## A mathematical treatise on vibrations in railway bridges |

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### Contents

Deflections of beams obtained by methods of harmonic | 1 |

Oscillations produced by moving loads of constant magni | 26 |

Oscillations produced by a moving alternating force taking | 36 |

9 other sections not shown

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### Common terms and phrases

2irNt 2irqrt 2ttx accuracy alternating force anti-phased approximation bridge oscillations central deflection due central dynamic deflection Chapter coefficients corresponding crawl-deflection critical frequency curve of deflection damping resistance deduced differential equation driving-wheels dynamic bending-moment dynamical increment effect expressed feet span feet units forced oscillation formula free oscillation fundamental frequency girder hammer-blows harmonic analysis harmonic component harmonic series Hence higher critical inertia couples inertia forces live-load allowance load distribution loaded frequencies locomotive characteristics locomotive is passing long-span bridges magnitude mathematical analysis maximum central dynamic measured in feet measured in tons method mode of vibration moving load natural frequency obtained oscillations due passing the centre quadratic equation railway bridges resonance section distant shewn in Fig shews short-span bridges similar locomotives skidding locomotive speed spring friction spring movement spring-borne mass starting conditions statical superposed takes the form tion total mass uniformly distributed unit length vertical