Structural Damping Effects on Dynamic Instability of Subtangentially Loaded and Shear Deformable Beck’s Columns

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.