4.7 Article

A novel reduced-order dynamic-stiffness formulation for locally resonant metamaterial plates

Journal

COMPOSITE STRUCTURES
Volume 280, Issue -, Pages -

Publisher

ELSEVIER SCI LTD
DOI: 10.1016/j.compstruct.2021.114811

Keywords

Metamaterial plate; Local resonance; Dynamic-stiffness method; Model-order reduction

Funding

  1. Italian Ministry of Education, University and Research (MIUR) [2017J4EAYB]

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The study introduces a novel dynamic-stiffness formulation for analyzing the dynamics of locally resonant metamaterial plates. The method accurately calculates the natural frequencies and modal responses of the plates, providing closed analytical forms for modal responses under arbitrary loading conditions assuming classical damping. The comparison with finite-element results in ABAQUS demonstrates the accuracy and effectiveness of the proposed reduced-order dynamic-stiffness formulation.
A novel dynamic-stiffness formulation is presented to study the dynamics of locally resonant metamaterial plates. Focusing on an assembly of plates coupled by periodic arrays of resonators, the formulation hinges on a reduced-order dynamic-stiffness model obtained by exact dynamic condensation of the degrees of freedom within the resonators. Two are the main results. First, a reduced-order global dynamic-stiffness matrix is constructed, to calculate natural frequencies and undamped modes by the Wittrick-Williams algorithm. Second, two specific orthogonality conditions are derived for the modes of the plates only, which lead to closed analytical forms for the modal response under arbitrary loading, in time and frequency domains, under the assumption of classical damping. Remarkably, the modal response is obtained for the whole set of response variables, including those within the resonators. The comparison with finite-element results obtained in ABAQUS substantiates accuracy and effectiveness of the proposed reduced-order dynamic-stiffness formulation.

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