Maximum entropy modeling of discrete uncertain properties with application to friction

The first part of the present investigation focuses on the formulation of a novel stochastic model of uncertain properties of media, homogenous in the mean, which are represented as stationary processes. In keeping with standard spatial discretization methods (e.g., finite elements), the process is discrete. It is further required to exhibit a specified mean, standard deviation, and a global measure of correlation, i.e., correlation length. The specification of the random process is completed by imposing that it yields a maximum of the entropy. If no constraint on the sign of the process exists, the maximum entropy is achieved for a Gaussian process the autocovariance of which is constructed. The case of a positive process is considered next and an algorithm is formulated to simulate the non-Gaussian process yielding the maximum entropy. In the second part of the paper, this non-Gaussian model is used to represent the uncertain friction coefficient in a simple, lumped mass model of an elastic structure resting on a frictional support. The dynamic response of this uncertain system to a random excitation at its end is studied, focusing in particular on the occurrence of slip and stick.