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Stability analysis of a substructured model of the rotating beam

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Abstract

One of the most well-known situations in which nonlinear effects must be taken into account to obtain realistic results is the rotating beam problem. This problem has been extensively studied in the literature and has even become a benchmark problem for the validation of nonlinear formulations. Among other approaches, the substructuring technique was proven to be a valid strategy to account for this problem. Later, the similarities between the absolute nodal coordinate formulation and the substructuring technique were demonstrated. At the same time, it was found the existence of a critical angular velocity, beyond which the system becomes unstable that was dependent on the number of substructures. Since the dependence of the critical velocity was not so far clear, this paper tries to shed some light on it. Moreover, previous studies were focused on a constant angular velocity analysis where the effects of Coriolis forces were neglected. In this paper, the influence of the Coriolis force term is not neglected. The influence of the reference conditions of the element frame are also investigated in this paper.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Structural Engineering, Mechanics and Materials, University of California, Berkeley, CA, 94720, USA

    J. Valverde

  2. Department of Mechanical and Materials Engineering, University of Seville, Camino de los Descubrimientos s/n, 41092, Seville, Spain

    D. García-Vallejo

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  1. J. Valverde
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  2. D. García-Vallejo
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Correspondence to J. Valverde.

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Valverde, J., García-Vallejo, D. Stability analysis of a substructured model of the rotating beam. Nonlinear Dyn 55, 355–372 (2009). https://doi.org/10.1007/s11071-008-9369-8

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