Abstract
A frequency equation of externally and internally damped and shear-flexible cantilever columns subjected to a subtangentially follower force is analytically derived in a dimensionless form with relation to the linear instability theory of Beck’s columns. Some parametric studies are then performed with variation of two damping coefficients under the assumption of Rayleigh damping. Based on the analysis results, it is demonstrated that three damping cases in association with flutter loads of Beck’s columns can be selected including one case representative of structural damping. Finally, stability maps of shear-flexible and damped Beck’s columns are constructed for the three damping cases and discussed in the practical range of damping coefficients and shear parameters. In addition, flutter loads and time history analysis results are presented using dimensionless FE analysis and compared with exact solutions.
Highlights
The dynamic instability problem of a cantilever column subjected to a follower force has been well known and various interesting related topics have been intensively studied by many researchers since Beck [1] solved this problem analytically
It is worth referring to the monographs by Ziegler [2], Bolotin [3], and Leipholz [4] who addressed the static and dynamic stability of a nonconservative system
According to the linear stability theory of nonconservative systems, external damping tends to increase flutter loads but columns under small internal damping lose their stability at the flutter load drastically deceased
Summary
The dynamic instability problem of a cantilever column subjected to a follower force has been well known and various interesting related topics have been intensively studied by many researchers since Beck [1] solved this problem analytically. According to the linear stability theory of nonconservative systems, external damping tends to increase flutter loads but columns under small internal damping lose their stability at the flutter load drastically deceased In this case, Beck’s columns subjected to follower forces slightly larger than internally damped flutter loads become unstable in form of oscillations with a slow growth of amplitude, which is sometimes called a quiet flutter. Beck’s columns subjected to follower forces slightly larger than internally damped flutter loads become unstable in form of oscillations with a slow growth of amplitude, which is sometimes called a quiet flutter This destabilizing effect of small internal damping on the stability of nonconservative systems, Ziegler’s paradox, has been one of attractive research topics [5,6,7,8,9]. (4) stability maps of shear deformable and damped Beck columns are newly constructed using the analytical solution, which is compared with the FE solution in the practical range of damping coefficients and shear parameters
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
