ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

1aPA7. Acoustic reciprocity-type and energy conservation theorems for flow-structure problems.

Oleg A. Godin

NOAA/Atlantic Oceanogr. and Meteorolog. Lab., 4301 Rickenbacker Cswy., Miami, FL 33149

Recently the reciprocity principle was proved for acoustic fields in motionless fluid/solid structures [A. N. Norris and D. A. Rebinsky, J. Acoust. Soc. Am. 94, 1714--1715 (1993)] and a flow reversal theorem (FRT) was established for sound and acoustic-gravity waves in 3-D inhomogeneous, moving fluids [O. A. Godin, J. Acoust. Soc. Am. 97, 3396(A) (1995)]. The FRT is counterpart of the reciprocity principle when ambient flow is present. The theorem states symmetry of some field quantity with respect to interchange of the source and receiver positions and the simultaneous reversal of flow. An FRT will be presented which generalizes results of the above-mentioned works to include waves in flow/solid structures of arbitrary geometry. Parameters of the medium are allowed to be spatially inhomogeneous but time independent. Wave propagation and ambient flow are considered as adiabatic thermodynamic processes. It is assumed the prestresses in the solids due to ambient flow are small. Conservation of a quasienergy for the wave is established and its relation to known acoustic energy corollaries as well as to the FRT is discussed. Some possible applications of the general theorems will be considered. [Work supported by NRC.] [sup a)]On leave from P. P. Shirshov Oceanography Institute, Moscow, Russia.