Periodically arranged acoustic metamaterial in industrial applications: The need for uncertainty quantification. (1st January 2020) - Henneberg, J.
Highlights: Non-sampling based stochastic methods are combined with the wave finite element method for uncertainty quantification in periodic structures. The influence of uncertainties within periodic structures can be approximated with the introduced super cell approach. Guidelines to apply the presented approach to a wide range of periodic structures are presented. Abstract: Structures with periodically arranged resonators have attracted attention within vibroacoustics recently. These periodic structures attenuate wave propagation in a defined frequency range. Engineers can tune the resonators to produce structures with a desired band gap behavior. The majority of the established stop band materials is produced by additive manufacturing today. While promising scientific results have been achieved with this method, it is not yet fit for industrial applications. In order to develop new manufacturing approaches and to close the gap between science and industry, the influence of uncertainties of periodic structures has to be quantified. In this study, the influence of geometrical uncertainties on periodic structures is investigated. The authors develop a finite element model of an epoxy plate with beam resonators for this purpose. In a parameter study, the influence of some parameters is identified. Afterwards, the behavior of stop band material with uncertain input parameters is studied using spectral stochastic methods. Having predefined probability density functions, the generalized polynomial chaos expansion is used to propagate the uncertainty of these parameters. The stop band behavior is accordingly represented by the generalized polynomial chaos having unknown deterministic coefficients. A collocation-based stochastic simulation is used to estimate the coefficients employing the deterministic finite element model as a black-box. The results show the necessity of regarding uncertainties in periodic structures. The performed stochastic simulations are suitable to define manufacturing tolerances for the production of stop band material.