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

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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.

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Authors and Affiliations

  1. Electrical Engineering Department, University of California, 405 Hilgord Avenue, 90024-1594, Los Angeles, CA, USA

    A. V. Balakrishnan

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  1. A. V. Balakrishnan
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Research supported in part under Grant No. 88-0252, AFOSR, USAF.

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Balakrishnan, A.V. Damping operators in continuum models of flexible structures: Explicit models for proportional damping in beam bending with end-bodies. Appl Math Optim 21, 315–334 (1990). https://doi.org/10.1007/BF01445168

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  • DOI: https://doi.org/10.1007/BF01445168

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