Dynamic stability of cantilever columns under a tip-concentrated subtangential follower force

Abstract

The dynamic stability of a uniform cantilever column under a tip-concentrated subtangential follower force is examined. The governing two-point boundary value problem is converted to an initial value problem. A simple numerical iterative scheme is followed to generate a load versus frequency curve (eigencurve) in order to study the critical and post-critical behavior of the columns subjected to a tip-concentrated follower force. For the load rotation parameter greater than 1 2 , the coalesce frequency and the corresponding critical load are obtained. The deformed configurations of cantilever columns are generated for different load rotation parameters. The details of the critical load parameter, tip angle and tip coordinates of the columns for the specified load rotation parameter are presented. The critical load parameter increases with the load rotation parameter.

How valid are Sugiyama׳s experiments on follower forces?

“…The moment-curvature relationship of a uniform cantilever column subjected to a tip-concentrated subtangential follower load (P) is [14] EI ∂ϕ ∂s…”

“…In general, static stability loads are those loads at which the eigencurve meets the load axis, whereas the dynamic stability loads are those loads at which two branches of eigencurves coalesce. A simple and reliable iterative procedure [14] is followed to obtain the relationship between the load parameter (λ) and the frequency parameter (ω) for the specified tip-angle (ϕð0Þ) and the subtangential parameter (β). Static stability loads are arrived from the loads at which the eigencurve meets the load axis at λ ¼ λ cr .…”

“…The dynamic stability of elastic cantilever columns under a tipconcentrated subtangential follower force has formed the subject of a large number of publications [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. There is a need for experimental verification to support the reality of the follower forces [16,17].…”

On The Simulation of Beck Column through a Simple Xiong-Wang-Tabarrok Experimental Model of Centripetally Loaded Column

“…Dynamic stability of elastic structures is a fascinating topic. After Beck in 1952, many researchers have examined theoretically considering a cantilever column under a tip-concentrated tangential load (the so-called Beck column) [1][2][3][4][5][6][7][8][9][10][11][12][13]. The column stability is assessed by generating the load versus frequency curve, namely the eigencurve.…”

“… ( s ) is the angle between the tangent to the deformed column and its vertical axis. BQ=  , is the distance from the tip (B) of the un-deformed column to the point (Q) where the tangent line AQ at the free end of the deformed column intersects the column axis OB at Q. Denoting E and I as the Young's modulus and the moment of inertia respectively, Mutyalarao et al [13,26] have presented a system of nonlinear differential equations assuming harmonic motion for large deflections of a cantilever column based on the moment (M)-…”