Wave propagation with long-range forces and mistuning effects

Abstract

The present paper investigates the effects induced by long-range connections embedded within a classical D’Alembert waveguide, characterized by the number of connections and the distance between the linked sections of the structures. This new connectivity pattern induces unconventional effects, such as wave-stopping and negative group velocity, which can be adjusted by the features of the superstructure. Furthermore, a mistuning effect is met as consequence of the perturbation of the long-range connection distance. This perturbation may produce the amplification of the nonconventional propagation phenomena, even when the other physical and geometrical properties are unchanged.

Gradient continuum model of nonlocal metamaterials with long-range interactions

“…The long-range interactions in nonlocal material microstructures between subsets of resonant unit cells are designed. Rezaei et al [25] attacked the problem of the nonconventional propagation phenomena in a classical waveguide within which a long-range connectivity pattern is embedded. Then, Rezaei et al [26] investigated wave propagation in a conventional rod integrated with nonlocalities that provide long-range interactions.…”

Propagation of waves in nonlocal-periodic systems

“…The discrete model presented Carpentieri et al [14], which shares resemblance with that of Zingales [15] assumes a modified version for the stress-strain relation equipped with a particular attenuation function, which causes fractional derivatives to appear in the associated dynamics. To identify the existing propagation regimes in one-dimensional long-range systems, Carcaterra and co-authors [16][17][18][19][20][21] confirmed the existence of some unusual regimes such as negative and hypersonic group velocity, providing a general mapping of these effects, even in the presence of delay in nonlocal propagation. In the light of these points, introduction of nonlocalities seems promising to improve the design of acoustic metamaterials.…”