Green's function of a periodically supported, infinite beam describes rail responses to moving loads, where the excitation may depend on roughnesses, varying rail receptance together with vehicle weight including the wheel inertia. The frequency domain solution of the linear differential equation governing rail response, yields a simple, comprehensive and computation efficient tool in sound/vibration optimising track constructions. A railway wheel traversing a sleeper-supported rail 'sees' a varying receptance downwards. This parametric excitation, causing the wheel to move up and down at the sleeper-passing frequency (50-100 Hz), is a source of low frequency structure-borne sound and vibration, with implications for nearby buildings, passanger compartments and radiation from railway bridges. Coincidence, between the sleeper-passing frequency and wheel-ballast resonance, results in great amplitudes. A comparison with long-scale 'roughness' excited rail vibrations shows that parametric excitation dominates below the wheel-ballast resonance, assuming the same 'roughness' amplitude as the static deflection variation. The dynamic contact force caused by short-scale roughnesses fluctuates through the sleeper bays, with stiff pads providing an extra excitation mechanism around the pinned-pinned frequency (similar to 1000 Hz). Softer pads may lower vibration levels at the sleeper-passing frequency and around the pinned-pinned frequency; at the same time, however, other levels may increase. [References: 24]
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