Resonance and cancellation in torsional vibration of monosymmetric I-sections under moving loads

This paper is concerned with the lateral and torsional coupled vibration of monosymmetric I-beams under moving loads. To this end, a train is modeled as two subsystems of eccentric wheel loads of constant intervals to account for the front and rear wheels. By assuming the lateral and torsional displacements to be restrained at the two ends of the beam, both the lateral and torsional displacements are approximated by a series of sine functions. The method of variation of constants is adopted to derive the closed-form solution. For the most severe condition when the last wheel load is acting on the beam, both the conditions of resonance and cancellation are identified. Once the condition of cancellation is enforced, the resonance response can always be suppressed, which represents the optimal design for the beam. Since the condition for suppressing the torsional resonance is exactly the same as that for the vertical resonance, this offers a great advantage in the design of monosymmetric I-beams, as no distinction needs to be made between the suppression of vertical or torsional resonance.