Response to Arbitrarily Time-Varying Forces Using Convex Model

An energy-bound convex model is used to estimate the maximum structural response of single-degree-of-freedom and multiple-degree-of-freedom structural systems which are subjected to arbitrarily time-varying forces. Convex models specify uncertainties in the absence of detailed probabilistic information about the variables of interest. The concept of convex models provides an alternative way of analysis when a limited amount of information about the excitation is available. The subjective decisions which result when using convex models to incorporate uncertainty do not involve the element of chance. In general, convex models yield estimates of the maximum response that are conservative. In the present paper, equations for reduction factors are given for arbitrary time-varying forces of unknown shape. The reduction factors are independent of the value of the energy bound. The resulting predictions obtained by the reduced convex model estimates are within reasonable agreement to the maximum response obtained by time-history analysis of the arbitrarily time-varying forces.