Authors: Chatterjee, Tanmoy
Karličić, Danilo 
Cajić, Milan 
Adhikari, Sondipon
Friswell, Michael I.
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Uncertainty quantification in inerter-based quasiperiodic lattices
Journal: International Journal of Mechanical Sciences
Volume: 249
First page: 108258
Issue Date: 2023
Rank: ~M21a
ISSN: 0020-7403
DOI: 10.1016/j.ijmecsci.2023.108258
Abstract: 
Inerter-based periodic structures have attracted significant interest among the research community due to their wide range of applications. However, existing studies on quasiperiodic structures, especially with inerters, are limited. Therefore, this timely work investigates the dynamics of novel one-dimensional inerter-based quasiperiodic lattices with and without local resonators. The quasiperiodicity is introduced through the modulation of both spring and inerter properties resulting in the well-known Hofstadter-like butterfly spectrum having a fractal structure. Moreover, by considering the appropriate boundary conditions and many mass–spring-inerter subsystems, the bulk spectrum of the system is investigated demonstrating the existence of multiple edge states in lower and higher frequency ranges. The deterministic study showed that the effect of inertia amplification is to reduce the frequencies of the Hofstadter-like butterfly and to widen the low frequency band gaps. The second contribution of this work involves investigating the effect of parametric uncertainty for the acoustic-metamaterial-like chain based on Monte Carlo simulations. Moreover, to address the computational aspect of the problem, grey-box modeling using machine learning was performed. A Gaussian process model was trained on a limited dataset and was found to capture the stochastic responses of the lattices adequately. The statistical variation of parameters with different levels of uncertainty demonstrated significant effects on the Hofstadter-like butterfly, band gaps, corresponding edge states and frequency responses. The sensitivity of the dynamic behavior in quasiperiodic lattices to variabilities reveal the need to account for system uncertainties for their targeted performance as future vibration absorbers and energy harvesters. The study also paves the way to utilize the results as useful prior information for robust design optimization of real inerter-based quasiperiodic lattice devices.
Keywords: Acoustic metamaterials | Edge states | Gaussian process | Hofstadter's butterfly | Quasiperiodic lattices | Uncertainty quantification
Publisher: Elsevier

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