Chapter Three - Critical Excitation for Nonproportionally Damped Structural Systems

Abstract

This chapter explains a new probabilistic critical excitation method for nonstationary inputs to nonproportionally damped structural systems. In contrast to most of the conventional critical excitation methods, a stochastic response index is treated as the objective function. The power and the intensity of the excitations are fixed and the critical excitation is found under these restrictions. The key for finding the new nonstationary random critical excitation for nonproportionally damped structural systems is the exchange of the order of the double maximization procedures with respect to time and to the power spectral density (PSD) function. Numerical examples of a 6-degree-of-freedom shear building model with nonproportional damping subjected to nonstationary inputs are presented. These examples disclose the time-varying characteristics of the nonstationary transfer function multiplied by the envelope function of the input motion model. These demonstrate the validity of the present critical excitation method.