Broadband wave reflection by fluid-plate interaction

Abstract

Sound reflection is a very useful tool to control low to medium frequency noise in a duct. Recently, a device utilizing the full interaction between a tensioned membrane and sound is introduced to achieve broadband sound reflection. The membrane is backed by a rigid-walled cavity external to the duct to prevent breakout noise. The performance of this device, called drum-like silencer, has been thoroughly characterized and tested. Before the device can be applied in engineering use, two technical problems emerge: one is the difficulty to apply the required high tension on a thin membrane whose edges are slippery, and the other is that the tension may also vary with environmental temperature. To overcome these problems, it is proposed that the membrane is replaced by a light and yet stiff plate, which relies on its bending stiffness to restore structural equilibrium instead of the applied tensile force. The new prototype is called a plate silencer. The plate silencer is shown, theoretically, to have even better performance than the drum-like silencer. Literature survey shows that the use of a plate as a side-branch sound reflector is novel, and the present thesis reports the full numerical study using finite element and preliminary experimental study of the new device. To analyse the performance of the plate-type wave reflector, a coupled two-dimensional system, including an acoustic domain and a structural-mechanics domain, is introduced. Two different models, mindlin-plate model and the plane-stress model, are used to simulate the plate with various boundary conditions. A comparison between the results of different boundary conditions shows that a simply-supported boundary condition has a better performance than the clamped boundaries since the former allows more freedom for the plate to respond to incident sound. However, it is difficult to achieve a simply-supported boundary condition in practice. A non-uniform plate in which the thickness is reduced at the clamped ends is used to approximate the design of simply-supported uniform plate. The finite element simulation shows that, by changing the length of the two thinner ends, four peaks appear in the spectrum of the transmission loss, and they are well connected producing a wide stopband. Modal analysis has been conducted for both the simply-supported uniform plate and the clamped non-uniform plate. Typically, spectral peaks appear at the frequency where there is no interference between the even modes and the odd modes of the in-vacuo plate vibration. The energy flux of the sound reflected by the odd modes is simply added to that from the even modes. The above model is two dimensional for both the acoustics in air and the plate, which is in fact a beam. In reality, such model can only be implemented by a three dimensional plate with a very small gap between the plate and the lateral duct walls. Further numerical simulation is conducted for the leakage effect of the gap. The result shows that, if the gap size is smaller than about 0.5% of the duct width, the effect on the transmission loss is insignificant. The study also shows that the performance deteriorates drastically if a three dimensional plate is used with all edges fixed. Experimental studies for both two-dimensional and three-dimensional models are conducted to validate the theoretical results. The methods used for the transmission loss measurement and the material property quantification are described. In the experiment, a 3mm-thick uniform foam plate is used. This plate does not conform to the optimal parameters predicted by the theory, but the experimental results do validate the theoretical findings corresponding to the actual material properties. It is hoped that, when the optimal material and structural properties are found, the broadband transmission loss spectrum can be realized for the device.