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Sound radiation quantities arising from a resilient circular radiator
Ronald M Aarts1, Augustus J E M Janssen
1Philips Research Europe, HTC 36 (WO-02), NL-5656AE Eindhoven, The Netherlands. ronald.m.aarts@philips.com
The Journal of the Acoustical Society of America
|October 10, 2009
Summary
This study derives power series expansions for acoustic radiators, generalizing previous findings for applications like loudspeakers. It unifies calculations for radiator pressure, force, and power using Bessel and Struve functions.
Area of Science:
- Acoustics
- Mechanical Engineering
- Applied Mathematics
Background:
- Accurate modeling of acoustic radiators is crucial for applications such as loudspeakers.
- Previous studies have analyzed radiator performance, but a unified approach is lacking.
- Harmonically excited, flat, circular radiators in infinite baffles present complex acoustic phenomena.
Purpose of the Study:
- To derive power series expansions for key acoustic parameters of a flat, circular radiator.
- To generalize and unify existing results for radiator performance calculations.
- To explore the relationship between near-field and far-field radiated power.
Main Methods:
- Utilized Stenzel and Zernike velocity profiles for the radiator surface.
- Applied King's integral for acoustic pressure calculations.
- Derived power series expansions for integrals involving products of Bessel functions.
Main Results:
- Obtained power series expansions for radiator edge pressure, reaction force, and total radiated power.
- Expressed results in terms of Bessel functions of the first kind and Struve functions.
- Generalized and unified numerous prior results, providing a comprehensive analytical framework.
Conclusions:
- The derived power series expansions offer a unified method for analyzing radiator performance.
- The findings are applicable to various acoustic systems, notably loudspeakers.
- A clear relationship between near-field and far-field radiated power was established.
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