The normalized acoustic power of a thin clamped annular plate vibrating in a flat screen around a perpendicular semi-infinite circular cylinder

• The axisymmetric vibrations of a thin clamped annular plate.
• The acoustic power and the acoustic impedance coefficients.
• The rigorous mathematical manipulations using the Weber transform and the asymptotic analysis.
• The influence of the circular cylindrical baffle on the acoustic power.

The Neumann boundary value problem is presented for the time harmonic excited steady-state vibrations of a thin clamped annular plate embedded in a flat rigid baffle around a perpendicular circular cylindrical rigid semi-infinite baffle. The system of two coupled differential equations is solved for this purpose, one of them being the wave equation of the fluid filling the space between the two baffles and the other being the equation of motion of the plate for its excited vibrations. First, the acoustic pressure is presented in its spectral form using the Weber inverse transform. Then, the time-averaged acoustic power is presented using the plate׳s modal impedance coefficients and the coupling factors. The modal coefficients are presented as the integrals together with the corresponding asymptotic formulations. The influence of the cylindrical baffle on the acoustic power is analyzed numerically. The fluid loading and the internal attenuation of the plate׳s vibrations are both included whereas the attenuation of the acoustic waves in fluid is neglected.