Dynamic Instability Analysis of Thin Shell Structures subjected to Follower Forces : (2nd Report) Numerical Solutions and some Theoretical Concepts

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Dynamic instability behaviour of thin shell structures subjected to follower forces are governed by several geometric and physical factors like curvature, boundary conditions, loading, disturbances and so on, contributing to the overall possibility of a dynamic failure at intervals of its deformation history. However, an actual threat to the ultimate stability or the static critical points may not be posed, unless and until when the pertinent damping forces are overcome. Disturbance forces of various types, which are omnipresent in a marine environment, may be the single most serious factor that could undermine all the other considerations and lead the structure to exhibit dynamic instabilities at a much earlier stage than that could be predicted by a static stability criterion. In the previous paper, we proposed a general governing equation in monoclinically convected coordinates to deal with shell deformations and validified the applicability of the method of small disturbances to unravel the problems of shell instabilities, in general, through analyzing the natural frequencies of deflected shells at subsequent disturbed equilibrium states. Here, the proposed method is used extensively to investigate the same problem in more detail and reached at some generalisations for singly and doubly curved shells. Also, a discretized approximate equation is proposed to get an insight into the total problem in a much simplified way.
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Dynamic Instability Analysis of Thin Shell Structures subjected to Follower Forces : (2nd Report) Numerical Solutions and some Theoretical Concepts

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