Vertical Rail Vibrations: Pointforce Excitation

Fourier transform methods together with Floquet's theorem yield Green's function of the periodically supported rail. The track model includes an infinite Euler-Bernoulli beam, pads with stiffness and damping, flexible sleepers plus a massless ballast with stiffness and damping. The exact analytic solution, in the frequency domain, of the linear differential equation governing rail response, yields a simple, comprehensive and computation efficient tool in sound/vibration optimising track constructions. Laboratory rail receptance measurements were taken on a full-scale piece of stiff-padded rail, resting on 13 ballast-embedded concrete sleepers. Measurements/calculations agree well up to 1800 Hz. The curve fitting provides values of pad/ballast parameters. Rails with broad/pronounced attenuation regions radiate less noise; attenuation, influenced by damping and structural irregularity, increases with pad stiffness, shown by numerical examples. With stiff pads, the attenuation coefficient has local minima near sleeper resonances. The pinned-pinned mode, with minute support motion, propagates through periodically supported rails with any pad stiffness. Finally, it is clearly demonstrated how changed pad stiffness and sleeper spacings alter the receptance, affecting both structure-borne sound and vibrations at the sleeper-passing frequency (50–100 Hz) plus noise generation at the pinned-pinned frequency (around 1000 Hz).