ON A-TWO-PARAMETER DYNAMIC BUCKLING OF A VISCOUSLY DAMPED BUT CLAMPED COLUMN STRESSED BY A STEP LOAD
Abstract
In this investigation, we extend our search on the dynamic buckling loads of some elastic structures to that of a clamped column lying on a nonlinear (cubic) elastic foundation but impacted upon axially by a step load. In order to ensure a uniformly valid solution, we employ multi–scaling two–timing regular perturbation procedures in asymptotic expansions of the variables. It is shown that (a) clamped columns buckle at higher buckling loads than columns with simply–supported ends irrespective of whether the columns are loaded statically or dynamically and whether damped or undamped, (b) Specifically, the inequalities satisfied by the static buckling load and dynamic buckling load in the clamped case are respectively given as and as against and for simply–supported end conditions, (c) At low values of the static buckling load , there is no appreciable change in the values of the dynamic buckling load but at higher values of , increases sharply with increased static buckling load . However, the increase seems to decrease with increased damping. We are able to mathematically relate the dynamic buckling load to the static buckling load and thereby by–passing the labour of repeating the entire process for different imperfection parameters. Thus, given either or , we can predict either value without the actual knowledge of the size of the small imperfection parameter.
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