Some closed-form solutions in random vibration of Bernoulli-Euler beams
College
Engineering and Computer Science
Department
Ocean and Mechanical Engineering
Document Type
Article
Publication/Event/Conference Title
International Journal of Engineering Science
Publication Status
Version of Record
Abstract
The only closed-form solutions for random vibration of beams are that due to Houdijk, for the tip mean-square displacement of a cantilever beam under space- and time-wise ideal white noise, and that due to Eringen 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 Crandall and Yildiz 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. © 1984.
First Page
1291
Last Page
1301
DOI
10.1016/0020-7225(84)90022-3
Publication Date
1-1-1984
Recommended Citation
Elishakoff, Isaac and Livshits, David, "Some closed-form solutions in random vibration of Bernoulli-Euler beams" (1984). Faculty Scholarship. 668.
https://digitalcommons.fau.edu/faculty_papers/668