Acoustic forcing of flexural waves and acoustic fields for a thin plate in a fluid

Consistency with conservation of energy for coupled acoustic fields and plate flexural waves, discussed in another paper for this conference, is used to derive the amplitude and phase of flexural and acoustic waves for an infinite thin plate -fluid system excited by an incident acoustic plane wave. The acoustic interaction of the plate -fluid system is defined by 1. specula reflection from the plate surface, 2.transmission through the plate material and 3. plate flexural waves taking into account fluid loading. This reproduces the well-known peak in plate flexural wave amplitudes above the coincidence frequency where the trace wavenumber of the incident acoustic plane wave along the plate equals the plate -vacuum flexural wavenumber. This is essentially a resonance with the resonant frequency that varies with the direction of the incident plane wave. The width of the resonance is governed by fluid loading which manifests as radiation damping of the flexural waves. It is found that flexural waves affect the acoustic reflectivity of the plate through coherent interference of the acoustic field from flexural waves with the specula reflected field, but only if there is a nonzero phase shift in specula reflection. Energy conservation considerations predict that a plate becomes acoustically soft close to the resonance condition. A simple formula for the approximate resonance width is also derived