On the dynamic behaviour of an elastically supported beam of infinite length, loaded by a concentrated force

  • W. L. Esmeijer


An elastically supported beam of infinite length, initially at rest, carries a variable concentrated force\(\overline K (\overline t )\) at a prescribed point A. General expressions are given for the deflection and the bending moment at A (6.3 and 6.4). Three special cases are considered; the first one is defined by\(\overline K (\overline t )\)=0 for\(\overline t \) and\(\overline K (\overline t )\)=K=const. for\(\overline t \); the second one by\(\overline K (\overline t )\)=0 for 0 >\(\overline t \)>\(\overline t _s \),\(\overline K (\overline t )\) given function of\(\overline t \) for 0⩽\(\overline t \)\(\overline t _s \); the third one applies to problems in which, during the period of impact,\(\overline K (\overline t )\) itself is an unknown. The results given here may be of use in those railway-engineering problems in which a rail can be considered as a beam of infinite length, and in which the supporting ground has the required properties.


Elastic Foundation Concentrate Force Infinite Length Impact Problem Railway Wheel 
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Copyright information

© The Hague Martinus Nijhoff 1949

Authors and Affiliations

  • W. L. Esmeijer
    • 1
  1. 1.Nijverheidsorganisatie T.N.O.Werkgroep TrillingsonderzoekDelft

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