Free vibration of viscoelastically supported beam bridges under moving loads: Closed-form formula for maximum resonant response

In this paper, a closed-form approximate formula for estimating the maximum resonant response of beam bridges on viscoelastic supports (VS) under moving loads is proposed. The methodology based discrete approximation fundamental vertical mode non-proportionally damped Bernoulli–Euler beam, which allows derivation expressions modal characteristics and amplitude free vibration at mid-span VS beams. Finally, an to estimate acceleration beams passage articulated trains has been Verification studies prove that estimates peaks with good accuracy useful tool preliminary assessment railway considering effect soil-structure interaction resonance. combination use full train signatures through Residual Influence Line (LIR) method, proposed solution yields results also in lower range speeds, where sub-harmonics are more intensely reduced by damping.