Free Vibrations of an Elastically Restrained Euler Beam Resting on a Movable Winkler Foundation

Figure 3

First four mode shapes for ten degenerate cases with a static Winkler foundation (solid line) and with a movable Winkler foundation (circle) when : (a) Sl-Fi, (b) Fr-Sl, (c) Fr-Fi, (d) Pi-Sl, (e) Sl-Sl, (f) Pi-Pi, (g) Fr-Fr, (h) Fi-Fi, (i) Fr-Pi, and (j) Pi-Fi. Mode shapes of rigid-body vibration are omitted for cases of Fr-Fr and Fr-Pi.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)