Post-critical behaviour of the beck problem

Post‐Critical Behaviour of a Tapered Cantilever Column Subjected to a Tip‐Concentrated Follower Force

“…By using a modification in the iterative procedure as described in ref. 21, the relationship between the load parameter, A, and the frequency parameter, w, for the specified values of the subtangential parameter, y, and the tip angle, CI, can be obtained from equations (8)- (15).…”

Second-order work criterion and divergence criterion: a full equivalence for kinematically constrained systems

“…It is worth mentioning that the stability limit under kinematic constraints is the generalization of the one under some specific constraints especially applied to the boundaries of the system. For instance, Ingerle [1969] found a dimensionless divergence buckling load p = 20.19 in the presence of a specific constraint applied to the end of the column (the application point of the follower load), whereas the free Beck column admits a flutter instability value of 20.05, as calculated by Beck [1952] (see also [El Naschie 1976;1977] for this result). However, consider that any kinematic constraint reduces this value to π 2 as mentioned above as was observed by Ingerle [2013] and as has been definitively proved by Lerbet et al [2017].…”

Comment on "A Finite-Element Approach for Nonlinear Panel Flutter"

“…The critical load for this structure P c =53.75 Ellf was probably quoted for the first time by the author in Ref. 1. This value is also the critical value of a fixed-pinned Euler column.…”