Frequencies of resonance of axisymmetric modes of open prolate spheroidal shells

Governing differential equations are derived for the axisymmetric motion of an open prolate spheroidal shell with inner and outer surfaces defined by prolate spheroidal coordinate surfaces. Transverse shear and rotary inertia terms are included in the shell equations. The open end of the shell, defined by a circumferential coordinate line, is assumed clamped. Approximate solutions for the axisymmetric frequencies of resonance of the in-vacuo and fluid-loaded shell are derived using the Galerkin method. For the in-vacuo shell, good agreement with published results for the exact frequencies of resonance of a spherical shell is obtained. Results are presented for the frequencies of resonance of open prolate spheroidal shells as a function of shell eccentricity, mode number, shell thickness, and opening angle, with and without fluid loading.