ON UPPER AND LOWER BOUNDS OF THE PROBABILITY OF FAILURE OF SIMPLE STRUCTURES UNDER RANDOM EXCITATION.
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 2>0) that a separable process x(t) crosses barriers at -lambda sub 1 and lambda sub 2 in the interval (O, T) under zero initial condition x(O) = 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1963
- Accession Number
- AD0602528
Entities
People
- M. Shinozuka
Organizations
- Columbia University