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02.07 Vibro-Acoustics of Metamaterials

Predicting robust complete and full band gaps in three-dimensional frame structures
Time: 3:40 pm

Author: Luiz Henrique Marra da Silva Ribeiro

Abstract ID: 1842

Vibration can cause structural damage in dynamic systems when not designed properly. Recently, several approaches are emerging in structural dynamics as possible alternatives for passive vibration and noise control, such as phononic crystals and metamaterials. In this work, a three-dimensional frame that presents intersection of longitudinal, flexural and torsional band gaps is investigated. For periodic structures, the Irreducible Brillion Zone (IBZ) gives information for any possible angle of propagation of a wave. The manufacturing process induces variability along each three-dimensional frame element. The present study verifies the robustness of the band gaps of the three-dimensional structure against spatially varying geometry and mechanical properties. The spatial random fields are modeled using the expansion optimal linear estimator (EOLE). Bayesian statistics is used to infer on the stochastic response simulated using the Monte Carlo method combined with the EOLE. The three-dimensional frame is modeled via Euler-Bernoulli beam and ordinary shaft theories as well as  with Timoshenko and Saint-Venant theories. It is shown that the three-dimensional frame structure exhibits a complete (for all waves) and full (throughout the IBZ) robust band gap against the proposed variability. Both models are able to predict this robust band gap.

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(Generalized) Bloch mode synthesis for the fast dispersion curve calculation of 3D periodic metamaterials
Time: 3:20 pm

Author: Vanessa Cool

Abstract ID: 2052

Metamaterials, i.e. artificial structures with unconventional properties, have shown to be highly potential lightweight and compact solutions for the attenuation of noise and vibrations in targeted frequency ranges, called stop bands. In order to analyze the performance of these metamaterials, their stop band behavior is typically predicted by means of dispersion curves, which describe the wave propagation in the corresponding infinite periodic structure. The input for these calculations is usually a finite element model of the corresponding unit cell. Most common in literature are 2D plane metamaterials, which often consist of a plate host structure with periodically added masses or resonators. In recent literature, however, full 3D metamaterials are encountered which are periodic in all three directions and which enable complete, omnidirectional stop bands. Although these 3D metamaterials have favorable vibro-acoustic characteristics, the computational cost to analyze them quickly increases with unit cell model size. Model order reduction techniques are important enablers to overcome this problem. In this work, the Bloch Mode Synthesis (BMS) and generalized BMS (GBMS) reduction techniques are extended from 2D to 3D periodic structures. Through several verifications, it is demonstrated that dispersion curve calculation times can be strongly reduced, while accurate stop band predictions are maintained.

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Phononic crystal sandwich for broadband and low frequency acoustic insulation under diffuse field
Time: 4:40 pm

Author: Natacha Aberkane-Gauthier

Abstract ID: 2098

Light and thin structures exhibiting high sound insulation over a wide frequency range are a major industrial concern, especially in the transport and building sectors. Phononic crystals constitute promising solutions to solve this issue due to their particular dispersion properties. In this work, we build a system consisting of a well-known sandwich panel comprising a soft elastic core layer hosting periodically arranged rigid inclusions. Diffuse field measurements show a huge improvement of the Transmission Loss compared to the system without inclusions. In fact, for this kind of panel, the structured core enables Bragg band-gap opening for guided slow propagating waves leading to low frequency and broadband enhancement of the Transmission Loss. Using a 3cm-thick material we are able to improve the response from 300 Hz on (?/38 in air). We then develop a finite elements model to achieve a precise description and understanding of the problem. We also propose a numerical tool to analyze the system’s band-structures from a vibroacoustic point of view. It proves very useful for the further development of practical solutions.

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Variance Quantification of Different Additive Manufacturing Processes for Acoustic Meta Materials
Time: 1:20 pm

Author: Manuel Bopp

Abstract ID: 2211

Many concepts for acoustic meta materials rely on additive manufacturing techniques. Depending on the production process and material of choice, different levels of precision and repeatability can be achieved. In addition, different materials have different mechanical properties, many of which are frequency dependent and cannot easily be measured directly. In this contribution the authors have designed different resonator elements, which have been manufactured utilizing Fused Filament Fabrication with ABSplus and PLA, as well as PolyJet Fabrication with VeroWhitePlus. All structures are computed in FEA to obtain the calculated Eigenfrequencies and mode shapes, with the respective literature values for each material. Furthermore, the dynamic behavior of multiple instances of each structure is measured utilizing a 3D-Laser-Scanning Vibrometer under shaker excitation, to obtain the actual Eigenfrequencies and mode shapes. The results are then analyzed in regards to variance between different print instances, and in regards to accordance between measured and calculated results. Based on previous work and this analysis the parameters of the FEA models are updated to improve the result quality.

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Resonant metamaterial designs for a broadband mitigation of flow-induced vibrations
Time: 4:00 pm

Author: Felipe Alves Pires

Abstract ID: 2344

Resonant metamaterials have recently emerged as lightweight and performant noise and vibration solutions for the hard-to-address low-frequency ranges. These engineered materials are made by an assembly of resonant elements onto a host structure. Their interaction leads to tuneable frequency ranges, known as stop bands, in which they can outperform classical noise control measures. However, these stop bands have a limited frequency range effect. To broaden the noise and vibration performance also outside the stop band, this paper presents a design approach for a finite resonant metamaterial plate. Two regularly spaced grids of resonant elements are both added to a plate. In the first grid, the resonant elements are tuned to the same nominal frequency and stop band behaviour is achieved. In the second grid, the tuned frequency of each resonant element is found through an optimisation procedure, with the goal of minimising the dynamic response of the plate outside the stop band. To speed up the optimisation, model order reduction and a dynamic sub-structuring method are employed. The performance of this finite resonant metamaterial plate design is validated by evaluating its vibration response due to a broadband grazing flow excitation and comparing it to a plate with equivalent mass additions.

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Metamaterial plate with an arrangement of different resonators
Time: 4:20 pm

Author: Giovanna Pisicchio Zanoni

Abstract ID: 2571

Local resonant metamaterials have been widely studied for vibration suppression in the last 20 years. They produce band gaps, which are frequency regions where the wave is not allowed to propagate. They are an alternative to reduce vibration levels at lower frequencies when compared to phononic crystals, which require larger periodic cells to create band gaps at lower frequencies. The most common configuration for a local resonant metamaterial is a periodic cell of a known structure with one attached resonator. In this study, a plate with a periodic cell using two different resonators is analyzed. Some configurations of mass and stiffness for the two resonators will be discussed to pursue the best compromise between a wider band gap and a more considerable vibration attenuation. The dispersion relation for the proposed metamaterial unit cell will be calculated using the Wave Finite Element Method to evaluate these configurations. The frequency response function for a finite structure with the proposed arrangement will also be calculated using the Finite Element Method to compare the results.

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