Analysis of Critical Velocities for an Infinite Timoshenko Beam Resting on an Elastic Foundation Subjected to a Harmonic Moving Load

Figure 1

The change curves of the phase and group velocities of naturally propagating waves versus wave number 𝑁 in the Timoshenko beam for 𝑘=1.6×10⁷ N/m².

(a) The curves of the phase velocities 𝑣₁, 𝑣₂ varying with wave number 𝑁, and the lowest phase velocity of naturally propagating waves in the Timoshenko beam is 𝑣_1min=558.9 m/s

(b) The curves of the group velocities 𝑈₁, 𝑈₂ varying with wave number 𝑁, and the maximum value of the group velocity 𝑈₁ is 𝑈_1max=1512.9 m/s