Bending-torsional vibration response of modified Timoshenko thin-walled beams under moving harmonic loads

In this paper, a new method is proposed for calculating the bending-torsional vibration response of modified Timoshenko thin-walled beams under moving harmonic loads. The boundary conditions of the beams are considered to be simply supported at both ends. By using Fourier and Laplace transformations, analytical solutions for vibration responses are derived. For the validation of the proposed method, the results obtained using the proposed method are compared with those acquired by the finite element method (FEM). Through the parametric analysis, the effects of cross-sectional properties as well as the load magnitude, velocity, and eccentricity are further investigated. The results indicate that: (1) compared to the method that ignores shear rotary inertia, the vertical displacement of the beam at the midspan calculated by the proposed method shows an accuracy improvement of up to 6.87%; (2) the bending-torsional vibration frequency increases with the growth of the torsional moment of inertia; (3) when the velocity increases from 20 m/s to 80 m/s, the difference in the maximum displacement at the midspan is essentially within 5%; (4) the bending-torsional vibration response is significantly influenced by the load magnitude and eccentricity, whereas the vibration frequency of the beam remains unaffected by these variations; (5) an increase in load velocity does not always lead to a greater response from the beam, which can be explained from the perspective of resonance.