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