Uncertainty quantification of tunable elastic metamaterials using polynomial chaos

Abstract

Owing to their periodic and intricate configurations, metamaterials engineered for acoustic and elastic wave control inevitably suffer from manufacturing anomalies and deviate from theoretical dispersion predictions. This work exploits the Polynomial Chaos theory to quantify the magnitude and extent of these deviations and assess their impact on the desired behavior. It is shown that uncertainties stemming from surface roughness, tolerances, and other inconsistencies in a metamaterial's unit cell parameters alter the targetted band gap width, location and the confidence level with which it is guaranteed. The effect of uncertainties are projected from a Bloch-wave dispersion analysis of three distinct phononic and resonant cellular configurations and are further confirmed in the frequency response the finite structures. The analysis concludes with a unique algorithm intended to guide the design of metamaterials in the presence of system uncertainties.

Wave and vibration analysis of elastic metamaterial and phononic crystal beams with slowly varying properties

“…Similarly, Wu et al [32] also proposed a first order perturbation strategy along with interval parameter to evaluate the upper and lower bounds of acoustic metamaterials. Al Ba'ba'a et al [33] investigated the effects of uncertainty on the unit cell parameters of elastic metamaterial using the polynomial chaos expansion. A Bayesian approach for wavenumber identification was proposed by Souza et al [34] using experimental measurements in a elastic metamaterial produced from 3D printing.…”

A Power-Based Framework for Quantifying Parameter Uncertainties in Finite Vibroacoustic Metamaterial Plates

“…As the performance of VAMM depends primarily on the properties of the resonators, any uncertainty or variability in the resonator parameters, such as mass, spring stiffness, and the damping ratio, has an impact on the vibroacoustic performance of the VAMM [ 25 , 26 ]. In the context of industrial applications, the material and manufacturing tolerances can also introduce disturbances that affect the periodicity [ 27 , 28 ].…”

Wave propagation in randomly parameterized 2D lattices via machine learning

“…The influence of uncertainties in geometric parameters, such as plate thickness, resonator radius and resonator length, on the centre position and the bandgap width was studied in [27] by a spectral method based on generalized polynomial chaos (gPC). Uncertainties were evaluated at the unit-cell dispersion level and then via full-scale simulations of finite meta-materials with a prescribed number of cells and a scheme which ensures the desired bandgap [35]. Three different configurations were analyzed using gPC, namely (i) periodic structures with periodic variations, representative of conventional phononic crystals, (ii) a lattice with a periodic elastic foundation, and (iii) a locally resonant meta-material.…”