Learning to Predict Structural Vibrations

TL;DR

This paper introduces a new deep learning model for predicting vibrations in mechanical structures, providing a faster alternative to traditional simulations, with a benchmark dataset and evaluation metrics to assess performance.

Contribution

A novel Frequency-Query Operator architecture for operator learning of vibration patterns, outperforming existing neural network models on a comprehensive vibrating plates benchmark.

Findings

The proposed model achieves higher accuracy than DeepONets and Fourier Neural Operators.

The benchmark dataset includes 12,000 diverse plate geometries with numerical solutions.

The method enables efficient vibration prediction for design optimization.

Abstract

In mechanical structures like airplanes, cars and houses, noise is generated and transmitted through vibrations. To take measures to reduce this noise, vibrations need to be simulated with expensive numerical computations. Deep learning surrogate models present a promising alternative to classical numerical simulations as they can be evaluated magnitudes faster, while trading-off accuracy. To quantify such trade-offs systematically and foster the development of methods, we present a benchmark on the task of predicting the vibration of harmonically excited plates. The benchmark features a total of 12,000 plate geometries with varying forms of beadings, material, boundary conditions, load position and sizes with associated numerical solutions. To address the benchmark task, we propose a new network architecture, named Frequency-Query Operator, which predicts vibration patterns of plate geometries given a specific excitation frequency. Applying principles from operator learning and implicit models for shape encoding, our approach effectively addresses the prediction of highly variable frequency response functions occurring in dynamic systems. To quantify the prediction quality, we introduce a set of evaluation metrics and evaluate the method on our vibrating-plates benchmark. Our method outperforms DeepONets, Fourier Neural Operators and more traditional neural network architectures and can be used for design optimization. Code, dataset and visualizations: https://github.com/ecker-lab/Learning_Vibrating_Plates