# Accession Number:

## AD0602528

# Title:

## ON UPPER AND LOWER BOUNDS OF THE PROBABILITY OF FAILURE OF SIMPLE STRUCTURES UNDER RANDOM EXCITATION.

# Descriptive Note:

## Technical rept.

# Corporate Author:

## COLUMBIA UNIV NEW YORK INST FOR THE STUDY OF FATIGUE AND RELIABILITY

# Personal Author(s):

# Report Date:

## 1963-12-01

# Pagination or Media Count:

## 26.0

# Abstract:

Upper and lower bounds are given for the probability P sub x T - lambda sub 1, lambda sub 2 lambda sub 1, lambda sub 20 that a separable process xt crosses barriers at -lambda sub 1 and lambda sub 2 in the interval O, T under zero initial condition xO O. The displacement of a damped oscillator with one degree of freedom due to a nonstationary Gaussian random input is investigated as an illustration of an analysis that does not require the input to be white noise. If failure of the system is assumed to occur when the absolute value of the displacement exceeds a critical value lambda, then P sub x infinity -lambda, lambda is the probability of failure of the system. Under certain conditions, approximations for lower and upper bounds of P sub x infinity - lambda, lambda are numerically evaluated with the aid of an electronic digital computer. The result shows that the present method estimates P sub x infinity - lambda, lambda in a sufficiently narrow interval and over a sufficiently wide range of the probability values as required in reliability analysis. Applications to air and spacecraft subject to infrequent severe atmospheric turbulence and to structures subject to earth quake accelerations are suggested. Author

# Descriptors:

- *PROBABILITY
- *STRUCTURES
- *OSCILLATORS
- RELIABILITY
- RELIABILITY
- FAILURE(MECHANICS)
- LINEAR SYSTEMS
- STRESSES
- MECHANICAL PROPERTIES
- SPACECRAFT
- ATMOSPHERIC MOTION
- EARTHQUAKES
- MOTION
- EQUATIONS
- STATISTICAL FUNCTIONS
- STOCHASTIC PROCESSES
- CALCULUS OF VARIATIONS
- COMPUTER PROGRAMMING
- DIGITAL COMPUTERS
- STATISTICAL ANALYSIS