Dynamic Instability Analysis of Thin Shell Structures subjected to Follower Forces : (5th Report) Disturbance Threshold Curves of Dynamic Stability

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In the unpredictable world of various natural phenomena under which the shell structures are designed to function, their intended strength and dynamic stability may become negotiable when subjected to unknown parameters. This dilemma for the structural engineer is a common feature of most marine shell constructions. The general governing equations of equilibrium and dynamic stability for thin shell structures subjected to follower loads and undergoing large deformations have already been developed for the general shell defined in a monoclinically convected coordinate system.In a previous report, the complex peninsular shaped instability regions of a shell at various disturbed equilibrium positions have been numerically illustrated. This paper expands on the same direction and reaches at a demonstration of the disturbance threshold curves for the dynamic stability of a shell. The numerical results for subsequent equilibrium positions show that the shell stability slips suddenly over a threshold point of dynamic equilibrium from the heteronomous state to an autonomous state of self-sustained motions. Beyond this point the dynamic behaviour becomes highly irregular until the static critical point is reached, at which deep shells generally fail and the shallow shells enter the next phase of post-collapse stability.
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