Sound induced vibration and duct noise control

Abstract

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 invacuo 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. Detailed analysis shows the behaviour of the membrane under tension and the performance of the system in terms of reflecting low frequency duct noise. It is found that the first two in-vacuo modes of the membrane play a dominant role. The first mode is most effective in reflecting sound, but it is very difficult to excite due to the relative incompressibility of air inside the cavity. The second mode does not involve the change of cavity volume and is therefore easier to excite, but the radiation efficiency is low due to its dipole-like feature. The third and higher order modes are not very receptive to the incoming sound, and they are ineffective in reflecting sound. It is shown that a high tension applied on the membrane promotes the response of the membrane in lower order modes, and the system becomes effective in reflecting sound. The spectra of sound reflection and transmission loss show many peaks at frequencies where sound is almost completely reflected. The performance of the membrane at frequencies between two adjacent peaks can be maintained at a rather high level when appropriate membrane properties are chosen. For a typical example in which the duct height is hand the cavity has a dimension of depth h by length 5h, the system provides over 10dB transmission loss for a frequency band wider than an octave. All theoretical results are validated by experiments. The test rig consists of a versatile tensile gear to adjust the membrane tension, and an efficient Labview code which controls both noise generation and data acquisition via DA and AD cards. The fourmicrophone, two-load method is used for the transmission loss measurement. Detailed analysis is carried out to understand the sound energy loss in a system without any deliberate design of damping element. Typically, a 10% to 30% loss is encountered and part of these is attributed to the normal friction on the duct walls. The existence of an optimal tension is proved experimentally. For the typical configuration of h by 5h cavity, the optimal tension is found to be around 3/4 of the atmospheric pressure times the duct cross section. This is within but close to the elastic limit of normal metal foils. Practical problems such as possible molecular relaxation, acoustic fatigue and flow-induced membrane instability are discussed. The conclusion is that all predictions are validated despite some uncertainties occurring in the test rigs, and that the cavity backed membranes can indeed provide an alternative engineering solution for low frequency duct noise problems. The project goes further to see how the required cavity volume can be minimized by filling a low-impedance gas like helium. The result shows that the wave reflection capability of a shallow cavity is substantially enhanced. This feature may become very useful in engineering applications with very limited sideway space. Both theoretical prediction and experimental validation are conducted. Initial studies are also conducted on the use of different tensions on the membranes on the two sides of a two-dimensional channel, and four membranes installed on four sides of a realistic duct. Stopband with very high transmission loss is found for four membranes with equal tensions.