Nonstationary random critical excitation for nonproportionally damped structural systems

Abstract

During the last three decades, the critical excitation methods have been developed extensively to account for inherent uncertainties in predicting forthcoming earthquake events and to construct design earthquake ground motions in a reasonable way. Most of the proposed theories are based on deterministic approaches. In contrast to the conventional critical excitation methods, a stochastic response index is treated in this paper as the objective function to be maximized. The power (area of power spectral density, PSD, function) and the intensity (magnitude of PSD function) are fixed and the critical excitation is found under these restrictions. It is shown that the original idea for stationary random inputs can be utilized effectively in the procedure for finding a critical excitation for nonstationary random vibrations of nonproportionally damped structural systems. The key for finding the new nonstationary random critical excitation is the exchange of the order of the double maximization procedures with respect to time and to the PSD function.