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      Generalized Kelvin–Voigt Damping for Geometrically Nonlinear Beams

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          Abstract

          Strain-rate-based damping is investigated in the strong form of the intrinsic equations of three-dimensional geometrically exact beams. Kelvin–Voigt damping, often limited in the literature to linear or two-dimensional beam models, is generalized to the three-dimensional case, including rigid-body motions. The result is an elegant infinite-dimensional description of geometrically exact beams that facilitates theoretical analysis and sets the baseline for any chosen numerical implementation. In particular, the dissipation rates and equilibrium points of the system are derived for the most general case and for one in which a first-order approximation of the resulting damping terms is taken. Finally, numerical examples are given that validate the resulting model against a nonlinear damped Euler–Bernoulli beam (where detail is given on how an equivalent description using our intrinsic formulation is obtained) and support the analytical results of energy decay rates and equilibrium solutions caused by damping. Throughout the paper, the relevance of damping higher-order terms, arising from the geometrically exact description, to the accurate prediction of its effect on the dynamics of highly flexible structures is highlighted.

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          Most cited references27

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          Classical Normal Modes in Damped Linear Dynamic Systems

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            Geometrically Exact, Intrinsic Theory for Dynamics of Curved and Twisted Anisotropic Beams

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              A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams

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                Author and article information

                Contributors
                Journal
                aiaaj
                AIAA Journal
                AIAA Journal
                American Institute of Aeronautics and Astronautics
                1533-385X
                30 October 2020
                January 2021
                : 59
                : 1
                : 356-365
                Affiliations
                Imperial College London , London, England SW7 2AZ, United Kingdom
                Author notes
                [*]

                Graduate Research Assistant, Department of Aeronautics, Room CAGB 308, South Kensington Campus; marc.artola16@ 123456imperial.ac.uk . Student Member AIAA.

                [†]

                Senior Lecturer, Department of Aeronautics, Room CAGB 340, South Kensington Campus; a.wynn@ 123456imperial.ac.uk .

                [‡]

                Professor in Computational Aeroelasticity, Department of Aeronautics, Room CAGB 338, South Kensington Campus; r.palacios@ 123456imperial.ac.uk . Associate Fellow AIAA.

                Article
                J059767 J059767
                10.2514/1.J059767
                5347b1aa-d597-490a-9f82-99e94750e620
                Copyright © 2020 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the eISSN 1533-385X to initiate your request. See also AIAA Rights and Permissions www.aiaa.org/randp.
                History
                : 06 May 2020
                : 23 July 2020
                : 20 August 2020
                Page count
                Figures: 7, Tables: 2
                Funding
                Funded by: H2020 Marie Skłodowska-Curie Actionshttp://dx.doi.org/10.13039/100010665
                Award ID: 765579
                Categories
                Regular Articles
                p2235, Structures, Design and Test
                p2668, Stress-Strain Analysis
                p1977, Flexible and Active Structures
                p2056, Structural Analysis
                p6300, Mechanical and Structural Vibrations
                p20598, Mechanism and Machines
                p2057, Finite Element Method
                p6151, Beam (Structures)
                p1947, Structural Modeling and Simulation
                p6299, Structural Kinematics and Dynamics

                Engineering,Physics,Mechanical engineering,Space Physics
                Variational Asymptotic Method,Beam (Structures),Stiffness Matrices,Damping Mechanisms,Total Energy,Structural Dynamics,Proportional Damping,Euler Bernoulli Beams,Flexible Structures,Stress Distribution

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