A reduced-order macroscopic homogenized continuum for locally resonant metamaterials
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This study proposes a computational homogenization framework to study the dynamics of locally resonant acoustic metamaterial structures. On applying well-established scale transition relations to a representative volume element incorporating the resonant units at the microscale, a reduced-order macroscopic homogenized continuum is recovered with governing equations that do not involve additional variables to describe the microscale dynamics. In particular, the model-order reduction is carried out by formulating the micro- and macroscale problems in the frequency domain, discretizing the two problems by a standard finite-element approach and performing an exact dynamic condensation of all degrees of freedom at the microscale. The transient dynamics is captured by means of an appropriate inverse Fourier transform relying on the Exponential Window Method. The proposed computational framework is numerically validated by transient dynamic analyses on a 2D acoustic metamaterial structure, comparing the results obtained from the homogenized continuum against the corresponding results of direct numerical simulations in ABAQUS.
