Abstract

Two kinds of numerical approaches able to predict the dynamic response of periodic structures and metamaterials are presented. Both of them are model reduction techniques which can be used to obtain the response functions of the structures at a low computational cost. The first kind of approaches employs the wave finite element (WFE) method for modeling 1D periodic structures made up of complex substructures, e.g., 2D cells of arbitrary shapes. Resonant metamaterials are particular cases of periodic structures where the substructures possess local resonances — e.g., layered substructures involving soft layers and heavy layers/core —, which in turn lead to band gap effects and low vibration levels. Although well-suited for modeling periodic structures in the frequency domain, the WFE method also works for periodic structures subject to time-dependent excitations. The second kind of approaches employs finite element (FE) procedures for modeling 2D periodic structures, and 2D nearly periodic structures involving substructures with slightly varying (random) geometrical properties. For nearly periodic structures like plates with disordered resonant 2D cells, results show that the vibrational energy is localized around the excitation sources.

Highlights

  • Periodic structures are frequently encountered in engineering applications, e.g., in the aeronautic and railway industries

  • This paper aims at investigating the modeling of 1D and 2D periodic structures, of finite dimensions, subject to various kinds of excitations and boundary conditions

  • For 2D periodic structures, a reduced finite element (FE) modeling of the substructures based on the CB method has been proposed

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Summary

Introduction

Periodic structures are frequently encountered in engineering applications, e.g., in the aeronautic (fuselages, turbines) and railway industries. The forced response analysis of periodic structures is much less reported This especially means developing numerical models able to predict the dynamic response of periodic structures of finite dimensions with various kinds of boundary conditions, or assemblies of finite dimensions involving several periodic structures and other non-periodic components which are systems of practical interest in engineering applications. In this case, the analysis of the band gap effects does rely on the wave propagation properties, and on the boundary and coupling conditions which induce energy conversion between waves

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