Keywords: modal analysis, frequency domain, seismological Fourier spectrum, response.

The need for stochastic dynamic analysis of engineering systems stems from the fact that an important class of structural loads, which evolves with time, exhibits strong variability in both amplitude and frequency content [1]. Excitation processes display a wider power spectrum density function compared with the corresponding response function [2]. The significance of this result is that it verifies the assumption of wide band-limited noise (or even white noise), which is often made for the input of structural dynamic systems.

In random vibration theory, the probability density for the response of a system under Gaussian white noise or band-limited excitation can be calculated based on the frequency information of excitation [3]. This information only requires the computation of the Fourier amplitude spectrum of excitation, which can be calculated based on the seismological method. One of the essential characteristics of the seismological method is that it distills what is known about the various factors affecting ground motions into different functional forms. For regions where the recorded ground motion data is scarce, it becomes imperative to use physical models to represent the ground motion generation and propagation. An advantage of physical models over empirical ones is that meaningful parameters pertaining to source, path attenuation, and site effects can be inferred from the data, thus promoting physical understanding of the underlying processes of strong ground motion generation and attenuation [4].

The formulation of the response in the frequency domain is very efficient in the computation and evaluation of the stochastic response spectrum, which the frequency domain approach is appropriate for probabilistic analyses. In the present paper an attempt has been made to study the effect of the variability in earthquake ground motion variables such as source, path, and site variables on the stochastic response of different frames modelled. The presented frequency domain formulation for the modal response variability is the utilization of suitable explicit relationships between the modal characteristics and the uncertain earthquake ground motion variables.

Dispersion in the drift demand for a given intensity measure of excitation is important in calculating the probability of exceeding a structural limit state. These results provide an important basis for the understanding of the sensitivity of earthquake variables and reveal the effect of these variables on the response of structure. The results reveal that the coefficients of variation of the response in irregular structures are larger than those for regular structures.

1

G.D. Manolis, P.K. Koliopoulos, "Stochastic Structural Dynamics in Earthquake Engineering", WIT, UK, 2001.

2

Y.K. Lin, G.Q. Cai, "Probabilistic Structural Dynamics", McGraw-Hill, 2004.

3

J. Solnes, "Stochastic Processes and Random Vibration: Theory and Practice", John Wiley, New York, 1997.

4

D.M. Boore, "Prediction of ground motion using the stochastic method", Pure Appl. Geophys., 160, 635-676, 2003. doi:10.1007/PL00012553

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