FREQUENCIES OF RESONANCE OF AXISYMMETRICAL MODES OF OPEN PROLATE SPHEROIDAL SHELLS

Governing differential equations are derived for the axisymmetric moti on of an open prolate spheroidal shell with inner and outer surfaces d efined by prolate spheroidal coordinate surfaces. Transverse shear and rotary inertia terms are included in the shell equations. The open en d of the shell, defined by a circumferential coordinate line, is assum ed 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 publishe d 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, m ode number, shell thickness, and opening angle, with and without fluid loading.