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ASYMPTOTIC APPROXIMATION OF THE MODAL ACOUSTIC IMPEDANCE OF A CIRCULAR MEMBRANE

Department of Acoustics, Institute of Physics, University of Rzeszów, Al. Rejtana 16A, 35-310 Rzeszów, Podkarpackie, Poland

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WITOLD J. RDZANEK

Department of Acoustics, Institute of Physics, University of Rzeszów, Al. Rejtana 16A, 35-310 Rzeszów, Podkarpackie, Poland

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KRZYSZTOF SZEMELA

Department of Acoustics, Institute of Physics, University of Rzeszów, Al. Rejtana 16A, 35-310 Rzeszów, Podkarpackie, Poland

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https://doi.org/10.1142/S0218396X1000422XCited by:7 (Source: Crossref)

Abstract

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.

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