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Nonstationary Response of Structures and its Application to Earthquake Engineering


Hou, Zhikun (1990) Nonstationary Response of Structures and its Application to Earthquake Engineering. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/db5g-6572.


This thesis presents a simplified state-variable method to solve for the nonstationary response of linear MDOF systems subjected to a modulated stationary excitation in both time and frequency domains. The resulting covariance matrix and evolutionary spectral density matrix of the response may be expressed as a product of a constant system matrix and a time-dependent matrix, the latter can be explicitly evaluated for most envelopes currently prevailing in engineering. The stationary correlation matrix of the response may be found by taking the limit of the covariance response when a unit step envelope is used. The reliability analysis can then be performed based on the first two moments of the response obtained.

The method presented facilitates obtaining explicit solutions for general linear MDOF systems and is flexible enough to be applied to different stochastic models of excitation such as the stationary models, modulated stationary models, filtered stationary models, and filtered modulated stationary models and their stochastic equivalents including the random pulse train model, filtered shot noise, and some ARMA models in earthquake engineering. This approach may also be readily incorporated into finite element codes for random vibration analysis of linear structures.

A set of explicit solutions for the response of simple linear structures subjected to modulated white noise earthquake models with four different envelopes are presented as illustration. In addition, the method has been applied to three selected topics of interest in earthquake engineering, namely, nonstationary analysis of primary-secondary systems with classical or nonclassical dampings, soil layer response and related structural reliability analysis, and the effect of the vertical components on seismic performance of structures. For all the three cases, explicit solutions are obtained, dynamic characteristics of structures are investigated, and some suggestions are given for aseismic design of structures.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:structures ; response ; earthquake engineering
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Iwan, Wilfred D.
Group:Earthquake Engineering Research Laboratory
Thesis Committee:
  • Unknown, Unknown
Defense Date:27 April 1990
Other Numbering System:
Other Numbering System NameOther Numbering System ID
EERL Report90-01
Funding AgencyGrant Number
Record Number:CaltechThesis:03112014-153421620
Persistent URL:
Related URLs:
URLURL TypeDescription ItemTechnical Report EERL 90-01 in CaltechAUTHORS
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8125
Deposited By: Kathy Johnson
Deposited On:12 Mar 2014 21:51
Last Modified:17 Aug 2021 19:53

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