Probabilistic solution for one-dimensional plane wave propagation in homogeneous bilinear hysteretic materials

This paper describes the development of a probabilistic solution for stress wave propagation in homogeneous bilinear hysteretic materials subjected to an exponentially decaying surface airblast pulse. The partial derivative method is used to calculate the time histories of the moments of the dependent (output) variables, consisting of particle displacement, particle velocity, and stress, in terms of functions of moments of the independent (input) variables. The partial derivatives are evaluated numerically using finite-difference approximations. Several sensitivity analyses are conducted to illustrate how the solution technique can be used to quantify and rank the relative effects of input variabilities or uncertainties on the dispersion of output quantities. Finally, application of the methodology for conducting probabilistic analyses of airblast-induced vertical ground shock is demonstrated.