Influence of initial imperfections on nonlinear free vibration of elastic bars
type: Item
instance of: scholarly article
title: Influence of initial imperfections on nonlinear free vibration of elastic bars
zbMATH Open document ID: 0567.73068
DOI: 10.1007/BF01175801
author: J. Blot
published in: Acta Mechanica
publication date: 1985-01-01T00:00:00Z
review text: Nonlinear free vibration of elastic bars possessing initial imperfections is studied. This generalizes the problem of a perfect bar studied previously by \textit{S. Woinowsky-Krieger} [J. Appl. Mech. 17, 35-36 (1950; Zbl 0036.133)] and \textit{D. Burgreen} [ibid. 18, 135-139 (1951)]. For the vibration frequency the differential equation is solved exactly in terms of complete elliptic integrals. Numerical results demonstrate that the initial imperfections usually reduce the frequency of nonlinear free vibration of elastic bars subjected to moderate compression, but there are exceptions with the opposite effect. The exact solution is contrasted with timewise single-term and two-term Galerkin approximations. It turns out that while the single-term treatment fails to show the increase, the two-term treatment brings it out with attendant close agreement with the exact solution.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 3905979
zbMATH Keywords: Nonlinear free vibration
zbMATH Keywords: elastic bars
zbMATH Keywords: initial imperfections
zbMATH Keywords: vibration frequency
zbMATH Keywords: differential equation
zbMATH Keywords: solved exactly
zbMATH Keywords: terms of complete elliptic integrals
zbMATH Keywords: Numerical results
MaRDI profile type: Publication
cites work: Q5794184
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description: scientific article; zbMATH DE number 3905979