Non-linear vibration of a traveling tensioned beam
type: Item
instance of: scholarly article
title: Non-linear vibration of a traveling tensioned beam
zbMATH Open document ID: 0779.73025
DOI: 10.1016/0020-7462(92)90016-Z
published in: International Journal of Non-Linear Mechanics
publication date: 1993-04-01T00:00:00Z
review text: (From author's abstract.) Free nonlinear vibration of an axially moving, elastic, tensioned beam is analyzed over the sub- and supercritical transport speed ranges. The pattern of equilibria is analogous to that of Euler column buckling and consists of the straight configuration and of non-trivial solutions that bifurcate with speed. A perturbation theory for the near-modal free vibration of a general gyroscopic system with weakly nonlinear stiffness and/or dissipation is derived through the asymptotic method of Krylov, Bogolyubov and Mitropol'skij. The contribution of nonlinear stiffness to the response increases with subcritical speed, grows most rapidly near the critical speed, and can be several times greater for a translating beam than for one that is not translating. In the supercritical speed range, asymmetry of the nonlinear stiffness distribution biases finite-amplitude vibration toward the straight configuration and lowers the effective modal stiffness. The linear vibration theory underestimates stability in the subcritical range, overestimates it for supercritical speeds, and is most limited in the near-critical regime.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 150205
zbMATH Keywords: Euler column buckling
zbMATH Keywords: perturbation theory
zbMATH Keywords: asymptotic method of Krylov, Bogolyubov and Mitropol'skij
zbMATH Keywords: nonlinear stiffness
zbMATH Keywords: subcritical speed
zbMATH Keywords: critical speed
zbMATH Keywords: supercritical speed
zbMATH Keywords: stability
author: J. A. Wickert
reviewed by: J. Genin
MaRDI profile type: Publication
full work available at URL: 0020-7462(92)90016-z
OpenAlex ID: W1992909849
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description: scientific article; zbMATH DE number 150205