# Wave propagation in one-dimensional diatomic metastructure with high- static-low-dynamic stiffness

## Palavras-chave:

HSLDS, Metastructure, Dispersion relation, Bandgap## Resumo

In this work, we explore wave propagation in a one-dimensional diatomic periodic structure with high-

static-low-dynamic stiffness (HSLDS) characteristics, which is a geometric nonlinearity. A diatomic chain consists

of two different masses per unit cell, and diatomic periodic structures can present interesting dynamic characteris-

tics, in which waves can attenuate within frequency bands that are called bandgaps. A periodic structure consists

fundamentally of identical components, the cells, connected in a way that characteristics of mass, stiffness, and or

damping are spatially repeated, and present interesting characteristics for vibration attenuation that are not found

in classical structures. These characteristics have been explored for automotive and aerospace applications, among

others, as structures with low mass are paramount for these industries, and keeping low vibration levels in a wide

frequency range is also desirable.

We use closed-form first-order approximation via perturbation analysis to study wave propagations by disper-

sion relations of the infinite structure considering the effect of nonlinear terms. We verify the nonlinear bandgap

seen via the dispersion relation by comparing it to the transmissibility of a finite structure. We use the disper-

sion relation to analyse how some parameters can influence the bandgaps, such as the mass ratio between the cell

elements and amplitude.