Random Vibrations of Structures Under Parametric and Non-Parametric Earthquake Loads
Shih, Teng-Yuan
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Permalink
https://hdl.handle.net/2142/67475
Description
Title
Random Vibrations of Structures Under Parametric and Non-Parametric Earthquake Loads
Author(s)
Shih, Teng-Yuan
Issue Date
1980
Department of Study
Aeronautical and Astronautical Engineering
Discipline
Aeronautical and Astronautical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Aerospace
Language
eng
Abstract
The primary objective of the present study is to assess the effects of gravity force and vertical component of earthquake acceleration on the seismic response of structures. These effects have not been adequately investigated previously, especially from the point of view of random vibration. The secondary objective is to demonstrate the versatility of the mathematical theory of the Markov random process in structural dynamics applications.
This study includes the following topics at increasing complexity: (1) single degree of freedom system with linear elastic behavior, (2) multi-degree of freedom system with linear elastic behavior, (3) single degree of freedom system with nonlinear elastic behavior, (4) single degree of freedom system with type I hysteretic behavior, (5) single degree of freedom system with type II hysteretic behavior, (6) soil-structure system.
Major conclusions of this study are: (1) The deterministic gravity force reduces the lateral stiffness against the floor motion; therefore, lateral structural displacement is increased due to the gravity force. (2) The vertical earthquake acceleration plays the role of a random parametric excitation in the equation of motion for the floor mass. The importance of this parametric excitation depends heavily on the magnitude of the lateral structural displacement itself, the larger the displacement, the more important the vertical earthquake acceleration. (3) In some hysteretic systems, the gravity force and the vertical earthquake excitation not only increase the amplitude of the structural motion, but also increase greatly the permanent deformation of a structure after the structural motion stops. (4) For the particular soil-structure system investigated, the gravity force and vertical earthquake acceleration play even more important roles than if the base of the structure were fixed. (5) The correlation between the horizontal and vertical earthquake accelerations has a contribution to the mean-square structural response if the mean response of the system is not zero. Therefore, this correlation relationship may be important when the structure has an initial displacement either due to foundation settlement or due to forces other than earthquakes. (6) Any practical spectral density of an excitation can be approximated by a rational function of frequency; therefore, the powerful Markov theory always can be applied, although numerical computations may be excessive in some cases.
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