振動物體的輻射效率及複數聲音功率

陳柏台

《中華民國振動與噪音工程學會論文集》 1997 (1997/05) Pp. 579-589

https://doi.org/10.30028/CSSVANNUAL.199705.0579

摘要

本計劃探討振動物體的表面複數聲音功率其虛部所代表的意義。根據高斯發散定理，可以推導出複數聲音功率的虛部對映至聲場中所儲存的應變能及動能之差，而聲音功率的實部則對映至遠場中所輻射的能量。由此等觀察，聲場可以視爲由聲音壓縮的應變及慣性效用所形成的質量／彈簧系統，而其遠場的輻射效應則可視爲阻尼效應，如此聲場可視爲質量／彈簧／阻尼系統，此系統的作用力是物體表面的振動推擠聲音介質，而功率的實部及虛部則分別代表系統中消耗的能量及儲存的應變能及動能之差，因此實部及虛部可以指示此系統的功率輻射效率。
在這裹我們應用先前所建立的聲音模態[1]，將任意的速度分佈以聲音速度模態展開，並探討了每一個模態的輻射效率隨頻率變化的情形。最後，我們計算了圓球和細長橢圓體的數值實例，並顯示了橢圓體較圓球體更易輻射出聲音。

關鍵字

輻射效率 ； 複數功率 ； 聲音模態

並列摘要

The paper explores the physical meaning of a surface complex acoustic power computed from a vibrating body immersed in an infinite extent acoustic medium. Derived by Gaussian Divergent theorem, the imaginary part of the surface complex acoustic power indicates the difference between potential energy and kinetic energy of the acoustic particles stored in the acoustic medium, while the real part of the complex power denotes the acoustic power radiating into far field. Base on such observations, the acoustic field can be viewed as a composition of infinitestimal springs and masses, and the radiation of acoustic energy into far field is regarded as dashpots at the far field boundary. Thus, the acoustic field due to the vibrating body is a mass/spring/dashpot system. The exciting force of the system is the surface pressure exerting on the acoustic medium. The radiation efficiency of the body is defined as the ratio of the real part of the complex power to the magnitude of the complex power.
Having had the insight of the radiation efficiency in relation to the radiated acoustic power, the study further extends to situations of arbitrarily distributed velocity profiles. The previous established acoustic radiation mode [1] is employed to investigate such situations and to study radiation efficiencies for radiation modes. The radiation efficiencies of radiation acoustic modes are computed for a spherical and a slender spheroidal body which show that the spheroidal body radiates power more efficiently than the spherical body.

並列關鍵字

radiation efficiency ； complex acoustic power ； acoustic radiation mode