DeepF-fNet: A novel framework for vibration-based structural optimization

Structural optimization is crucial for designing secure, efficient, and durable components with minimal material usage. Traditional methods, however, face challenges when optimizing structures to damp vibrations across specific frequency ranges due to the complexities of the inverse eigenvalue problem involved. As a result, conventional solutions often rely on active systems to mitigate vibrations of unpredictable intensity and frequency, which can lead to potential structural failure. To date, no structural optimization approach has effectively addressed this issue within this context. This study demonstrates that machine learning can efficiently solve inverse eigenvalue problems, potentially replacing the need for active systems to suppress critical vibrations. We introduce DeepF-fNet, a novel framework for vibration-based structural optimization that uses DeepONets within the context of physics-informed neural networks. This approach incorporates both data and the governing physical laws during training. The proposed framework was validated through a case study involving a locally resonant metamaterial designed to isolate a representative structure from undesired vibrations within a custom frequency range. The results showed that DeepF-fNet outperforms state-of-the-art algorithms, such as genetic algorithms, particularly in terms of computational efficiency.