Some closed-form solutions in random vibration of Bernoulli-Euler beams
type: Item
instance of: scholarly article
title: Some closed-form solutions in random vibration of Bernoulli-Euler beams
zbMATH Open document ID: 0556.73088
DOI: 10.1016/0020-7225(84)90022-3
author: David Livshits
author: Isaac Elishakoff
published in: International Journal of Engineering Science
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74H50
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 3887236
zbMATH Keywords: structural damping
zbMATH Keywords: closed-form solutions
zbMATH Keywords: uniform, simply supported beams
zbMATH Keywords: stationary excitation
zbMATH Keywords: white both in space and time
zbMATH Keywords: rotary damping mechanisms
zbMATH Keywords: space-time correlation functions of displacement
zbMATH Keywords: velocity
zbMATH Keywords: stress
zbMATH Keywords: divergence of the mean-square stress
zbMATH Keywords: Voigt damping
zbMATH Keywords: probabilistic characteristics
zbMATH Keywords: separate or combined dampings
MaRDI profile type: Publication
full work available at URL: 0020-7225(84)90022-3
OpenAlex ID: W1978825970
cites work: Q3249463
cites work: The Brownian Motion of Strings and Elastic Rods
cites work: Q3270412
cites work: Random Vibration of Beams
cites work: Q3258376
cites work: Q4131788
cites work: Q3690379
cites work: Q3671491
Recommended article: A remarkable nature of the effect of boundary conditions on closed-form solutions for vibrating inhomogeneous Bernoulli-Euler beams
Recommended article: A solution method for Euler-Bernoulli vibrating discontinuous beams
Recommended article: Closed-form solutions for Euler-Bernoulli arbitrary discontinuous beams
Recommended article: Random Eigenvalue Problems for Bending Vibrations of Beams
Recommended article: Exact solutions for stochastic Bernoulli-Euler beams under deterministic loading
Recommended article: Mean-square response of an infinite Bernoulli-Euler beam to nonstationary random excitation
Recommended article: Q3820097
Recommended article: Apparently first closed-form solutions for inhomogeneous vibrating beams under axial loading
Recommended article: Closed-form solutions of Euler-Bernoulli beams with singularities
Recommended article: Apparently first closed-form solution for vibrating inhomogeneous beams
description: scientific article; zbMATH DE number 3887236