| The objective of this project is twofold. One is to understand the full coupling between sound and sound induced vibration, and the other is to see whether such interaction can be utilized for passive duct noise control. The theoretical model consists of a two-dimensional channel partly lined with flexible membranes under tension. The flexible segment responds to grazing incident sound and the induced vibration radiates sound to both upstream, i.e. towards the noise source, and downstream. The upstream radiation forms sound reflection, while the downstream radiation is superimposed with the incident wave to form the transmitted wave. Acoustic energy flux conservation ensures that the transmitted wave is reduced whenever there is sound reflection. One of the main technical objectives is to see how such reflection can be maximized in the low to medium frequency range, a range which is extremely difficult to tackle by means other than the currently expensive active control system. As such lined duct does not change its cross section, there will be no extra pressure drop. In addition, the membrane surface can be flat and air-tight, a feature which gives an important environmental advantage when compared with traditional porous media which trap dusts from the airflow in the duct. In order to prevent the break-out noise, i.e. the acoustic radiation of the membrane to the outside environment, a rigid walled cavity has to be added under the membrane. The system becomes a membrane-cavity system. The full coupling and behaviour of such a system forms the focus of the theoretical investigation.; Theoretically, the coupled dynamics of the membrane vibration is solved by the standard Galerkin approach in which the membrane vibration is expressed in terms of the in-vacuo modes of a simply supported string. This differs from the usual approach of using the cavity modes. The work also distinguishes itself from related studies in that the membrane to air mass ratio is of the order of unity, hence very strong coupling, and that the fluid loading induced on the surface of the membrane external to the cavity is fully taken into account. (Abstract shortened by UMI.)... |
