### ASA 124th Meeting New Orleans 1992 October

## 5aPAa9. Elastic Helmholtz resonators.

**Andrew Norris
**

**
Gerry par
**
*Dept. of Mech. & Aerospace Eng., Rutgers Univ., P.O. Box 909, Piscataway,
NJ 08855-0909
*

*
Dept. of Math., Univ. of Manchester, Manchester M13 9PL, UK
*

*
*
The influence of wall elasticity on the response of a Helmholtz resonator
is examined by analyzing the canonical case of a thin elastic spherical shell
with a circular aperture subject to plane-wave excitation. By neglecting the
thickness of the wall and representing the elasticity via a thin shell theory
the problem is reduced to one of solving an integral equation over the aperture
for the polarization velocity, which is related to, but distinct from, the
radial particle velocity of the fluid. The integral equation can be solved by
asymptotic methods for small apertures, yielding closed-form expressions for
the major resonator parameters. In general, wall compliance reduces the
resonance frequency in comparison with an identically shaped rigid cavity. The
Q value of the resonance is increased and the scattering strength of the cavity
at resonance is enhanced by wall compliance. The asymptotic results are
supported and supplemented by numerical calculations for thin steel shells in
water. [Work supported by ONR.]