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Title New approximation of structure-external acoustic interactions, part I : model derivation
Author Moonseok Lee, Youn-Sik Park, K. C. Park
Conference 13th International Congress on Sound and Vibration, July 2~6, Vienna University of Technology, Vienna, Austria
Year of Pub. 2006
File paper-icsv13_part1_KCPark_Lee.pdf
In most existing approximate models, first, the two limiting cases have been modeled: early-time response and late-time response by employing the initial-value and final-value theorems of the Laplace transform. Approximate models that cover the entire time spectrum are then constructed by asymptotically matching the two limiting models. Existing approximate models have been proven to be adequate for characterizing the acoustic radiation damping affecting the structural responses that are dominated by low-frequency components. For medium and high-frequency transients, however, most existing approximate structure-external acoustic interaction models suffer from both frequency distortions and inaccurate radiation damping. In addition, a careful examination of most approximate models for ideal structural geometries, when compared with the exact models obtained via Kirchhoff's formula, has revealed that the dominant acoustic scattering pressure modes are often not represented. Hence, most existing approximate models, while adequate for structural response calculations, may not be applicable to inverse acoustics problems wherein the primary objective is to identify the sound sources. In the present work (Part I), we present new approximations of structure-acoustic interactions by employing a finite-amplitude parameter expansion of Kirchhoff's retarded formula for general structural surface geometries. The new approximate models thus derived show that: (1) the so-called added mass is associated only with the structural inertia acting on the acoustic boundary and not with the acoustic transient pressure as most existing models have assumed; (2) The maximum convergent order of the coupled acoustic pressure equation is at most two in terms of its time derivatives; (3) the first and second derivatives of the pressure terms are associated with projected added mass and projected area matrices, respectively. A critical evaluation of the present approximate models are reported in the companion paper, Part II.