Analysis of dispersive waves in repetitive lattices based on homogenized second-gradient continuum models

• Published in: Composite structures 2016-09, Vol.152, p.712-728
• Main Authors: Reda, H., Rahali, Y., Ganghoffer, J.F., Lakiss, H.
• Format: Article
• Language: English
• Subjects: Beams (radiation); Continuums; Dispersive waves; Dissipative effects; Engineering Sciences; Homogenization; Homogenizing; Lattices; Mathematical models; Networks; Pantograph; Pantographs; Periodic lattices; Second-gradient models; Wave propagation
• ISSN: 0263-8223; 1879-1085
• DOI: 10.1016/j.compstruct.2016.05.080

We analyze the dispersion of elastic waves in periodic beam networks based on second order gradient models obtained by the homogenization of the initially discrete network. The lattice beams have a viscoelastic behavior described by Kelvin–Voigt model and the homogenized second gradient viscoelasticity model reflects both the lattice topology, anisotropy and microstructural features in terms of its geometrical and micromechanical parameters. The continuum models enriched with the higher-order gradients of the displacement and velocity introduce characteristic lengths parameters which account for microstructural effects at the mesoscopic level. A comparative study of the dispersion relations and damping ratio evolutions for the longitudinal and shear waves has been done for four lattices (the chiral diamond lattice, the classical and reentrant lattices, and the pantograph). The developed model allows analyzing both the effects of damping and internal length scale through the second order displacement gradients on the wave propagation characteristics. An important increase of the natural frequency due to second order effects is observed. For the pantograph lattice, the phase velocity for the longitudinal and shear modes is identical and is not influenced by the direction of wave propagation. The obtained results show overall that the pantograph lattice present the best acoustic characteristics.