In order to develop an accurate one-dimensional model for wave propagation in heterogeneous beams with uniform cross sections, a Hamilton-type principle is developed by incorporating Reissner’s semi-complimentary energy function. Trial displacement and transverse stress fields are constructed from the solutions of micro-boundary value problems (MBVP’s) defined over the cross section. The MBVP’s are developed from asymptotic expansions that assume a small diameter cross section compared to the axial length and a typical signal wavelength. Saint Venant’s semi-inverse torsion and flexure problems are included in the system of MBVP’s. By utilizing the displacement and transverse stress fields constructed from the numerical solutions of the MBVP’s, the constitutive relations are developed. The model generalizes the Mindlin-Hermann rod model and the Timoshenko beam model for anisotropic heterogeneous beams. The accuracy of the model is assessed by comparing the predicted phase velocity spectra to those computed by using a semi-analytical finite element method. Numerical results are shown for reinforced concrete beams with exterior composite layers. [S0021-8936(01)00601-8]
Development of One-Dimensional Models for Elastic Waves in Heterogeneous Beams
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, November 6, 1998; final revision, June 6, 2000. Associate Technical Editor: A. K. Mal. Discussion on the paper should be addressed to the Technical Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Murakami, H., and Yamakawa, J. (June 6, 2000). "Development of One-Dimensional Models for Elastic Waves in Heterogeneous Beams ." ASME. J. Appl. Mech. December 2000; 67(4): 671–684. https://doi.org/10.1115/1.1334860
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