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The Neumann axisymmetric boundary value problem is considered for a vibrating thin clamped circular plate embedded in the flat rigid screen in the outlet of the circular cylindrical cavity. It is assumed that the two pistons, one cylindrical and the other one annular/circular, are vibrating inside the cavity with the same single frequency and different initial phases. The pistons are the only sources of excitation of the fluid. The acoustic pressure difference on both sides of the plate forces its vibrations. The acoustic waves are radiated into the half-space above it. A rigorous theoretical analysis of sound radiation has been performed based on the exact solution of the problem of free vibrations of the plate. The system of three coupled partial differential equations is solved. They are the two Helmholtz equations for the cavity and for the half-space, and the equation of motion of the plate. Consequently, the acoustic pressure distribution in both spaces is presented as well as the acoustic power radiated.

The coefficient of performance (COP) and relative coefficient of performance (COPR) of the standing wave thermoacoustic refrigerator (SWTAR) were investigated. The components of the SWTAR are a resonator tube, a stainless-steel bowl-shaped resonator cone, a commercial loudspeaker, a spiral stack, a cold side heat exchanger (CSHX) with miniature heat pipes (MHPs) and a hot side heat exchanger (HSHX). An operating frequency of 163Hz was used in this study, with an acoustic power (AP) supply of 10, 20 and 30W. Cooling loads were heat provided from a thermoelectric module (TEM) by joining the hot side of the TEM to the copper heat absorber and transferring heat to the CSHX through MHPs. The COP of the SWTAR increased with increasing cooling load. The slopes of the COP curves decreased with increasing AP. The COPR of the SWTAR increased with increasing cooling load until it was approximately 30% of AP.