NDLI: Transverse Vibration of Two Axially Moving Beams Connected by an Elastic Foundation

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Gaith, Mohamed Mu¨ftu¨, Sinan
Copyright Year	2005
Abstract	Transverse vibration of two axially moving beams connected by a Winkler elastic foundation is analyzed analytically. The system is a model of paper and paper-cloth (wire-screen) used in paper making. The two beams are tensioned, translating axially with a common constant velocity, simply supported at their ends, and of different materials and geometry. Due to the effect of translation, the dynamics of the system displays gyroscopic motion. The Euler-Bernoulli beam theory is used to model the deflections, and the governing equations are expressed in the canonical state form. The natural frequencies and associated mode shapes are obtained. It is found that the natural frequencies of the system are composed of two infinite sets describing in-phase and out-of-phase vibrations. In case the beams are identical, these modes become synchronous and asynchronous, respectively. Divergence instability occurs at the critical velocity; and, the frequency-velocity relationship is similar to that of a single traveling beam. The effects of the mass, flexural rigidity, and axial tension ratios of the two beams, as well as the effects of the elastic foundation stiffness are investigated.
Sponsorship	Dynamic Systems and Control Division
Starting Page	1833
Ending Page	1840
Page Count	8
File Format	PDF
ISBN	0791842169
DOI	10.1115/IMECE2005-80377
e-ISBN	0791837696
Volume Number	Dynamic Systems and Control, Parts A and B
Conference Proceedings	ASME 2005 International Mechanical Engineering Congress and Exposition
Language	English
Publisher Date	2005-11-05
Publisher Place	Orlando, Florida, USA
Access Restriction	Subscribed
Subject Keyword	Geometry Mode shapes Vibration Euler-bernoulli beam theory Deflection Wire screens Dynamics (mechanics) Papermaking Stiffness Tension Textiles
Content Type	Text
Resource Type	Article

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