Small oscillations of truss bridge with three-section deck

Bridge with three deck sections. Five movable joints (points) in a plane – so 10 degrees of freedom and the resulting 10 modes.

Here we can already identify the fundamental and one higher harmonic mode of transverse and longitudinal oscillation, these are modes No. 10 and No. 8 (transverse) and No. 9 and No. 7 (longitudinal).

The constant ω₀ is given by the mass of the rods and their stiffness, ω₀ = ω₀(m, k). Its specific value is not important.

Mode No. 1, ω = 1.98 · ω₀

Mode No. 2, ω = 1.89 · ω₀

Mode No. 3, ω = 1.57 · ω₀

Mode No. 4, ω = 1.55 · ω₀

Mode No. 5, ω = 1.26 · ω₀

Mode No. 6, ω = 1.13 · ω₀

Mode No. 7, ω = 1.09 · ω₀

Mode No. 7 corresponds to the second mode of longitudinal oscillations of the bridge.

Mode No. 8, ω = 0.7 · ω₀

Mode No. 8 corresponds to the second mode of transverse oscillations of the bridge.

Mode No. 9, ω = 0.45 · ω₀

Mode No. 9 corresponds to the first mode of longitudinal oscillations of the bridge.

Mode No. 10, ω = 0.27 · ω₀

Mode No. 10 corresponds to the first mode of transverse oscillations of the bridge.

Small oscillations of truss bridge with three-section deck

Mode No. 1, ω = 1.98 · ω0

Mode No. 2, ω = 1.89 · ω0

Mode No. 3, ω = 1.57 · ω0

Mode No. 4, ω = 1.55 · ω0

Mode No. 5, ω = 1.26 · ω0

Mode No. 6, ω = 1.13 · ω0

Mode No. 7, ω = 1.09 · ω0

Mode No. 8, ω = 0.7 · ω0

Mode No. 9, ω = 0.45 · ω0

Mode No. 10, ω = 0.27 · ω0