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Nonlinear, three-dimensional beam theory for dynamic analysis

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Abstract

For beams undergoing large motions but small strains, the displacement field can be decomposed into an arbitrarily large rigid-section motion and a warping field. When applying beam theory to dynamic problems, it is customary to assume that all inertial effects associated with warping are negligible. This paper examines this assumption in details. It is shown that inertial forces affect the beam’s dynamic response in two manners: (1) warping motion induces inertial forces directly, and (2) secondary warping arises that alters the beam’s constitutive laws. Numerical examples demonstrate the range of validity of the proposed approach for beams made of both homogeneous isotropic and heterogeneous anisotropic materials. For low-frequency warping, it is shown that inertial forces associated with warping and secondary warping resulting from inertial forces are negligible. To examine the dynamic behavior of beams over a wider range of frequencies, their dispersion curves, natural vibration frequencies, and mode shapes are evaluated using both one- and three-dimensional models; good correlation is observed between the two models. Applications of the proposed beam theory to multibody problems are also presented; here again, good correlation is observed between the prediction of beam models and of full three-dimensional analysis.

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Authors and Affiliations

  1. University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai, 200240, China

    Shilei Han

  2. Department of Aerospace Engineering, University of Maryland, College Park, Maryland, 20742, USA

    Olivier A. Bauchau

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  1. Shilei Han
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  2. Olivier A. Bauchau
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Correspondence to Shilei Han.

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Han, S., Bauchau, O.A. Nonlinear, three-dimensional beam theory for dynamic analysis. Multibody Syst Dyn 41, 173–200 (2017). https://doi.org/10.1007/s11044-016-9554-3

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