Nonlinear Stresses and Deflections of Beams Subjected to Random Time Dependent Uniform Pressure

The nonlinear mean-square multimode response of beams subjected to uniform pressure uncorrelated in time is investigated. The method of equivalent linearization is used to obtain mean-square stresses and displacements in beams with arbitrary end conditions. Calculations are carried out for beams with both ends either simply-supported or clamped, for the case of white noise excitation. Although the maximum displacement can be obtained with the use of only a single-degree-of-freedom model, it is necessary to consider as many as 100 modal functions for accurate determination of the stresses. The maximum mean-square deflection of the clamped beam is found to be somewhat less than the simply-supported beam, whereas the maximum mean-square stresses are as much as twice as large.