Dynamic Instability Analysis of Thin Shell Structures Subjected to Follower Forces : (4th Report) Quantitative Stability of Disturbed Equilibriums

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Shell structures intended for operations under disturbed equilibrium conditions at large deformations are a common feature of most marine constructions, Unpredictability of their real loading conditions adds to the critical nature of such dynamic stability problems. In the previous reports, the general governing equations of equilibrium and stability for thin shell structures subjected to follower loads and undergoing large deformations have been developed for the general shell defined in a monoclinically convected coordinate system. Numerical results were also given to substantiate the accuracy and applicability of this formulation. A simplified stability formulation was presented in the previous report to express the qualitative nature and the complexity involved in the problem of shell stability. This paper deals more thoroughly and quantitatively with the essence of the problem at its core, and shows how the disturbances in a real world situation can be fatal to the shell structure at various deflected positions under given loading conditions. The governing equations for this purpose have been developed using the method of disturbed small motions and the equation of dynamic stability presented here is considered to be unique in its approach to this problem. Numerical results bring out the complex peninsular shaped instability regions in the excitation force field for shells under given conditions of loading. This result is believed to be capable of explaining the often found disagreement between numerical and experimental results for shells in the vicinity of their theoretical points of static instability.
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Dynamic Instability Analysis of Thin Shell Structures Subjected to Follower Forces : (4th Report) Quantitative Stability of Disturbed Equilibriums

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