Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Damping operators in continuum models of flexible structures: Explicit models for proportional damping in beam bending with end-bodies

Damping operators in continuum models of flexible structures: Explicit models for proportional... A convenient “working” model for passive damping in a flexible structure is proportional damping. Strictly proportional damping requires that the damping operator be (essentially) the square root of the stiffness operator. In this paper we present an explicit calculation of the square root for the case of the bending of a uniform Bernoulli beam clamped at one end and subject to control forces and moments at the other end, and we show that nonlocal terms are added in the interior as well as at the ends in contrast to the case where there are no end-masses and both ends are simply supported. We show that if strict proportionality is relaxed to require only asymptotic proportionality, then we can avoid the nonlocal feature although the boundary equations will still need to include additional terms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Damping operators in continuum models of flexible structures: Explicit models for proportional damping in beam bending with end-bodies

Applied Mathematics and Optimization , Volume 21 (1) – Mar 23, 2005

Loading next page...
 
/lp/springer-journals/damping-operators-in-continuum-models-of-flexible-structures-explicit-FurE5uF9zl

References (10)

Publisher
Springer Journals
Copyright
Copyright © 1990 by Springer-Verlag New York Inc.
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/BF01445168
Publisher site
See Article on Publisher Site

Abstract

A convenient “working” model for passive damping in a flexible structure is proportional damping. Strictly proportional damping requires that the damping operator be (essentially) the square root of the stiffness operator. In this paper we present an explicit calculation of the square root for the case of the bending of a uniform Bernoulli beam clamped at one end and subject to control forces and moments at the other end, and we show that nonlocal terms are added in the interior as well as at the ends in contrast to the case where there are no end-masses and both ends are simply supported. We show that if strict proportionality is relaxed to require only asymptotic proportionality, then we can avoid the nonlocal feature although the boundary equations will still need to include additional terms.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Mar 23, 2005

There are no references for this article.