Some closed-form solutions in random vibration of Bernoulli-Euler beams
The only closed-form solutions for random vibration of beams are that due to \textit{A. Houdijk} (1928), for the tip mean-square displacement of a cantilever beam under space- and time-wise ideal white noise, and that due to \textit{A. C. Eringen} [J. Appl. Mech. 24, 46-52 (1957; Zbl 0081.184)] for a simply-supported beam under identical excitation. In both instances, beams possessing transverse damping were treated. In the present study closed-form solutions are found for uniform, simply supported beams subjected to a stationary excitation that is white both in space and time. The beams possess either structural, Voigt or rotary damping mechanisms. Expressions are obtained for the space-time correlation functions of displacement, velocity and stress. Previously derived interesting conclusions by \textit{S. H. Crandall} and \textit{A. Yildiz} [ibid. 29, 267-275 (1962; Zbl 0108.378)] on divergence of the mean-square stress for a beam with Voigt damping, and its convergence for the beam with combined transverse and rotary damping, are confirmed. Moreover, the closed form solution is obtained for the probabilistic characteristics of a beam under a number of separate or combined dampings.
space-time correlation functions of displacement
scientific article; zbMATH DE number 3887236
scientific article