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

Figure 6

Critical velocity 𝑣_cr varies with loading frequency 𝜔 for 𝑘=1×10¹⁰ N/m².

(a) Critical velocity 𝑣_cr versus loading frequency 𝜔

(b) The phase velocity 𝑣₁ and group velocity 𝑈₁ of naturally propagating waves versus wave number 𝑁, 𝑣_1min=𝑣_𝑐1=1399.7m/s, 𝑈_1max=1395.2m/s<𝑣_𝑐1