Scanning the vertical and radial frequencies of curved bridges by a single-axle vehicle with two orthogonal degrees of freedom

This paper scans for the first time the vertical and radial (lateral) frequencies of a horizontal curved beam from the respective motions of a single-axle test vehicle by a theoretical approach. The vehicle is innovatively treated as a system with two orthogonal degrees of freedom (DOFs), each of a spring-dashpot unit, to capture both the vertical and lateral motions. To start, closed-form solutions are derived for the out-of-plane vibration (under the vertical and torsional contact forces) and in-plane vibration (under the centrifugal force) of the curved beam. Then the vertical and lateral motions of the vehicle are derived. Based on this, a generalized formula is derived for the corresponding contact responses. From the analyses using the generalized contact formula, it was demonstrated that: (1) the contact responses outperform the vehicle responses in that more higher bridge fre-quencies (out-of-plane and in-plane) can be identified; (2) the radius of curvature affects significantly the radial frequencies of the curved beam; (3) the eccentricity of the scanning vehicle has little effect on frequency identification; and (4) pavement roughness' effect can be remedied by random traffic, and it does not appear in the radial contact response.