Development of a broadband silencer in flow duct

Abstract

A broadband passive silencer, which works effectively in the low frequency range in a flow duct, is developed in the present work. When a segment of a rigid duct is replaced by a plate backed by a hard-walled cavity, grazing incident sound waves induce plate bending motion, hence sound reflection. The principle of acoustic energy conservation guarantees that, whatever amount of sound reflection is, the same amount of reduction is induced in the sound energy flux transmitted to the downstream of the device. As the sound reflection is solely caused by the vibration of the plate, such a device is called plate silencer. The present study focuses on the theoretical modelling, the performance optimization, as well as the experimental realization of the proposed plate silencer. A two-dimensional analytical model is first established for a typical plate silencer which consists of an expansion chamber with two side-branch cavities covered by light but stiff plates. The leading and trailing edges of the plate can be either simply supported or clamped, while the other two lateral edges are set free. The plate response to a grazing incident wave is formulated by solving the fully coupled dynamic equations of motion of the plate and acoustic radiation. Mean flow effect is taken into account in the analytical modelling. The theoretical model is tested experimentally using balsawood. The spectral peaks and shapes of the measured transmission loss curve are in agreement with those calculated theoretically. Attempts are made to account for the considerable sound absorption in the test rig. Silencing performance of the plate silencers is studied and optimized based on the validated theoretical model. It is found that the clamped boundary condition is easier to implement in practice than the simply supported one, but the stopband of the clamped plate silencer shrinks and the lower band limit is pushed to higher frequency. Theoretical study suggests that the performance of the clamped plate silencer can be enhanced by adopting nonuniform plates with softer ends. Analyses show that the performance improvement is attributed to the increased acoustic radiation efficiency over the bulk length of the nonumiform plate, which behaves like a rigid plate. The acoustic benefit of using three-dimensional configurations in a plate silencer is also investigated with a verified finite element model. Simulation shows that the three-dimensional design expands the bandwidth in both lower and higher frequency regions. Hybrid arrangement, which combines plate silencer and traditional dissipative chambers in parallel, is also studied to achieve a silencer effective from low to high frequency range. Theoretical studies show that a good plate silencer requires light but extremely stiff plates, which are out of the reach of existing homogeneous materials. Hence, the feasibility of using sandwich construction is explored. A broadband low frequency plate silencer is realized using sandwich plate and experimentally tested. The prototype plate silencer demonstrates much better silencing performance than the expansion chamber of the same geometry (duct cross section: 100 mm XI00 mm; expansion ratio: 3), with a stopband from 133 Hz to 274 Hz in which the transmission loss is higher than 10 dB over the whole frequency band. The possibility of modelling the sandwich plate silencer using a simplified mathematical model is also investigated. As far as low frequency is concerned, the experimental results are in fair agreement with the predictions. Sandwich plates with different mechanical properties are also tested and compared, which partially confirms the theoretical findings on the effect of plate properties on the silencer performance.