Table 8 shows the dimensionless frequencies of shearrigid Beck's columns subjected to follower forces 1% more or less than the damped flutter loads, which are [P.
It is apparent from the sign of the real part of frequencies in Table 8 that the system is stable under a follower force less than the damped flutter load but unstable under a follower force more than the damped load.
Lastly, three damped Beck columns subjected to a lateral impulse force are analyzed under the same conditions as in Figure 8, except that the shear parameter S is increased and the damping ratio is fixed at 2%.
A dimensionless frequency equation of shear-flexible and damped Beck's columns under a subtangential follow force was analytically derived in a closed form.
2) To construct a dimensionless stability map of shear-flexible and damped Beck's columns, external and internal damping can be estimated from Case 3 without introduction of additional parameters.
5) Dimensionless stability maps of shear-flexible and damped Beck's columns can be constructed using an analytical approach or a FE approach.
Saetta, "Finite element solution of the stability problem for nonlinear undamped and damped systems under nonconservative loading," International Journal of Solids and Structures, vol.
D'Annibale, "Bifurcation analysis of damped visco-elastic planar beams under simultaneous gravitational and follower forces," International Journal of Modern Physics B, vol.
Kim, "Sub-tangentially loaded and damped Beck's columns on two-parameter elastic foundation," Journal of Sound and Vibration, vol.