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The Quarterly Journal of Mechanics and Applied Mathematics 1956 9(2):195-206; doi:10.1093/qjmam/9.2.195
© 1956 by Oxford University Press
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A THEORY FOR THE FORCED VIBRATIONS OF A RAILWAY BRIDGE UNDER THE ACTION OF MOVING LOADS

K. MISE and S. KUNII {dagger}

The problem studied is that of the vibrations of a flexible beam supporting a moving locomotive; associated with the locomotive is an alternating load caused by the ‘hammer-blow’ effect. A fundamental differential equation is established and an approximate solution of this equation is derived by making use of the Fourier expansions of certain Jacobian elliptic functions. The predicted ‘dynamic’ defloxions of a bridge of 80 metres span are in good agreement with measured values. The critical speed of the locomotive, for which the dynamic deflexion reaches a maximum value, is predicted accurately.


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