Bernoulli–Euler beams with random field properties under random field loads: fractal and Hurst effects

Responses of Bernoulli–Euler beams with random field properties and also possibly under random field forcing are studied for random fields with linear, Matérn, Cauchy, and Dagum covariances. The latter two allow decoupling of the fractal dimension and Hurst effect. We find second-order characteristics of the beam displacement under various boundary conditions. In a number of cases, the results may be obtained in explicit analytical (albeit lengthy) forms, but as Cauchy and Dagum models are being introduced, one has to resort to numerics.