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Two classes of exact solutions in the linear elastodynamics of transversely isotropic solids

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Abstract

Due to the formal resemblance of some models for the Cauchy stress tensor of elastic solids and viscous fluids, some classes of exact solutions for the equations governing the flows in Navier–Stokes fluids have been generalized to linear and nonlinear elastodynamics. In this paper, we study the conditions under which two special classes of generalized Beltrami flows, the vortices in lattice form and Kelvin’s cat’s eye solutions, are solutions of the equations governing the motions in a linearly elastic transversely isotropic solid.

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Notes

  1. Note that since \(\varvec{B}\) and \(\varvec{D}\) have different physical dimensions, the infinitesimal shear modulus in (2) and the viscosity in (3) have different physical dimensions although they are usually denoted with the same greek letter (\(\mu \)).

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Acknowledgements

GS and LV are supported by NextGenerationEU PRIN2022 grant no. 2022P5R22A.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Texas A &M University, 400 Bizzell Street, College Station, TX, 77843, USA

    Kumbakonam R. Rajagopal

  2. Dipartimento di Ingegneria, Università degli Studi di Perugia, Via Goffredo Duranti 93, 06125, Perugia, Italy

    Giuseppe Saccomandi & Luigi Vergori

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  1. Kumbakonam R. Rajagopal
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  2. Giuseppe Saccomandi
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  3. Luigi Vergori
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Correspondence to Giuseppe Saccomandi.

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Rajagopal, K.R., Saccomandi, G. & Vergori, L. Two classes of exact solutions in the linear elastodynamics of transversely isotropic solids. Ricerche mat 73 (Suppl 1), 275–291 (2024). https://doi.org/10.1007/s11587-023-00845-2

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