### Abstract

Original language | English |
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Pages (from-to) | 1776-1787 |

Number of pages | 12 |

Journal | Journal of the Acoustical Society of America |

Volume | 126 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 |

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*Journal of the Acoustical Society of America*, vol. 126, no. 4, pp. 1776-1787. https://doi.org/10.1121/1.3206580

**Sound radiation quantities arising from a resilient circular radiator.** / Aarts, R.M.; Janssen, A.J.E.M.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Sound radiation quantities arising from a resilient circular radiator

AU - Aarts, R.M.

AU - Janssen, A.J.E.M.

PY - 2009

Y1 - 2009

N2 - Power series expansions in ka 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-(/a)2)n, with the radial coordinate on the radiator, or linear combinations of Zernike functions Pn(2(/a)2-1), with Pn 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.

AB - Power series expansions in ka 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-(/a)2)n, with the radial coordinate on the radiator, or linear combinations of Zernike functions Pn(2(/a)2-1), with Pn 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.

U2 - 10.1121/1.3206580

DO - 10.1121/1.3206580

M3 - Article

VL - 126

SP - 1776

EP - 1787

JO - Journal of the Acoustical Society of America

JF - Journal of the Acoustical Society of America

SN - 0001-4966

IS - 4

ER -