Dynamic Instability Analysis of Thin Shell Structures subjected to Follower Forces (1st Report) : The Shell Governing Equations in Monoclinically Convected Coordinates

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The deformation and dynamic instability mechanisms of submerged thin shell marine structures are in principle of a nonconservative nature since the associated loads are of the follower type hydrostatic pressure and drag forces which may persistently undergo disturbances due to several causes. In the region of large deformations, especially in the case of geometrically deep shell structures, the system could be much more accurately defined in a monoclinically convected material coordinate description than the conventional spacial description. Also, a complete analysis of a nonconservative system requires a dynamic criterion since the system can have multiple ranges of stability and instability involving both divergence and flutter. This paper presents the basic formulations and development of the governing equations for the finite deformations of thin shells defined in a monoclinically convected coordinate description and applies the same to different cases of shell deformations. The validity of the formulations is verified for finite deformations and disturbed small vibrations of some common types of shell structures. The examples of some geometrically special shell structures are presented as well to show the feasibility of the present formulation.
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