Wave propagation and non-local effects in periodic frame materials: Generalized continuum mechanics

Céline Chesnais (1) , Claude Boutin (2) , Stéphane Hans (2)

1 IFSTTAR/GERS/SV - Séismes et Vibrations
2 CeLyA - centre Lyonnais d'Acoustique

Through the analysis of the wave propagation in infinite two-dimensional periodic frame materials, this paper illustrates the complexity of their dynamic behavior. Assuming the frame size is small compared to the wavelength, the homogenization method of periodic discrete media coupled with normalization is used to identify the macroscopic behavior at the leading order. The method is applied on a frame material with the vertical elements stiffer than the horizontal elements. Such a material is highly anisotropic and presents a large contrast between the rigidities of the possible mechanisms. Thus the waves associated with different kinematics appear in different frequency ranges. Moreover, the stiffer elements can deform in bending at the macroscopic scale. The equivalent continuum is a second-grade medium at the leading order and shear waves can be dispersive. A criterion is proposed to easily determine when this bending effect has to be taken into account. Second-grade media, generalized media

Mots clés: PROPAGATION DES ONDES; HOMOGENEISATION; DYNAMIQUE; RESONANCE; MATERIAU RETICULE; METAMATERIAU

Domaines: Acoustique [physics.class-ph]

Céline Chesnais, Claude Boutin, Stéphane Hans. Wave propagation and non-local effects in periodic frame materials: Generalized continuum mechanics. Mathematics and Mechanics of Solids, 2015, 20 (8), pp 929-958. ⟨10.1177/1081286513511092⟩. ⟨hal-00967960v2⟩