Sub-tangentially loaded and damped Beckʹs columns on two-parameter elastic foundation

The dynamic stability of the damped Beckʹs column on two-parameter elastic foundation is investigated by using Hermitian beam elements. For this purpose, based on the extended Hamiltonʹs principle, the dimensionless finite element (FE) formulation using the Hermitian interpolation function is presented. First, the mass matrix, the external and internal damping matrices, the elastic and the geometric stiffness matrices, Winkler and Pasternak foundation matrices, and the load correction stiffness matrix due to the sub-tangential follower force are obtained. Then, evaluation procedure for the flutter and divergence loads of the non-conservative system and the time history analysis using the Newmark-β method are shortly described. Finally, the influences of various parameters on the dynamic stability of non-conservative systems are newly addressed: (1) variation of the second flutter load due to sub-tangentiality, (2) influences of the external and the internal damping on flutter loads by analysis of complex natural frequencies, (3) the effect of the growth rate of motion in a finite time interval using time history analysis, and (4) fluctuation of divergence and flutter loads due to Winkler and Pasternak foundations.