Two Degree-of-Freedom Elastoplastic Response to a Step Velocity Pulse

The response of a two-degree-of-freedom elastoplastic system subjected to an instantaneous change in velocity is presented. The specific excitation considered is of interest in problems involving severe shocks of short duration, and, specifically, to problems of vehicular collision, package cushioning of sensitive equipment, air delivery, and building frames subject to ground shock. The approach used consists in studying first the response on the assumption that one of the two springs remains elastic while the other spring deforms beyond the limiting elastic range. For example, it was found that when only base spring yielding is allowed, the law of variation of the maximum deformation of the base spring conforms to that of a single-degree-of-freedom elastoplastic system. Next, consideration is given to systems for which both springs can yield, and, for certain combinations of the parameters, approximate relationships are presented for defining conditions under which yielding is likely to be localized in one of the springs.