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

Summary

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.