The First Passage Time Problem for Simple Structural Systems

[+] Author and Article Information
J. W. Shipley

Martin Marietta Corporation, Orlando, Fla.

M. C. Bernard

School of Engineering Science and Mechanics, Georgia Institute of Technology, Atlanta, Ga.

J. Appl. Mech 39(4), 911-917 (Dec 01, 1972) (7 pages) doi:10.1115/1.3422890 History: Received June 10, 1971; Online July 12, 2010


This paper presents an analysis of the first passage time problem. A lumped-parameter model for a structural system is considered, and the excitation is limited to white noise. The response of this type of system is a Markov process on a multidimensional position-velocity space (for a damped harmonic oscillator the position-velocity space is two-dimensional). The Markov property is used to develop an integral equation for the first passage time-density function. Numerical results are presented for the damped harmonic oscillator. A rest start condition is considered, i.e., position and velocity are zero, and symmetric position boundaries are considered for the region of safe operation.

Copyright © 1972 by ASME
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