Internal instability of thin-walled beams under harmonic moving loads. (May 2022) - Yang, Y.B.; Shi, K.; Mo, X.Q.; Wang, Zhi-Lu; Xu, Hao; Wu, Y.T.
Abstract: Frequent resonance may result in excessive vibrations and endanger the safety of bridges. Firstly, the governing equations of motion are derived for the vertical, lateral and torsional vibrations of a mono-symmetric thin-walled box beam under a harmonic moving load. Then the resonance conditions are derived by letting the denominator of the response of concern equal to zero. For the mono-symmetric beam, the vertical resonance is uncoupled, but the torsional and lateral resonances are coupled. When in vertical resonance, the vertical motion of the beam will diverge by growing to a maximum during the acting period of the moving load. Similar phenomenon exists for the torsional–flexural resonance. A specific case occurs when the above two resonance frequencies coincide, for which the critical length of the beam can be determined. The phenomenon of simultaneous resonance is a kind of internal instability featured by the fact that the beam can transform repetitively from the vertical mode to the torsional–flexural mode, and vice versa, with no additional energy input. To avoid the inherent internal instability, a beam should be designed with a length not equal or close to the critical length presented in this paper. All the aforementioned resonances have been extensively studied for cases involving both harmonic and random moving loads and validated by the finite element analysis. Highlights: Derive new closed-form solutions for a thin-walled beam under a harmonic moving load. Present the resonance conditions for the vertical flexural and torsional–flexural resonances. Show a specific case when the above two resonances coincide to result in the internal instability. Propose an expression to determine the critical length for the specific case.