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Homogenization theory for periodic distributions of elastic cylinders embedded in a viscous fluid
Edgar Reyes-Ayona1, Daniel Torrent, José Sánchez-Dehesa
1Grupo de Fenómenos Ondulatorios, Universitat Politècnica de València, Camino de Vera s.n. (Edificio 7F), ES-46022 Valencia, Spain.
Abstract:
A multiple-scattering theory is applied to study the homogenization of clusters of elastic cylinders distributed in a isotropic lattice and embedded in a viscous fluid. Asymptotic relations are derived and employed to obtain analytical formulas for the effective parameters of homogenized clusters in which the underlying lattice has a low filling fraction. It is concluded that such clusters behave, in the low frequency limit, as an effective elastic medium. Particularly, it is found that the effective dynamical mass density follows the static estimate; i.e., the homogenization procedure does not recover the non-linear behavior obtained for the inviscid case. Moreover, the longitudinal and transversal sound speeds do not show any dependence on fluid viscosity. Numerical simulations performed for clusters made of brass cylinders embedded in glycerin support the reliability of the effective parameters resulting from the homogenization procedure reported here.
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