Dynamic plastic behaviour of a notched free-free beam subjected to step-loading at one end

A rigid perfectly plastic model is developed to study the initial, small deflection response of a free-free beam with an initial notch along its span under a concentrated step-loading suddenly applied at one end of the beam. Complete solutions are obtained for various combinations of the magnitude of the load, the location of the notch and its defect-severity. The partitioning of the initial energy dissipation rates is discussed for some typical situations. It is concluded that: (i) the different initial deformation mechanisms and the initial energy dissipation rate of the beam depend not only on the magnitude of the load but also on the defect-severity and location of the notch; (ii) because of the influence of the notch, the structural response of the beam is far more complicated than that of the un-notched free-free beam; and (iii) for some cases the maximum rate of energy dissipation in plastic hinges will be more than 1/3 of the total input energy rate, while for an un-notched free-free beam, it has been demonstrated that the plastic dissipated energy is always less than 1/3 of the input energy [Int. J. Impact Engng 21 (1998) 165].