Convex models for impulsive response of structures

A nonprobabilistic method for determining the maximum response of a dynamic system to an impulse is presented. The method is based on the theory of convex models. Unlike the probabilistic approach, the convex model is described as a set of constraints in terms of the excitation energy The convex model requires less information about the uncertain nature of the excitation and its numerical evaluation is simpler than the probabilistic model. Two convex models are used to estimate the maximum response of dynamic systems subjected-td uncertain impulsive loads. The convex models are based on the assumption that the energy of the impulse is bounded. A reduction factor, defined by dividing the result obtained from the convex model to that obtained from the actual record, is used to calibrate the convex models. For impulses of known shape and duration, the reduction factor remains constant for different levels of the energy bound. An average reduction factor is also defined for impulses of unknown shape and duration but known energy bound, which still yields acceptable predictions of the maximum response.