Abstract
Theoretical analyses are presented for the title problem under four sets of boundary conditions. By the use of the Galerkin procedure, the Donnell equations modified with the transverse inertia force are reduced to the coupled Hill's equations. Stability regions are examined by utilizing Hsu's method. Calculations are carried out for typical shells and the instability boundary of the principal, secondary and combination parametric resonances are determined. It is found that unperturbed axisymmetric bending motion has a significant effect on the stability boundary for shells of moderate length while the effect of longitudinal resonance is generally negligible for thin shells.
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