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Some Observations on the Random Response of Hysteretic Systems


Paparizos, Leonidas G. (1987) Some Observations on the Random Response of Hysteretic Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/w5wv-5f87.


In this thesis, the nature of hysteretic response behavior of structures subjected to strong seismic excitation, is examined. The earthquake ground motion is modeled as a stochastic process and the dependence of the response on system and excitation parameters, is examined. Consideration is given to the drift of structural systems and its dependence on the low frequency content of the earthquake spectrum. It is shown that commonly used stochastic excitation models, are not able to accurately represent the low frequency content of the excitation. For this reason, a stochastic model obtained by filtering a modulated white noise signal through a second order linear filter is used in this thesis.

A new approach is followed in the analysis of the elasto-plastic system. The problem is formulated in terms of the drift, defined as the sum of yield increments associated with inelastic response. The solution scheme is based on the properties of discrete Markov process models of the yield increment process, while the yield increment statistics are expressed in terms of the probability density of the velocity and elastic component of the displacent response. Using this approach, an approximate exponential and Rayleigh distribution for the yield increment and yield duration, respectively, are established. It is suggested that, for duration of stationary seismic excitation of practical significance, the drift can be considered as Brownian motion. Based on this observation, the approximate Gaussian distribution and the linearly divergent mean square value of the process, as well as an expression for the probability distribution of the peak drift response, are obtained. The validation of these properties is done by means of a Monte Carlo simulation study of the random response of an elastoplastic system.

Based on this analysis, the first order probability density and first passage probabilities for the drift are calculated from the probability density of the velocity and elastic component of the response, approximately obtained by generalized equivalent linearization. It is shown that the drift response statistics are strongly dependent on the normalized characteristic frequency and strength of the excitation, while a weaker dependence on the bandwidth of excitation is noted.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Civil Engineering
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Civil Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Iwan, Wilfred D.
Group:Earthquake Engineering Research Laboratory
Thesis Committee:
  • Iwan, Wilfred D. (chair)
  • Knowles, James K.
  • Caughey, Thomas Kirk
  • Beck, James L.
  • Hall, John F.
Defense Date:3 October 1986
Other Numbering System:
Other Numbering System NameOther Numbering System ID
EERL Report86-02
Additional Information:Thesis title listed in 1987 Commencement Program varies from actual thesis: Some Observation on the Random Response of Hysteretic Systems.
Funding AgencyGrant Number
Fluor CorporationUNSPECIFIED
Record Number:CaltechTHESIS:04152019-163242410
Persistent URL:
Related URLs:
URLURL TypeDescription ItemTechnical Report EERL 86-02 in CaltechAUTHORS
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11467
Deposited By: Mel Ray
Deposited On:16 Apr 2019 14:30
Last Modified:23 Aug 2021 23:23

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