Dynamic stability of circular cylindrical shells under periodic compressive forces

Abstract

Based on the Donnell equations modified with the transverse inertia force, the dynamic stability of circular cylindrical shells under both static and periodic compressive forces is theoretically analyzed under four different boundary conditions, with the effect of the axisymmetric unperturbed bending vibration taken into consideration. The problem is first reduced to that of a finite degree-of-freedom system with the Galerkin procedure, the stability of which is examined by using Hsu's method. Calculations are carried out for typical cases and the instability regions of the principal, secondary and combination parametric resonances are determined for the frequency range covering up to several times the lowest natural frequency. It is found, among others, that the effect of the unperturbed motion is quite significant for shells with moderate length while that of the longitudinal resonance is generally negligible for thin shells.