Many structures such as support columns such as those for elevated expressways and towers tend to become larger and more flexible recently, thus the buckling or collapse of these structures is considered to easily occur than ever due to huge earthquakes. Actually, in the Hyogo-ken Nambu earthquake in Japan, buckling phenomena of tall support columns were observed every-where. Therefore, the evaluation technology on the dynamic stability is very important in order to ensure the seismic design reliability for these structures. The authors have ever studied the effects of the horizontal and vertical simultaneous excitations on the above-mentioned buckling phenomena of support columns experimentally. More-over, they also investigated the fundamental phenomena of the dynamic stability of the support columns subjected to the horizontal and vertical excitations simultaneously by numerical simulations using an analytical model where the support column is treated as a tall elastic cantilever beam. The purpose of this paper is on the dynamic instability, that is dynamic buckling, of a cylindrical shell structures such as those for elevated expressways, towers, containment vessels, LNG tanks and water tanks in various industrial plants so on subjected to horizontal and vertical excitations simultaneously. The coupled motion of equation with horizontal and vertical excitations simultaneously for these cylindrical shell structures is derived in this paper, and this modeling is shown to become a Mathieu type’s parametric excitation. The numerical simulation analysis is carried out for a cylindrical shell model with an attached mass on its tip. Comparing with the classical seismic analysis method, this proposed dynamic instability analysis method shows the larger deformation in horizontal direction due to the parametric excitation of the vertical seismic wave. As the results, the structures are apt to lose the structural stability more due to the coupling effects between the horizontal and vertical seismic simultaneous loadings.

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