A new theoretical method for torsional-flexural vibrations response of thin-walled beams with closed cross-sections under uniform distributed moving load

This article presents a new theoretical method for the torsional-flexural vibration response of a thin-walled beam with closed cross sections under a uniformly distributed moving load. Based on Vlasov's theory and restrained torsion theory, a comprehensive equation of motion for torsional flexural vibration is established by considering the effects of additional torque caused by the change of the shear center and the center of mass and the warpage coefficient. Using the Fourier transform, Laplace transform, and their inverse transformations, the torsional-flexural vibration response expression of thin-walled beams with closed cross-sections under a uniformly distributed moving load was derived. The results calculated by the analytical solutions in this study were compared with those from finite element method, demonstrating the reliability and superiority of the analytical solutions. Compared with the method that ignores the warpage coefficient, the lateral displacement and torsion angle of the beam calculated by the proposed theoretical method decreased by more than 12.00%. The effect of the cross-sectional properties on the natural frequency of the torsional-flexural vibration of thin-walled beams is analyzed, and the results show that the moment of inertia and mass per unit length have a considerable influence on the torsional-flexural frequency, which increases with the moment of inertia and decreases with an increase in the mass per unit length. The influences of the load magnitude, load velocity, and load eccentricity on the dynamic response were further investigated. According to the results, the lateral displacement of the beam increased significantly with increases in the load eccentricity and load magnitude. In practical engineering, the conclusions of this study can be used to limit the torsional-flexural vibration response of simple maglev support bridges to ensure the safety of vehicles and passengers.