Application of a two-scale perturbation theory to panel/frame structural-acoustics

The analysis of sound transmission across panel/frame structures is important in the design of noise reduction strategies for vehicular interior-noise control. A recently developed two-scale perturbation expansion theory for such problems formulates a composite periodic solution by superposing a periodic local solution on a smoothed global solution. The global solution reflects the general behavior of the panel/frame structure, while the local solution accounts for the detailed panel motions. An averaging procedure is used to incorporate the detailed panel motions as transfer functions for obtaining the global solution. The present work shows the application of this new theory to two problems for which the exact solutions are also available. The first problem is an infinitely long flexible beam supporting panels forced by a sweeping harmonic pressure wave. The panels are either dynamically identical or are tuned alternately to two different resonance frequencies, and the effect of the alternate resonance tuning on noise reduction is investigated. The second problem involves panels on a pinned-pinned beam spanning a channel. The boundary condition is incorporated only in the global problem, while a periodic local solution is used. Comparisons of the approximate and exact solutions for the two problems show that the perturbation theory predicts general panel/frame behavior with good accuracy over a wide range of scale separations, and is very accurate when the scale separation is reasonably high.

Duke Scholars

Author Donald B. Bliss Thomas Lord Department of Mechanical Engineering and Materia ...