Correlated disorder in rainbow metamaterials for vibration attenuation

Abstract

Metastructures are typically composed of periodic unit cells designed to present enhanced dynamic properties in which either single or multiple resonators are periodically distributed. Even though the periodic metamaterials can obtain bandgaps with outstanding vibration attenuation, the widths of bandgaps can still be narrow for some practical applications. Rainbow metamaterials have been proposed based on gradient or random profiles to provide further improved attenuation. Nonetheless, the effects of correlated random disorder on their attenuation performance remains an open challenge. This work presents an investigation on the effects of correlated disorder on the vibration attenuation of rainbow metamaterials. An analytical model using the transfer matrix approach is used to calculate the receptance functions in a finite length metastructure composed of evenly spaced non-symmetric resonators attached to a beam with Π-shaped cross-section, thus a multi-frequency metastructure. The correlated disorder is modelled using random fields and an analytical expression of the Karhunen-Loève expansion is used such that spatial correlation on the resonator properties is modified by various correlation lengths, i.e., the level of spatial smoothness. Individual samples of random fields are used to investigate the effects of the correlated disorder in the vibration attenuation of a multi-frequency metastructure. It is shown that the bandgap can be further widened when compared to uncorrelated disorder. The obtained results indicates that a combination of the gradient profile with some level of disorder, typically resulting from random fields with larger correlation lengths, tends to give improved vibration attenuation when compared to a optimized gradient rainbow metamaterial. It opens new and innovative ways for the design of broadband rainbow metastructures for vibration attenuation.

Vibration Characteristics of Asymmetric Flexible Cantilever Beams Connected to a Central Rigid Body

“…This phenomenon is known as disorder, i.e., real conditions deviating from the ideal ones [12][13][14]. Investigations have demonstrated that the dynamical properties of disordered systems create considerable changes due to the asymmetry of the structures, and many researchers have carried out studies on the vibration properties of disordered periodic structures [15][16][17][18]. Laxalde and Pierre [19] established the reducedorder dynamics model for multi-stage disordered cyclic symmetric bladed disk assemblies, explored the modal localization properties of the disordered bladed disk, and analyzed the influence of the disorder degree on the sensitivity of the bladed disk.…”

Acoustic performance of architected hybrid metamaterials for sound attenuation applications

“…[46][47][48][49] Whenever one wishes to calculate the dispersion curves of a porous structure, its main advantage is that it permits any frequency dependence and damping to be implemented in the problem. Moreover, recently researcher have proposed exciting novel architected metamaterials with improve attenuation and low-frequency phononic band-gaps such as 3D printed architected hollow sphere foams 50 and rainbow metamaterials based on gradient or random profiles. 51 This study investigated the sound absorption characteristics of various novel AMM UCs and some UCs adopted from literature.…”

Isolamento acústico de baixa frequência via metapainel de ressonadores de membrana decorada

“…Os metamateriais baseados em periodicidade só podem atenuar baixas frequências se forem grandes e volumosos, o que implica grande limitação de aplicações práticas. Já os fundamentados em ressonâncias locais, ainda que eventualmente não contem com investigações robustas o suficiente para a fabricação em massa, mostram frequentemente uma performance relevante mesmo com pouca massa e volume adicionados aos sistemas em que atuam (GAO et al, 2022;FABRO;CHRONOPOULOS, 2021).…”