Based on the symplectic transfer-matrix method, this paper develops a novel approach for the analysis of beams presenting periodic heterogeneities along their span. The approach, rooted in the Hamiltonian formalism, generalizes developments presented earlier by the authors for spanwise uniform beams. Starting from the kinematics of a unit cell, the approach proceeds through a set of structure-preserving symplectic transformations and decomposes the solution into its central and extremity components. The geometric configuration and material properties of the unit cell may be arbitrarily complex as long as the cell's two end cross sections are identical. The proposed approach identifies an equivalent, homogenized beam with uniform curvatures and sectional stiffness characteristics along its span. Numerical examples are presented to demonstrate the capabilities of the analysis. Predictions are found to be in excellent agreement with those obtained by full finite-element analysis.
On the Analysis of Periodically Heterogenous Beams
Department of Aerospace Engineering,
University of Maryland,
College Park, MD 20742
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 9, 2015; final manuscript received May 25, 2016; published online June 20, 2016. Assoc. Editor: Alexander F. Vakakis.
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Han, S., and Bauchau, O. (June 20, 2016). "On the Analysis of Periodically Heterogenous Beams." ASME. J. Appl. Mech. September 2016; 83(9): 091001. https://doi.org/10.1115/1.4033721
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