Dynamic Stability of Initially Curved Columns under a Time Dependent Axial Displacement of their Support
An accurate stability analysis of a vibrating system can be usually performed only by solving the original nonlinear differential equations for long enough periods of time1,2. Despite the availability of high speed computers and computational techniques quite often one has to overcome numerical difficulties arising from the nonlinear character of the governing equations of motion; difficulties which render numerical methods time-consuming. This drawback becomes more acute when a multiparametric discussion is needed. In view of these disadvantages one has to resort to efficient analytical techniques if such techniques exist or can be properly developed. The subsequent analysis is based exactly on the foregoing principles; that is the study of the motion will be based on the original nonlinear differential equation of motion — for a long period of time — which will be solved by a very efficient and simple to use approximate technique. This technique will be applied to the problem of dynamic stability of an, initially crooked, simply supported column having one end immovable and the other subjected to a time-dependent axial compressive displacement under various forcing functions. The case of an axial support displacement of constant velocity has been thoroughly discussed theoretically as well as experimentally by Hoff1,3. His findings presented in several publications, have also been checked by other investigators4,5. The availability of checked results was also a motive for the choice of the aforementioned model.
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