ASYMPTOTIC APPROXIMATION OF THE MODAL ACOUSTICrnIMPEDANCE OF A CIRCULAR MEMBRANE

摘要

The Neumann boundary value problem of the Helmholtz equation of a vibrating circular membrane embedded into a flat rigid baffle is solved. The membrane is excited asymmetrically and radiates acoustic waves into the half-space above the baffle. A set of elementary asymptotic equations for modal radiation self-impedance and mutual impedance is presented. The equations are necessary for numerical computations of the radiated active and reactive acoustic power including the acoustic attenuation. A few equations available in the literature are collected. All the missing equations have been obtained using the methods of analysis of contour integral and stationary phase. The presented equations cover a wide frequency band, with the exception of the lowest frequencies and the frequencies close to coincidence.