### ASA 127th Meeting M.I.T. 1994 June 6-10

## 3pSAa4. An eigenvalue problem relating to reactive acoustic power and
acoustic radiation.

**Pei-Tai Chen
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*Dept. of Naval Architecture, Natl. Taiwan Ocean Univ., 2 PeiNing Road,
Keelung 20224, Taiwan, Republic of China
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**Jerry H. Ginsberg
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*Georgia Inst. of Technol., GA 30332
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The acoustic power radiated for mono-frequency vibrations from submerged
bodies can be calculated by evaluating one half of surface integral of surface
pressure multiplying the complex conjugate of normal velocity. The real part of
the integral is the radiated power from bodies, whereas the imaginary part, or
the reactive power, is seldom used in the study of surface acoustics. The
present study is to explore the reactive power in the connection of dynamic
characteristics for surface pressure and normal velocity. This problem is
considered by investigating the quadratic expressions of complex surface
acoustic power as discretizations are introduced on the surface. A reciprocal
principle for acoustic medium is employed to assert the symmetry of the
matrices associated with the quadratic forms. Correspondingly, the
investigation of surface acoustics turns into the examination of symmetrical
eigenvalue problems associated with the matrices. Eigenvalues are identified as
the indication of phase differences between surface pressure and normal
velocity in the corresponding eigenvectors. These eigenvalues are then used to
classify the modes for strong or poor radiations. The triple quantities, which
are eigenvalues, modal modes for surface pressure, and normal velocity, provide
a full description of dynamic characteristics for submerged bodies. [Work
supported by Chinese National Science Foundation, NSC 82-0209-E-019-063 and
United States Office of Naval Research, Code 1132-SM.]