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Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition by Tim Mellow, Leo Beranek

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14.5. Green's function for a rectangular membrane

So far, we have only solved the homogeneous membrane wave equation (see Eq. 14.7) to find out what vibration modes may be possible, but which ones will actually be excited depends on the specific driving conditions. Different modes will occur depending on whether the membrane is driven with a uniform pressure distribution, for example, or a driving velocity is applied at a point off-center. Let us now write an inhomogeneous membrane equation by adding an arbitrary driving pressure distribution p ˜ 0 ( x , y ) image to the homogeneous one of Eq. (14.7)
( 2 + k D 2 )

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