Extension of the regulated stochastic linearization to beam vibrations

In this study, a version of the regulated stochastic linearization technique is proposed for the nonlinear random vibrations of Bernoulli–Euler nonlinear beams. For analysis, in order to balance the error of linearization, we utilize the regulated technique; namely, the appearing nonlinear terms are first replaced by higher-order nonlinear expressions that are subsequently reduced, in stages, to linear ones. It is demonstrated that this seemingly a “roundabout” way is extremely effective to derive a solution that turns out to be much closer to the results provided by the Monte Carlo simulation than those derived via the conventional or potential energy linearization techniques, in the cases of large nonlinearity.