Dynamic response of a thin-walled curved beam with a mono-symmetric cross-section under a moving mass

This paper presents analytical solutions for the dynamic response of thin-walled curved beams induced by moving vehicles. The solutions encompass vertical, torsional, radial, and axial motions. A comprehensive set of governing equations for the dynamic response of thin-walled curved beams is established by considering the mass inertia of moving vehicles, rotary inertia, and warping resistance. The solutions are obtained for the four-directional response of curved beams, involving vertical, torsional, radial, and axial motions, based on the Fourier finite integral transformation, the Laplace-Carson transformation, their inverse transformations, and the Galerkin approach. A comparison of the results calculated by the analytical solutions in this study are compared with those calculated by the moving-force solutions using the Galerkin approach reported in a related literature, demonstrates the reliability and superiority of the analytical solutions. Hence, an extensive parametric study is carried out to investigate the effect of the mass inertia of moving vehicles, velocities, higher-order modes of vibrations, and radii of curvature on the dynamic responses of beams. As per the results, the mass and velocity of the moving vehicles play important roles in the dynamic response of curved beams. Furthermore, the dynamic response for thin-walled curved beams increases significantly with heavier vehicles and higher velocities, confirming that it is necessary to consider the mass inertia effect to study the dynamic response of curved beams.