Stochastic incremental dynamics methodology for nonlinear structural systems endowed with fractional derivative terms subjected to code-compliant seismic excitation

Abstract

A novel stochastic incremental dynamics (SIDA) methodology is developed for nonlinear structural systems with fractional derivative elements exposed to a seismic excitation vector consistently aligned with contemporary aseismic codes provisions (e.g. Eurocode 8). Rendering to the concept of non-stationary stochastic processes, the vector of the imposed seismic excitations is characterized by evolutionary power spectra compatible in a stochastic sense with elastic response acceleration spectra of specified modal damping ratio and scaled ground acceleration [1]. The proposed stochastic dynamics technique relies on a combination of stochastic averaging and statistical linearization [2,3] which permits the determination of the response displacement probability density function (PDF) in an efficient and comprehensive manner. The commonly encountered in the literature IDA curves (typically around 7) have been replaced by a SIDA surface providing with reliable higher order statistics (i.e., PDFs) of the system response [4,5]. The determination of related fragilities is identified as a straightforward task whereas a significant attribute of the proposed method is the derivation of an associated response evolutionary power spectrum as a function of spectral acceleration. The method retains the coveted attribute of a particularly low associated computational cost. A structural system comprising the nonlinear model endowed with fractional derivative terms serves as a numerical example for demonstrating the reliability of the proposed methodology. Nonlinear response time-history analysis involving a large ensemble of Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed methodology in a Monte Carlo-based context.

References

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[2] Fragkoulis V. C., Kougioumtzoglou I. A., Pantelous A. A., Beer M., 2019. Non-stationary response statistics of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitation, Nonlinear Dynamics 97, 2291ﾖ2303.

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