Selected modes of small oscillations of truss bridge with 11-section deck
Following are animations of selected modes of small oscillations. In the animations, the period of one oscillation is always one second, in reality the oscillation periods are different according to the indicated angular frequencies, T = 2 π / ω!
The constant ω0 is given by the mass of the rods and their stiffness, ω0 = ω0(m, k). Its specific value is not important.
Transverse oscillations of the bridge
First four modes of transverse oscillations.
Angular frequencies are in order: ω1 = 0.03 · ω0, ω2 = 0.08 · ω0, ω3 = 0.17 · ω0, ω4 = 0.28 · ω0.
Angular frequency ratios: ω2 / ω1 = 2.74; ω3 / ω2 = 2.1; ω4 / ω3 = 1.6.
Higher harmonic modes of this type of oscillation not shown here are also present.
Longitudinal oscillations of the bridge
First four modes of longitudinal oscillations.
Angular frequencies are: ω1 = 0.17 · ω0, ω2 = 0.34 · ω0, ω3 = 0.55 · ω0, ω4 = 0.72 · ω0.
Angular frequency ratios: ω2 / ω1 = 1.96; ω3 / ω2 = 1.6; ω4 / ω3 = 1.32.
Higher harmonic modes of this type of oscillation not shown here are also present.
Transverse "opposite" oscillations
First four modes of bizarre transverse oscillations.
With angular frequencies: ω1 = 1.5 · ω0, ω2 = 1.51 · ω0, ω3 = 1.53 · ω0, ω4 = 1.55 · ω0.
Angular frequency ratios: ω2 / ω1 = 1.01; ω3 / ω2 = 1.01; ω4 / ω3 = 1.01.
Higher harmonic modes of this type of oscillation not shown here are also present.
Other obscure modes
In this particular case, there are 42 modes in total (since we have 21 movable points in 2D). Besides those shown above (including higher harmonics not shown), there are also more or less obscure modes without straightforward interpretation. For example
and many others...