Sound radiation quantities arising from a resilient circular radiator

• Published in: The Journal of the Acoustical Society of America 2009-10, Vol.126 (4), p.1776-1787
• Main Authors: Aarts, Ronald M., Janssen, Augustus J. E. M.
• Format: Article
• Language: English
• Subjects: Acoustics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/1.3206580

Power series expansions in k a are derived for the pressure at the edge of a radiator, the reaction force on the radiator, and the total radiated power arising from a harmonically excited, resilient, flat, circular radiator of radius a in an infinite baffle. The velocity profiles on the radiator are either Stenzel functions ( 1 − ( σ ∕ a ) 2 ) n , with σ the radial coordinate on the radiator, or linear combinations of Zernike functions P n ( 2 ( σ ∕ a ) 2 − 1 ) , with P n the Legendre polynomial of degree n . Both sets of functions give rise, via King's integral for the pressure, to integrals for the quantities of interest involving the product of two Bessel functions. These integrals have a power series expansion and allow an expression in terms of Bessel functions of the first kind and Struve functions. Consequently, many of the results in [ M. Greenspan , J. Acoust. Soc. Am. 65 , 608-621 ( 1979 ) ] are generalized and treated in a unified manner. A foreseen application is for loudspeakers. The relation between the radiated power in the near-field on one hand and in the far field on the other is highlighted.