Data driven fast optimization of resonant metamaterial structures

May 1, 2021
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In recent years, resonant metamaterials have garnered much interest because of their potential to break with traditional design principles in noise and vibration management. By virtue of a carefully designed micro- or mesostructure, metamaterials display exotic macroscopic properties such as vibrational band gaps, which do not exist in known bulk materials. However, modeling and optimizing these emergent properties is a challenging multiscale problem. The process remains computationally intractable in many cases due to the heavy reliance on expensive finite-element analyses and/or topology optimizations.To address this challenge, the present project focuses on applying data science techniques in the design of resonant metamaterial structures. In particular, we target vibration reduction in finite-sized elastic plates by integrating 3D-printed mechanical resonators, which is treated as an optimization problem in both the arrangement and the dynamics of the resonators. Where possible, costly high-fidelity simulations and optimizations will be replaced with data-driven surrogates to drastically reduce the computational load. On the one hand, the inverse design problem of creating resonators with a desired dynamic response will be addressed, for instance by applying tandem neural networks. On the other hand, we will investigate the optimal arrangement of resonators for maximum vibration reduction. Here, Bayesian optimization techniques may offer an efficient solution. The range of material and geometric properties obtainable via the 3D-printing process will be identified and taken into account.



SDSC Team:
Christian Donner

PI | Partners:

EMPA, Laboratory for Acoustics:

  • Prof. Bart Van Damme
  • Dr. Sander Dedonker

More info



In this project, we aim to reduce the vibration level of finite-size elastic plates by integrating mechanical resonators. This approach - based on locally-resonant metamaterials design - offers lightweight, economical, and flexible vibration reduction for high-end applications such as precision machinery and aerospace components. By using machine learning, we wish to bypass the costly design procedure used normally.

Proposed Approach / Solution

We tackle two problems in this project: 1) Positioning and designing multiple resonators on a host structure such that response to vibrations is minimized (Figure 1). 2) Designing a resonator, that dampens predefined frequencies (Figure 2). For the first problem, we use a sampling technique called simulated annealing to find the optimal positioning. This is a stochastic optimization algorithm, that adds, removes, and moves resonators on the host-structure randomly. Changes that dampen the vibrations are more likely to be accepted. In this way, the configuration gets incrementally improved, while still allowing the exploration of many different configurations. For the second problem, we use a conditional variational autoencoder (cVAE). A cVAE is composed of an encoder and a decoder (Figure 3). The encoder maps the resonator design into a latent space. The decoder takes this mapping, and additionally specific user-specified resonant properties, and outputs a new design. With the trained model, the decoder can be used to propose many new designs with on-demand resonant properties, that can be 3D printed and tested for their actual resonant properties (Figure 4).


We find data-driven techniques that allow us to design materials that are less prone to be damaged by resonant frequencies. This can help with several problems, including manufacturing materials with certain on-demand properties.

Figure 1: Schematic illustration of the host structure (black) and resonators (gray) for the beam case study. (Problem 1)
Figure 2: Example of a spiral resonator. (Problem 2)
Figure 3: At the training stage, the encoder gets the design parameters as input, maps it to some latent space, and tries to predict the resonant properties. The decoder gets resonant properties and latent mapping as input, and tries to predict the design again. After training, we use the encoder, to request a structure with certain resonance properties and sample a latent mapping randomly. For each sample we get a new design, which we then validated with ANSYS, a finite element software.
Figure 4: 3D printed resonators suggested by the variational autoencoder. (Problem 2)




  • Dedoncker, S., Donner, C., Taenzer, L., & Van Damme, B. (2023). Generative inverse design of multimodal resonant structures for locally resonant metamaterials. arXiv preprint arXiv:2309.04177. DOI: 10.48550/arXiv.2309.04177
  • Dedoncker, S., Donner, C., Taenzer, L., & Van Damme, B. (2022). Optimization of resonant absorbers for passive vibration control: a numerical approach and its experimental validation. Available at SSRN 4266071. DOI: 10.2139/ssrn.4266071

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