The bridge deck is modelled as a simply-supported beam. A moving axle load creates a deflection wave that travels with the train and lingers as damped oscillation behind it, following simple beam-bending and damped-harmonic-motion relations.
deflection(x) ~ P * a(L-x) / (6*L*E*I) * [approx. simply-supported beam under point load]
after load passes: y(t) = y0 * exp(-zeta*omega*t) * cos(omega*t) (damped free vibration)
stress ~ M(x) * c / I
- Train speed - how fast the axle-load point sweeps across the span; higher speed shortens dwell time per point but can excite resonance if it matches the span's natural frequency.
- Axle load - the point force from each axle, directly scaling peak deflection and bending stress at the load's position.
- Structural damping - how quickly residual vibration dies out after the train passes; low damping leaves the deck oscillating visibly longer.
- Send train - launches a multi-axle train across the span so you can watch the deflection wave travel and decay in real time.
Real-world application: this moving-load deflection and residual-vibration behaviour is exactly what rail bridge engineers check against fatigue and resonance limits when certifying a span for higher speeds or heavier freight.