@book{143a7438c1b04c438519785692996eab,

title = "Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods",

abstract = "Close approximations to the first passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first passage probability density function and the distribution function for the time interval spent below a barrier before outcrossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval, and hence for the first passage probability density. The results of the theory agree well with simulation results for narrow banded processes dominated by a single frequency, as well as for bimodal processes with 2 dominating frequencies in the structural response.",

keywords = "Random Vibration, Stochastic Processes, First Passage Failure, Bimodal Processes, Integral Equations, Random Vibration, Stochastic Processes, First Passage Failure, Bimodal Processes, Integral Equations",

author = "Nielsen, {S{\o}ren R.K.} and S{\o}rensen, {John Dalsgaard}",

year = "1986",

language = "English",

series = "Structural Reliability Theory ",

publisher = "Institut for Bygningsteknik, Aalborg Universitetscenter",

number = "R8618",

}