Chapter Twelve - Critical Excitation for Earthquake Energy Input Rate

Abstract

This chapter discusses a critical excitation method for earthquake energy input rate. It explores a new probabilistic critical excitation method for identifying the critical frequency content of ground motions maximizing the mean earthquake energy input rate to structures. The critical excitation problem includes a double maximization procedure with respect to time and to the power spectral density (PSD) function. The key to finding the critical frequency content is the order exchange in the double maximization procedure. No mathematical programming technique is required in the proposed method. It is shown that the proposed technique is systematic and the critical excitation can be found extremely efficiently within a reasonable accuracy. Extension of the proposed method is discussed for a more general ground motion model. The chapter discusses the process to derive a new expression on the probabilistic earthquake input energy and its rate in terms of uniformly modulated and nonuniformly modulated ground motion models. The process to formulate a new critical excitation problem with the probabilistic earthquake energy input rate as the criticality measure is mentioned. A deterministic expression of earthquake energy input rate to a base-isolated building model is also presented in order to capture the properties of earthquake energy input rate in more detail.