Keywords: power spectral density, spectrum compatible, earthquakes, nonstationary, stochastic process, random vibrations.

To date, elastic response spectrum is the most common method used by the practitioners to represent the seismic action according to various international codes. Due the well known limits of the response spectrum based techniques for determining the seismic response of either nonclassically damped or nonlinear behaving structures, two alternative strategies are usually adopted in the common engineering practice. The first one is based on the direct integration of the equation governing the motion of the structure along with a proper simulation of the accelerograms. This approach is widely used and accepted by various international seismic codes [1]. Unfortunately, international seismic codes do not give a method for generating the time-histories furnishing only the spectrum compatible criteria that have to be satisfied. As a consequence, several methods have been proposed in literature coping with the generation of spectrum compatible accelerograms [2,3]. The second approach assumes that the ground motion is modelled by a stochastic process. The seismic response of the structure is then determined in a probabilistic sense through methods belonging to the stochastic mechanics. Under the assumption that the ground motion is modelled as a zero mean Gaussian stochastic process the above alternative strategies require the definition of a proper power spectral density that have to be spectrum-compatible, i.e. the response spectrum should match the target response spectrum furnished by the seismic code within a certain tolerance.

Furthermore, it is well known that the dynamic response of nonlinear structures is highly influenced by the nonstationary behaviour of the input [4,5]. Thus, a more reliable representation of the seismic action would take into account the time variability of both intensity and frequency content of the ground motion. In this paper a method for determining the evolutionary non-separable spectrum compatible power spectral density is proposed. The method assumes that the ground motion stochastic process is modelled by the superposition of two contributions: the first one is a fully-nonstationary counterpart modelled by a non-separable stochastic process representing local geological and seismological conditions. The second one is a corrective term represented by a quasi-stationary process adjusting the response spectrum of the nonstationary process in order to make it spectrum compatible. The accuracy of the proposed approach is manifested by the matching of the response spectrum of the ensemble spectrum compatible generated earthquakes.

1

International Conference of Building Officials, Uniform Building Code, Vol. 2, 1997.

2

Ahmadi G. "Generation of artificial time-histories compatible with given response spectra - a review", SM archives 4(3): 207-239, 1979.

3

Vanmarcke E.H., Gasparini D.A. "Simulated earthquake ground motions", Proc. 4th Int. Conf. on Smirt, K1/9, San Francisco, 1977.

4

Yeh C.H., Wen Y.K. "Modeling of non-stationary ground motion and analysis of inelastic structural response", Structural Safety, 8(1-4): 281-298, 1990. doi:10.1016/0167-4730(90)90046-R

5

Wang J., Fan L., Qian S. and Zhou J. "Simulations of non-stationary frequency content and its importance to seismic assessment of structures", Earthquake Engineering and Structural Dynamics, 31: 993-1005, 2002. doi:10.1002/eqe.134.abs

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