Some closed-form solutions in random vibration of Bernoulli-Euler beams

Author Type

Outside Researcher

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

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

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