SFA, Inc., 1401 McCormick Dr., Landover, MD 20785
Naval Res. Lab., Washington, DC 20375-5000
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.