Theoretical study on identifying frequencies for beams with general boundary conditions by using a moving test vehicle

The paper presents a theory for retrieving the natural frequencies of the beam with general boundary conditions by using a moving test vehicle modeled as a single-DOF system. The general boundary conditions are simulated by using two vertical translation spring and two rotational springs placed on two ends of the beam. To start, closed-form solutions for the beam, vehicle and contact responses are newly derived. Then, the dichotomy is used to solve the transcendental equation for the frequency. The solution obtained can be readily degenerated to those closed-from ones for classical boundary conditions (i.e., simple, fixed and elastic) under a moving vehicle. The disturbing effect of surface roughness is eliminated by using the residual contact response of two connected identical vehicles. The reliability of the closed-from solutions and bridge frequencies identification are validated by comparison with the solution obtained by the finite element method (FEM) and previous work. The parametric study confirms that: (1) the contact response performs better than vehicle's response in retrieving bridge frequencies for all the scenarios considered; (2) a moderate speed of 20 km/h is recommended for use in the field test; (3) the first five frequencies can be identified with robustness for the bearings in different situations, reasonable levels of road roughness, bridge damping and noise.