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The use of plates in aerospace structures is widespread. In recent years with the practical application of active sound and vibration control, several studies have been devoted to plate response subject to different kinds of excitation and with various boundary conditions. The vibration of a plate’s surface and its interaction with the fluid medium results in the radiation of sound and a coupled vibro-acoustic problem. The solution for simply-supported plates is easy to obtain. It is much more difficult to obtain solutions for other boundary conditions. As computer resources become less expensive and more readily available, it is becoming increasingly practical to use computational methods to predict the propagation and radiation of sound and the behaviour of complex structural systems. An excellent review of the numerical techniques used to predict low frequency sound radiation has been presented by Atalla and Bernhard. Usually, for low frequencies, the sound power is calculated using the data obtained from a finite mesh on the structural surface for which the vibration velocities have been computed. Subsequently, the sound power is computed using the boundary element method. In general the mesh needed to compute the sound radiation need not be as fine as the mesh needed to calculate the structural vibration. Therefore, sometimes acoustical analysis can be very inefficient. Fahnline has reported that the efficiency of acoustical analysis for subsonic structural waves is increased significantly by expanding the structural finite element mesh into a much coarser acoustical element mesh. The sound power radiated by a plate can be calculated if its surface response is known. However, this makes it necessary to determine the acoustic field by using the Rayleigh integral (for the sound pressure distribution) and then to perform an integration over a closed control surface. Classical methods to find the surface response of a plate with complex boundary conditions include the superposition and Ritz methods using trial polynomials and trigonometric functions. These methods require the solution of simultaneous equations or high-order matrices, making the calculations of sound power radiated by vibrating structures even more difficult. An approach using the virtual work principle provides an easier methodology for calculating the surface response of a plate. A very good review concerning structural acoustics and the vibration behaviour of rectangular panels can be found in the work by Berry and Nicolas. Green functions can be theoretically derived for certain regular geometries. But for a complex and irregular geometric shape, or for a sound-radiating body not located in a free field, the function takes very complicated forms which are not easily determined mathematically. Since a homogeneous fluid at rest behaves like a linear elastic medium in response to small applied disturbances, the vibro-acoustic reciprocity principle can be used to avoid the Green function calculation.

Sound Radiation Efficiency of a Baffled Rectangular Plate Excited by Harmonic Point Forces Using its Surface Resistance Matrix