Solution on first passage problem for simple linear and nonlinear oscillators by finite element method

The problem of determining the probability that a structure becomes unsafe under random excitation over a given period of time is addressed. The excitation is modeled as zero mean Gaussian white noise, and the structure is modeled as a simple oscillator: linear, hardening Duffing, VanderPol, and power-law damped. Failure corresponds to first exceedance of symmetrically disposed absorbing barriers. This is the well known first passage problem in random vibration. A well posed initial-boundary value problem for the failure process is derived from Markov process theory and is solved by a Petrov-Galerkin finite element method. Also, a boundary value problem for the moments of the failure process is derived and similarly solved. Failure of higher dimensional systems is reviewed, and a model technique is proposed to compute a conservative bound to the failure distribution. Also, the temporal effects of dynamic load combinations on simple system reliability are studied by modulating the white noise excitation.National Science Foundation 83/11 NSF NEA 80 23263 83/1