Validation of a Fractional Derivative-Based Calculation Method for Dynamic Response of an Infinite Beam

This section validates the proposed calculation method by comparing numerical results with existing ones. We assume a first-order fractional derivative and select an infinite beam on a Kelvin foundation under moving loads with a constant velocity as our first example. We adopt EI=1.35×〖10〗^8 N∙m^2, ρA=375kg/m, k=68.9MPa, c=100kN∙s/m^2, P=50kN, and v=30m/s from reference [48]. It is reasonable to analyze the beam's response at any point, provided that the load passes through the coordinate origin (x=0) at time zero (t=0). For this study, we investigate the dynamic response at x=9m, where the displacement response of the beam over time is expected to peak around 0.3s. Figure 2 depicts the beam's displacement response over time.