various vibration and sound radiation parameters and provides a truthful description of the typical ABH phenomena. Vibration analyses on the ABH plates show a drastic increase in structural damping, by using only a small amount of damping material. ABH local modes are shown to be dominant in the damping increase which leads to remarkably reduced vibration responses above the cut-on frequency. Meanwhile, ABH plates exhibit broadband sound power and sound radiation efficiency reduction, compared with uniform plates. Below the critical frequency, the reduced radiation efficiency is caused by the weakening of the structural stiffness due to the ABH indentation. Above the critical frequency, a subsonic region inside the ABH cell containing acoustically slow structural waves may appear. This region, confined within a transonic boundary, is due to the ABH-specific phase velocity reduction of the bending waves. Visualization of the supersonic acoustic intensity allows identifying the effective sound radiation regions of ABH plates and their relationship with the transonic boundaries at different frequencies. Sound radiation analyses show that damping layers also increase the sound radiation efficiency of ABH plates due to their additional stiffness. The conflicting effect of damping layers in the increase of both structural damping and sound radiation efficiency calls for a balanced and meticulous design of their deployment to draw the best possible vibration or acoustic benefit. To tackle the problem, by combining the proposed model with an optimizer, the sound radiation of an ABH plate into a free space is minimized through adjusting the damping layer layout. Finally, an alternative ABH profile that is different from the standard ABH profiles is proposed for structural damping enhancement. Results show that a plate with optimized ABH profile entails significantly increased structural damping compared with a standard ABH plate. Local (n, 1) and (n, 2) modes that have n half waves in the circumferential direction and 1 or 2 half waves in the radial direction of the indentation dominate the modal damping increase. The optimized plate exhibits larger energy density ratio between the ABH portion and the uniform portion, which entails better energy dissipation. Also, a reduction in the sound radiation is observed which is confirmed by reduced energy level of the supersonic vibration components in wavenumber domain.