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Conserved Quantities in Nonlinear Beam Vibrations: An Intrinsic Approach


A. Wynn, Yinan Wang, R. Palacios, P.J. Goulart

Journal of Sound and Vibration, vol. 332, no. 21, pp. 5543-5558

An intrinsic form of the geometrically-nonlinear equations of anisotropic beams is used to identify conserved quantities in large-amplitude free vibrations. The intrinsic description uses both velocities and strains as primary degrees of freedom, with the arbitrarily-large displacements and rotations obtained -if needed- by a subsequent integration in either time or space. The duality between space and time variables in the intrinsic description is carried over to the definition of conserved quantities in time (the total energy) and space (the local cross-sectional power) for the nonlinear beam dynamics. It is further shown that the conservation of total energy can be carried over into truncated versions of the intrinsic equations in modal coordinates. This is studied for nonlinear beam dynamics about both deformed and undeformed reference conditions. In the deformed case, conserved quantities are obtained via Casimir functions. Numerical examples are used to illustrate the main theoretical results.

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% Autogenerated BibTeX entry
@Article { WynEtal:2013:IFA_4284,
    author={A. Wynn and Yinan Wang and R. Palacios and P.J. Goulart},
    title={{Conserved Quantities in Nonlinear Beam Vibrations: An
	  Intrinsic Approach}},
    journal={Journal of Sound and Vibration},
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