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Additional resources for Dynamic Stability of Structures. Proceedings of an International Conference Held at Northwestern University, Evanston, Illinois
Moreover, / increases monotonically with ξ under these conditions. Hence equation (32) will always be satisfied before equation (28) is satisfied. The same can be said for loading at the usual speeds of the conventional testing machine because the dynamic analysis h a s shown that the perturbation of the quasi-static state is negligibly small under these conditions. CONCLUSIONS Ziegler  concluded his paper in Advances in Applied Mechanics by stating that in difficult problems the stability analysis must be carried out with t h e aid of the kinetic criterion, and that initial deviations from the exact shape must also be taken into account.
SSSR, 123, 806 (1958). V. L. AGAMIROV and A . S. VOL'MIR, Povedenie cilindricheskikh obolochek pri dinamicheskom nagruzhenii vsestovonnego davleniya pri ocevogo szhatiya, Izvestiya Akademii Nauk, SSSR, 78, (1959); also Behavior of cylindrical shells under dynamic loading by hydrostatic pressure or by axial compression, ARS J. 31, 98 (1961). N . J. HOFF, Dynamic criteria of buckling, Proceedings of a Symposium of the Colston Research Society on Engineering Structures, Butterworths, London, and Academic Press, N e w York, 1949, p.
H O F F Substitution of quantities determined earlier leads to /i = - S / S T T T T ^ ^ - (57) Again, one can calculate the derivative with respect to ξ: Similarly f\ = Wt If terms multiplied by - 640g^ + 2 3 0 4 g y g - 1 1 4 0 e / ^ + 70/^ ^"^^;^-·"^"· (59) are next taken into account, one obtains the equation /'I+(1 - A / 2 + 1 / 0 / ? + u i f 2 - y ' f 2 = 0. (60) Hence /'ί + Ι / ο / ? ι-ξ+lfl-W (61) This can also be written as ^^I-/ 0 or as 32/^ / 2 = . Λ ' °3,9(640e^ - 2352^^2 + 1 IfAefl - 73/^).