Lutes, Loren D.2018-12-182018-12-181979Chen, Yutang. "First passage probability for two-mode systems." (1979) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/104408">https://hdl.handle.net/1911/104408</a>.https://hdl.handle.net/1911/104408No page 5 in graphsThis study deals with the first-passage time and maximum response statistics of linear systems with one and two degrees of freedom (SDOF and 2-DOF). Emphasis is placed on empirical studies of the first-passage time of 2-DOF systems. The empirical results were obtained from a digital computer simulation, with the Gaussian white noise excitation obtained from a random number generator subroutine. Maximum response distribution is compared with the Gumbel type 1 distribution as well as Poisson crossings, Vanraarcke's and Mark's analytical approximate results. A simple empirical approximation equation is determined for SDOF systems from the study of the probability of first-passage time distribution. This equation is shown to be in good agreement in general, with the empirical data and with numerical results obtained by Roberts. The Gumbel type 1 distribution is compared with the empirical data. It appears to fit quite well for moderate failure levels and diverge for very large failure levels for both SDOF and 2-DOF systems. The results of Poisson crossings, Vanmarcke's and Mark's analytical theories do not give good approximations to the maximum response distribution of 2-DOF systems, particularly for small damping values. A considerable amount of empirical data is obtained for first-passage probability of 2-DOF systems. Emphasis is placed on the limiting decay rate (a) of survival probability, since this has been shown to be a useful parameter to characterize first-passage probability in SDOF systems. In particular, the dependence of a on the barrier level (b) is studied, and similarities with and differences from SDOF results are considered. No general formula is obtained for predicting a from knowledge of b, and system parameters.144 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.ThesisRICE2043reformatted digitalTHESIS C.E. 1979 CHEN