Sound radiation from baffled finite elastic plates that are subjected to impulses occurring at random points on the surface, at random intervals, and with random strength is analyzed. The plate response is obtained in the Stieltjes integral form of the plate impulse response function with respect to the occurrence of impulses. The total sound power radiated from the plate is formulated according to Heckl’s approach. Explicit expressions for the expected value of the plate response and the radiated sound power are derived for the case in which the stream of impulses is uncorrelated. An approximate solution for the radiated sound power is obtained by assuming light damping of plates and by neglecting modal coupling effects. For comparison, the exact and approximate solutions are evaluated numerically for a plate with constant loss factors. The analysis is applied to the prediction of rainfall noise by expressing the expected value of the exciting force in terms of the size of raindrops, their terminal velocity, and the rainfall rate.
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