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Published August 15, 2009 | public
Journal Article

Wave propagation in a sandwich structure


The propagation of elastic waves in a sandwich structure with two thin stiff face-plates and a thick compliant core is considered in this paper. A complete description of the dispersion relation with no restrictions on frequency and wavelength is provided. This is accomplished by transforming the wave equation to a Hamiltonian system and then using a transfer matrix approach for solving the Hamiltonian system. To provide insight, particular regimes of the frequency–wavelength plane are then considered. First, an explicit formula is derived for all natural frequencies at the long wavelength limit. It is shown that all waves with finite limiting frequency have zero group velocity, while those with vanishing limiting frequency correspond to longitudinal, shear and flexural waves. The displacement of the flexural waves are reminiscent of Mindlin plates, and an asymptotic procedure to find the shear correction factor is presented. Second, the lowest branch of the dispersion relation is studied in detail and mode shapes are used to motivate explicit but accurate description of this lowest branch. This approximate model is anticipated to be useful in simulations of large structures with sandwich structures.

Additional Information

Copyright © 2009 Elsevier. Received 5 January 2008; revised 31 March 2009. Available online 6 May 2009. This work was carried out while Liping Liu held a position at the California Institute of Technology. The authors gratefully acknowledge the financial support of the US Office of Naval Research through the MURI Grant N00014-06-1-0730.

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