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

Figure 5

Critical velocity 𝑣_cr varies with loading frequency 𝜔 for 𝑘=1×10⁹ N/m².

(a) Critical velocity 𝑣_cr versus loading frequency 𝜔, in which 𝑣_1min=1305.4m/s<𝑣_𝑐1, 𝑈_1max=1425.7m/s>𝑣_𝑐1, as shown in Figure 5(b)

(b) The phase velocity 𝑣₁ and group velocity 𝑈₁ of naturally propagating waves versus wave number 𝑁, 𝑣_1min=1305.4m/s, 𝑈_1max=1425.7m/s