### ASA 125th Meeting Ottawa 1993 May

## 3aSA11. Thin elastic spherical shells: the nonaxisymmetric motion.

**Jin-Meng Ho
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*SFA, Inc., 1401 McCormick Dr., Landover, MD 20785
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Naval Res. Lab., Washington, DC 20375-5000
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This paper treats the nonaxisymmetric motion of a thin elastic spherical
shell; it is motivated by the problem of a finite cylindrical shell with
hemispheric shell endcaps. Here, the spherical shell is subject to intrinsic
azimuthal deflection, as opposed to the well-documented case where the
vibration is rendered axisymmetric by the special choice of coordinates. The
kinematics of deformation is discussed, based on the thin shell assumption
referred to in the literature as the Kirchhoff hypothesis. This leads to the
expressions of the total kinetic and potential energies and external work in
terms of the displacements of the middle shell surface; application of
Hamilton's principle then yields the desired dynamical equations of
nonaxisymmetric motion. It is found, as two special cases, that the spherical
shell undergoing free vibrations supports shear waves, in addition to
compressional and flexural waves; but that for fluid loading, the former
decouples from the acoustic wave while the latter observe the same dispersion
relations as in the axisymmetry case.