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TECHNICAL PAPERS

Development of One-Dimensional Models for Elastic Waves in Heterogeneous Beams

[+] Author and Article Information
H. Murakami

Department of Mechanical and Aerospace Engineering, University of California, 9500 Gilman Drive, La Jolla, CA 92093-0411

J. Yamakawa

Department of Mechanical Engineering, The National Defense Academy Yokosuka 239-8686, Japan

J. Appl. Mech 67(4), 671-684 (Jun 06, 2000) (14 pages) doi:10.1115/1.1334860 History: Received November 06, 1998; Revised June 06, 2000
Copyright © 2000 by ASME
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References

Kapania,  R. K., and Raciti,  S., 1989, “Recent Advances in Analysis of Laminated Beams and Plates, Part I: Shear Effects and Buckling,” AIAA J., 27, pp. 923–934.
Bank,  L. C., and Kao,  C. H., 1990, “Dynamic Response of Thin-Walled Composite Material Timoshenko Beams,” ASME J. Energy Resour. Technol., 112, pp. 149–154.
Song,  O., and Librescu,  L., 1993, “Free Vibration of Anisotropic Composite Thin-Walled Beams of Closed Cross-Section Contour,” J. Sound Vib., 167, pp. 129–147.
Kosmatka,  J. B., and Dong,  S. B., 1991, “Saint-Venant Solutions for Prismatic Anisotropic Beams,” Int. J. Solids Struct., 28, pp. 917–938.
Pecastaings,  F., Sun,  Z., and Davenne,  L., 1991, “A Saint Venant’s Heterogeneous Beam Theory,” Eur. J. Mech. A/Solids, 10, pp. 45–69.
Timoshenko,  S., 1921, “On the Correction for Shear of the Differential Equation for Transverse Vibration of Prismatic Bars,” Philos. Mag., 41, pp. 744–746.
Mindlin, R. D., and Herrmann, G., 1951, “A One-Dimensional Theory of Compressional Waves in an Elastic Rod,” Proceedings of the 1st U.S. National Congress of Applied Mechanics, ASME, New York, pp. 187–191.
Pochhammer,  L., 1876, “Ueber die Fortpflanzungsgeschwindigkeiten Kleiner Schwingungen in Einem Unbegrenzten Isotropen Kreiscylinder,” Z. Math., 81, pp. 324–336.
Love, A. E. H., 1927, A Treatise on the Mathematical Theory of Elasticity, 4th Ed., Cambridge University Press, London.
Graff, K. F., 1975, Wave Motion in Elastic Solids, Ohio State University Press, Columbus, Ohio.
Yamakawa,  J., and Murakami,  H., 1997, “Longitudinal and Flexural Wave Propagation in Reinforced Concrete Columns,” Int. J. Solids Struct., 34, pp. 4357–4376.
Onoe,  M., McNiven,  H. D., and Mindlin,  R. D., 1962, “Dispersion of Axially Symmetric Waves in Elastic Rods,” ASME J. Appl. Mech., 29, pp. 729–734.
Pao,  Y.-H., and Mindlin,  R. D., 1960, “Dispersion of Flexural Waves in an Elastic Circular Cylinder,” ASME J. Appl. Mech., 27, pp. 513–520.
Reissner,  E., 1984, “On a Certain Mixed Variational Theorem and a Proposed Application,” Int. J. Numer. Methods Eng., 20, pp. 1366–1368.
Murakami,  H., Reissner,  E., and Yamakawa,  J., 1996, “Anisotropic Beam Theories With Shear Deformation,” ASME J. Appl. Mech., 63, pp. 660–668.
Lekhnitskii, S. G., 1963, Theory of Elasticity of an Anisotropic Elastic Body, Holdin-Day, San Francisco (translated by P. Fern).
Reissner,  E., 1950, “On a Variational Theorem in Elasticity,” J. Math. Phys., 29, pp. 90–95.
Bensoussan, A., Lions, J. L., and Papanicolaou, G., 1978, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam.
Murakami,  H., and Hegemier,  G. A., 1986, “A Mixture Model for Unidirectionally Fiber-Reinforced Composites,” ASME J. Appl. Mech., 53, pp. 765–773.
Timoshenko, S., and Goodier, J. N., 1970, Theory of Elasticity, 3rd Ed., McGraw-Hill, New York.
Sokolnikoff, I. S., 1956, Mathematical Theory of Elasticity, 2nd Ed., McGraw-Hill, New York.
Murakami,  H., and Yamakawa,  J., 1998, “Torsional Wave Propagation in Reinforced Concrete Columns,” Int. J. Solids Struct., 35, pp. 2617–2637.
Cowper,  G. R., 1966, “The Shear Coefficient in Timoshenko’s Beam Theory,” ASME J. Appl. Mech., 33, pp. 335–340.
Dhamarajan,  S., and McCutchen,  H., 1973, “Shear Coefficients for Orthotropic Beams,” J. Compos. Mater., 7, pp. 530–535.
Yamakawa, J., 1996, “Mechanical Modeling of RC Beams,” Ph.D. dissertation, University of California at San Diego, La Jolla, CA.

Figures

Grahic Jump Location
Heterogeneous beams with (a) circular and (b) square cross sections
Grahic Jump Location
(a) A contour plot of torsional warping ũ3(2)(α) for the circular cross section, (b) a contour plot of torsional warping ũ3(2)(α) for the square cross section
Grahic Jump Location
(a) A contour plot of flexural warping u⁁3(3)(α) for the circular cross section, (b) a contour plot of flexural warping u⁁3(3)(α) for the square cross section
Grahic Jump Location
A contour plot of u⁁1(1)(α) for the square cross section
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(a) A contour plot of longitudinal warping u⁁3(2)(α) for the circular cross section, (b) a contour plot of longitudinal warping u⁁3(2)(α) for the square cross section
Grahic Jump Location
(a) Longitudinal phase velocity spectra for the beam with the circular cross section, (b) longitudinal phase velocity spectra for the beam with the square cross section
Grahic Jump Location
(a) Flexural phase velocity spectra for the beam with the circular cross section, (b) flexural phase velocity spectra for the beam with the square cross section
Grahic Jump Location
(a) Torsional phase velocity spectra for the beam with the circular cross section, (b) torsional phase velocity spectra for the beam with the square cross section

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