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BOUNDARY CONDITIONS FOR BEAMS IN BENDING

Here we recall the beam bending example of a cantilever beam with a transverse concentrated load of magnitude Fcos(Ωt) applied at x = ℓ at time t = 0. The displacement of the beam was
(1) ν(x, t) = (2F)/(mℓ)∞⎲⎳i = 1(( − 1)i + 1)/(ω2i − Ω2)[cos(Ωt) − cos(ωit)]φi(x)
After pressing play on the time slider bar, press the slower button until the simulation is running at a reasonable speed. Notice that we can see the clamped and free boundary conditions. The left side has no displacement or slope, and the right side is free to move.
In order to see the effects of the mode shapes, set the number of mode shapes to 1, and observe the beam. Notice that it bends, but does not wobble at all. As you increase the mode shapes you’ll see the beam start to slightly wobble.