Influence of Mass Representation on the Equations of Motion for Rotating Structures

Abstract

Fig. 5 Influence of the viscous damping coefficient on the critical load for several values of the elastic foundation modulus (4 = 0.0044). phenomenon reported in Ref. 1 that the elastic foundation reduces the critical load at which the column will undergo dynamic instability. The effect of viscoelastic damping 77 coupled with the elastic foundation modulus is plotted in Figs. 3 and 4 for Ie = 0.0001 and 0.0044, respectively. The striking phenomenon presented in Figs. 3 and 4 is the sharp reduction in the critical load p for a very lightly damped beam. A similar phenomenon is reported in Ref. 3 for the B-E beam. For shorter beams (higher values of Ie), the reduction in the critical load for very lightly damped beams is more pronounced for higher values of elastic foundation k (see Fig. 4). The results of Fig. 4 show that for lightly damped beams (17 0.025) the elastic foundation has a stabilizing effect. The viscous damping has a stabilizing effect for the B-E beam (small values of Ie), as reported in Ref. 3. Figure 5 shows the influence of the viscous damping coefficient on the critical load for a shorter beam (7^ = 0.0044) for several values of the elastic foundation modulus. The results of Figs. 4 and 5 show that for shorter beams and light damping (viscous and viscoelastic), the elastic foundation has a destabilizing effect. Increasing the damping coefficient beyond a certain value causes the elastic foundation to stabilize the system (a higher critical load for a higher elastic foundation coefficient).