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REVIEW ARTICLES

Response and Discretization Methods for Axially Moving Materials

[+] Author and Article Information
J. A. Wickert

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh PA 15213

C. D. Mote

Department of Mechanical Engineering, University of California, Berkeley CA 94720

Appl. Mech. Rev 44(11S), S279-S284 (Nov 01, 1991) doi:10.1115/1.3121365 History: Online April 30, 2009

Abstract

Through a convective acceleration component, the equations of motion for axially-moving materials are skew-symmetric in the state space formulation, so that the response problem is best analyzed within the broader context of continuous gyroscopic systems. With particular application to the prototypical traveling string and beam models, a modal analysis that associates degrees of freedom with the complex state eigenfunctions and their conjugates is presented. This procedure is well-suited for harmonic excitation sources, and in some instances, it is more convenient than previous methods which decompose the modal coordinates, eigenfunctions, and generalized forces into real and imaginary components. Also from the state space perspective, Rayleigh’s quotient for gyroscopic systems provides a variational method for determining the eigensolutions of axially-moving materials. Ritz discretization of the quotient can make effective use of the speed-adapting modes of the traveling string and beam models as they are rich in phase, as well as amplitude, content.

Copyright © 1991 by American Society of Mechanical Engineers
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