Wave propagation with long-range forces and mistuning effects

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.

Study of Abnormal Group Velocities in Flexural Metamaterials

Generally, it has been known that the optical branch of a simple one-dimensional periodic structure has a negative group velocity at the first Brillouin zone due to the band-folding effect. However, the optical branch of the flexural wave in one-dimensional periodic structure doesn’t always have negative group velocity. The problem is that the condition whether the group velocity of the flexural optical branch is negative, positive or positive-negative has not been studied yet. In consequence, who try to achieve negative group velocity has suffered from trial-error process without an analytic guideline. In this paper, the analytic investigation for this abnormal behavior is carried out. In particular, we discovered that the group velocity of the optical branch in flexural metamaterials is determined by a simple condition expressed in terms of a stiffness ratio and inertia ratio of the metamaterial. To derive the analytic condition, an extended mass-spring system is used to calculate the wave dispersion relationship in flexural metamaterials. For the validation, various numerical simulations are carried out, including a dispersion curve calculation and three-dimensional wave simulation. The results studied in this paper are expected to provide new guidelines in designing flexural metamaterials to have desired wave dispersion curves.