Fast vibro-acoustic response computations for finite periodic metamaterial plates using a generalized Bloch Mode Synthesis based sub-structuring approach

Abstract

Metamaterials have recently emerged and shown great potential for noise and vibration reduction in specific frequency ranges, called stop bands. To predict stop bands, their often periodic nature is exploited and dispersion curves are calculated based on a single representative unit cell, typically modeled using the finite element method. Since their sub-wavelength nature and often intricate design can lead to large unit cell models, model reduction methods such as the Generalized Bloch Mode Synthesis have been proposed to greatly accelerate dispersion curve calculations. In order to calculate forced vibro-acoustic responses of finite periodic elastic metamaterial plates composed of an assembly of unit cells, however, full order finite element models rapidly become computationally unaffordable. Therefore, in this work the Generalized Bloch Mode Synthesis is incorporated in a sub-structuring approach, which enables fast forced vibration response calculations of finite elastic metamaterial plates based on a single reduced order unit cell model. The main advantage as compared to a regular Craig-Bampton approach is the additional local reduction of unit cell boundary degrees of freedom, whereby a compatible basis for the identical neighboring unit cells is incorporated. In addition, by combining this Generalized Bloch Mode Synthesis based sub-structuring approach with the Elementary Radiator Approach, efficient sound transmission loss computations of finite periodic metamaterial plates are enabled. The performance of the proposed approach for fast vibro-acoustic response predictions is demonstrated for different cases.

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

“…With the help of dispersion curves, the stop bands of VAMMs could be predicted. Even though VAMMs do not require periodicity, they are often implemented for manufacturing reasons or modeling purposes [ 19 , 20 , 21 ]. The prediction of the stop band behavior with the methods mentioned earlier is purely based on the dynamic behavior of the UC model, representing infinite periodic structures, and not taking into consideration the real boundary conditions [ 19 , 22 ].…”