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Harmonic waves in elastic sandwich plates

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Abstract

Motions of a sandwich plate with symmetric facings are studied in the framework of the three-dimensional equations of elasticity. Both the core and facings are assumed to be isotropic and linearly elastic.

Harmonic wave solutions, which satisfy traction-free face conditions and continuity conditions of tractions and displacements at the interfaces, are obtained for four cases: symmetric plane strain solutions for extensional motion, antisymmetric plane strain solutions for flexural motion, and solutions for the symmetric and antisymmetric SH-waves. The dispersion relation for each of these cases is obtained and computed. In order to exhibit the effect of the ratios of facing to core thicknesses, elastic stiffnesses and densities, on the dynamic behavior of sandwich plates, dispersion curves are computed and compared for plates with “thick, light, and soft” facings as well as for plates with “thin, heavy, and stiff” facings. Asymptotic expressions of dispersion relations for extensional, flexural, and symmetric SH-waves are obtained in explicit form, as the frequencies and wave numbers approach zero.

The thickness vibrations in sandwich plates are studied in detail. The resonance frequencies and modal functions of the thickness-shear and thickness-stretch motions are obtained. Simple algebraic formulas for predicting the lowest thickness-shear and the lowest thickness-stretch frequencies are deduced. The orthogonality of the thickness modal functions is established.

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Authors and Affiliations

  1. Department of Civil Engineering, Princeton University, 08540, Princeton, N.Y., U.S.A.

    P. C. Y. Lee & Nagyoung Chang

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  1. P. C. Y. Lee
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  2. Nagyoung Chang
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Lee, P.C.Y., Chang, N. Harmonic waves in elastic sandwich plates. J Elasticity 9, 51–69 (1979). https://doi.org/10.1007/BF00040980

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  • DOI: https://doi.org/10.1007/BF00040980

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