Abstract
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.
Highlights
Flexural metamaterial is an artificially-made elastic metamaterial that tailors flexural waves by periodically arranged sub-wavelength unit cells
According to the previous researches on elastic metamaterials[30,31,32,33], the optical branch with both positive-negative group velocity is usually observed if the material is two- or three-dimensional structure[30,31], or if there exists any coupling between various elastic wave modes[32,33]
We found that the group velocity of the optical branch in flexural metamaterial is governed by a certain condition expressed by the stiffness and inertia ratio of the flexural metamaterial
Summary
Flexural metamaterial is an artificially-made elastic metamaterial that tailors flexural waves by periodically arranged sub-wavelength unit cells. In the previous section it was shown that there is a certain condition defined by the inertia ratio and stiffness ratio, that determines whether the optical branch has positive, negative or both positive-negative group velocity in flexural metamaterials.
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