The First Passage Problem in Random Vibration for a Simple Hysteretic Oscillator
Spencer, Billie Floyd, Jr.
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/71685
Description
Title
The First Passage Problem in Random Vibration for a Simple Hysteretic Oscillator
Author(s)
Spencer, Billie Floyd, Jr.
Issue Date
1985
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Abstract
A method to determine the ordinary statistical moments of time to first passage and to determine the probability of first passage failure for a simple oscillator, incorporating the modified Bouc hysteresis model, has been developed. Two boundary value problems are formulated from Markov process theory and solved by a Petrov-Galerkin finite element method. The first is known as a generalized Pontriagin-Vitt equation, which when solved yields the ordinary moments of time of first passage as a function of the oscillator's initial displacement, initial velocity and initial hysteretic force. In the second formulation, an initial-boundary value problem related to the backward Kolmogorov equation is derived and solved directly for the cumulative function of oscillator reliability, also in terms of the initial state of the oscillator. A comparison of the finite element results with those obtained by Monte Carlo simulation is then given to demonstrate the accuracy of the finite element method. Finally, a method to estimate the reliability of the hysteretic oscillator having prescribed the first few moments of first passage time is considered.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
