Transmission of sound through a pair of rectangular elastic plates
| Autor: | G. F. Butler, E. G. Broadbent, F. G. Leppington |
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| Rok vydání: | 2006 |
| Předmět: | |
| Zdroj: | IMA Journal of Applied Mathematics. 71:940-955 |
| ISSN: | 1464-3634 0272-4960 |
| DOI: | 10.1093/imamat/hxl017 |
| Popis: | Two thin elastic plates, which may have different physical parameters, occupy the parallel regions 0 < x < a, 0 < y < b, z = -d and 0 < x < a, 0 < y < b, z = 0, in a Cartesian coordinate system, where the separation distance d is much less than the dimensions a and b. The plates are simply connected to a structure that occupies the rest of the region -d < z < 0. The side walls (x = 0 or a, 0 < y < b, -d < z < 0 and y = 0 or b, 0 < x < a, -d < z < 0) are taken to be acoustically soft; the surfaces z = -d and z = 0, outside the rectangular regions occupied by the plates, are taken to be acoustically hard. Light compressible fluid (air) is in each of the half-spaces outside the plates and in the rectangular region between them. A sound field is induced by a high-frequency plane wave. Allowance is made for a small element of damping in the fluid trapped between the plates, as well as damping in the plates. Estimates are derived for the transmitted power, averaged over a frequency band and with respect to all incidence directions, in the asymptotic limits of small fluid loading and high frequency. For the case where the two plates have identical physical properties, detailed asymptotic estimates are given for the form of the peaks in the transmitted power, at a discrete set of operating frequencies, both above and below the plates' coincidence frequency. |
| Databáze: | OpenAIRE |
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