In the analysis of structural vibration it is generally assumed that the vibration is not affected by the surrounding media, so that the radiation field can be calculated directly from the vibration field. However, when there is mutual interaction between structures and acoustic fields their behavior must be solved simultaneously. This structural-acoustic coupling problem always arises in order to investigate noise going through structures and sound fields affected by flexible structures.
Numerous analytical and experimental investigations have been performed in this area. Dowell and Voss studied the effect of a cavity on panel vibration, and Lyon focused on the noise reduction in an enclosure with a flexible wall. Pretlove analyzed free and forced responses of a cavity-backed plate with in vacuo modes of the plate. All these studies were based on the assumption that there is interaction only between a cavity and a flexible structure. In the late 1960’s Morse considered transmission of sound through a circular membrane and in the late 1970’s Guy investigated sound transmission from an exterior field to an interior field through a panel. There have also been studies on structural-acoustic coupling in a system having more complex shapes. Fuller and Fahy investigated the interaction between cylindrical elastic shells filled with fluid. Nefske et al. used an FEM based model to discover the coupling mechanism in an irregular shaped system. Pan et al. even tried to reduce the noise transmitted through a panel into a cavity by using an active noise control technique.
However, the studies were restricted to interaction only between a structure and a finite cavity or a structure and acoustic fields of infinite size. The objective of this thesis is to investigate structural-acoustic coupling problem with more general configuration: a cavity with a partial opening. In the system a structure faces both a cavity of finite size and an external field of semi-infinite size. The important thing is that there is a hole which allows direct interaction between the cavity and the external field. For this purpose both theoretical and experimental approaches are used.
For theoretical analysis a cavity coupled with a membrane and an exterior field is used. The system is assumed to be two-dimensional and have rectangular geometry for its simplicity. Firstly, governing equations and mathematical expressions for boundary conditions are derived. To obtain solutions modal expansion approach was applied. As a result, matrix equations for modal coefficients are derived. During the derivation non-dimensional coupling coefficients and other parameters are obtained. For the purpose of verification and comparison, two other simple systems (a closed cavity and a partially opened cavity) are also studied. Simulation results show that the coupling effect gives a several additional pairs of peaks and troughs in frequency responses around the natural frequencies of the membrane only. The order of the peaks and troughs depends on whether they are higher or lower than the frequency of the Helmholtzs resonator mode ($f_H$). In the region lower than $f_H$ the peak frequencies are lower than trough frequencies and the orders of them are reversed in the range higher than $f_H$. Another fact we learn is that there are two kinds of couping mechanisims. At the peak frequencies, higer pressure is obtained above the hole and intensity plots show that the acoustic energy circulate around the membrane and hole. That result in low radiation efficiency. On the contrary, at trough frequencies, pressure above the membrane is higher and the most acoustic energy goes out through the membrane, which tells that sound radiates effectively. The big difference in radiation efficiency shows that the structural-acoustic coupling could be applied for noise control.
For better understanding the analysis of a simplified model is done. The model is obtained by simplifying the structure and exterior field to be 1DOF systems and by assuming low frequency range. The simulation results describe the physical meaning of the coupling mechanisms very well.
Experiments with a plate-cavity coupling system are performed to verify the coupling mechanism in such a system. An uncoupled system is also used for comparison. The uncoupled system is made by just covering plate with modeling clay, which prevents the plate vibration. Pressures inside and outside of the cavity are measured. Acoustic field variables (pressure, particle velocity, intensity) are estimated by using nearfiel acoustic holography. It is observed the same results that is acquired in the theoretical analysis. The presence of the vibrating structure gives additional pairs of peaks and troughs in frequency response and the two coupling mechanisms are observed.
