Long-Range Retarded Elastic Metamaterials: Wave-Stopping, Negative, and Hypersonic or Superluminal Group Velocity

Abstract

This paper investigates new phenomena in elastic wave propagation in metamaterials, characterised by long-range interactions. The kind of waves borne in this context unveil wave-stopping, negative group velocity, instability and hypersonic or superluminal effects, both for instantaneous and for nonlocal retarded actions. Closed form results are presented and a universal propagation map synthesizes the expected properties of these materials. Perspectives in physics, engineering and social dynamics are discussed.

Propagation of waves in nonlocal-periodic systems

“…The integral description of the long-range forces, replacing the summation of the previous examples, implies the existence of all possible interactions between the point and other points fallen within the window ( ). Similar cases are available in the literature [16][17][18][19], investigating the plane-wave response of systems with confined regions of interaction.…”

“…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.…”

Wave propagation with long-range forces and mistuning effects

“…Accordingly, a wide class of new applications arise both in the aerospace and mechanical engineering fields, ranging from cloaking, 5 energy absorption, 6 coupling of distant structures, 7,8 wave control, 9,10 but also swarm dynamics. 11,12 In all these cases, the new features produce effects in terms of changes in wave stability, the emergence of negative group velocity, 13 superfast group and phase propagation 14,15 and band gaps. 16,17…”

Aeroelastic Dynamic Feedback Control of a Volterra Airfoil

“…Moreover, analytical and semi-analytical solutions including describing function technique were used to analyze the instability of control surfaces of a wing with nonlinear stiffness [3]. In the last decade, different methods have been used to investigate nonlinear dynamic systems [4,5], some, based on perturbation method and stochastic approach [6], have been developed to analyze nonlinear aeroelastic systems such as perturbation incremental or transformation point method and homotropy method [7,8].…”