Abstract
We consider a linear complex elastic material whose body point motion is described by two vectorial generalised co-ordinates of any dimension. We suppose that the medium obeys Lagrange equations. Elastic energy depends on both of these vectorial generalised co-ordinates but does not depend on the gradient of one of them (“special” co-ordinate). Such a complex medium can be interpreted as a “bearing continuum” (corresponding to the non-special co-ordinate), whose body points are enhanced by body points of “continuum of dynamic absorbers” (corresponding to the special co-ordinate), the latter not connected directly between them. We obtain that under some restrictions for the strain energy bulk plane harmonic waves in this infinite medium have a band gap (or band gaps), the medium being thus a single negative acoustic metamaterial, and for some cases decreasing part(s) of dispersion curve, thus being a double negative acoustic metamaterial in this zone. We consider some examples of such continua with rotational degrees of freedom.
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Acknowledgements
This work was supported by the Russian Foundation for Basic Research (grant 17-01-00230), by Spanish Government Agency Ministerio de Economía y Competitividad (project No. FIS2014-54539-P) and by Andalusian Government (Junta de Andalucía), support for research group FQM-253.
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Grekova, E.F. (2019). Reduced Enhanced Elastic Continua as Acoustic Metamaterials. In: Altenbach, H., Belyaev, A., Eremeyev, V., Krivtsov, A., Porubov, A. (eds) Dynamical Processes in Generalized Continua and Structures. Advanced Structured Materials, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-030-11665-1_14
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DOI: https://doi.org/10.1007/978-3-030-11665-1_14
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