Dynamic Instability Analysis of Thin Shell Structures subjected to Follower Forces (3rd Report) Parametric Dependence of Stability

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The stability of thin shell structures subjected to follower type dynamic loads and undergoing large deformations has great significance in a real world marine environment. The general governing equations for this problem have been developed in the 1st report and some detailed numerical results were presented in the subsequent paper through analyzing the natural frequencies of deflected shells at subsequent disturbed equilibrium states. The critical nature of disturbances over a given equilibrium state when considering the dynamic behaviour of shell stability has been mentioned earlier. This paper elaborates upon the parametric dependence of shell stability under the effect of incremental disturbances to an equilibrium state. A first approximation of the general governing equations and a stability criterion using the method of small disturbances were developed and properly validated in the 2nd report, which are used here for the detailed numerical analysis of the dynamic nature of the stability of shells in equilibrium over a period of time under specified conditions. The validity of this simplified analysis has been suitably verified using the complete equation. It has been found that a sufficiently large increment to the displacement induced at a given state of equilibrium can lead to ultimate instability over a period of time under an existing parametric state. This shows that any intermediate state of equilibrium before the static limit point may equally be prone to a dynamic failure when subjected to the critically fatal environment.
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Dynamic Instability Analysis of Thin Shell Structures subjected to Follower Forces (3rd Report) Parametric Dependence of Stability

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