Generative inverse design of multimodal resonant structures for locally resonant metamaterials

In the development of locally resonant metamaterials, the physical resonator design is often omitted and replaced by an idealized mass-spring system. This paper presents a novel approach for designing multimodal resonant structures, which give rise to multi-band gap metamaterials with predefined ban...

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Bibliographic Details
Published in:Engineering with computers Vol. 41; no. 4; pp. 2671 - 2687
Main Authors: Dedoncker, Sander, Donner, Christian, Bischof, Raphael, Taenzer, Linus, Van Damme, Bart
Format: Journal Article
Language:English
Published: London Springer London 01.08.2025
Springer Nature B.V
Subjects:
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Classical Mechanics
Complex variables
Computer Science
Computer-Aided Engineering (CAD
Control
Design
Efficiency
Energy gap
Inverse design
Mass-spring systems
Math. Applications in Chemistry
Mathematical and Computational Engineering
Metamaterials
Optimization
Original Article
Resonators
Systems Theory
Resonator
Vibration
Generative design
Metamaterial
ISSN:0177-0667, 1435-5663
Online Access:Get full text
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Summary:In the development of locally resonant metamaterials, the physical resonator design is often omitted and replaced by an idealized mass-spring system. This paper presents a novel approach for designing multimodal resonant structures, which give rise to multi-band gap metamaterials with predefined band gaps. Our data science-based method uses a conditional variational autoencoder to identify non-trivial patterns between design variables of complex-shaped resonators and their modal effective parameters. After training, the cost of generating designs satisfying arbitrary criteria—frequency and mass of multiple modes—becomes negligible. An example of a resonator family with six geometric variables and two targeted modes is further elaborated. We find that the autoencoder performs well even when trained with a limited dataset, resulting from a few hundred numerical modal analyses. The method generates several designs that very closely approximate the desired modal characteristics. The accuracy of the best designs, proposed by the auto-encoder, is confirmed in tests of 3D-printed resonator prototypes. Further experiments demonstrate the close agreement between the measured and desired dispersion relation of a sample metamaterial beam.
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ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-025-02130-2