Learning to Predict Structural Vibrations

TL;DR

This work tackles the challenge of predicting steady-state vibrational responses of mechanical plates under harmonic excitation by introducing a large Vibrating Plates benchmark and a novel frequency-query operator (FQO) that leverages operator learning and implicit shape encoding to predict frequency-dependent vibration patterns. The study systematically evaluates multiple neural architectures, showing that frequency-query and velocity-field-based decoders yield superior accuracy over baselines such as DeepONet and Fourier Neural Operators, especially for resonance-dominated spectra. It demonstrates strong transfer learning and design-optimization capabilities, including substantial data-efficiency gains and the ability to guide beadings-based design using gradient-driven diffusion models. The work provides a practical path to accelerate vibroacoustic design and offers a rigorous benchmark for future surrogate models in frequency-domain structural dynamics.

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

Figures (12)

• Figure 1: Left: We introduce the Vibrating Plates dataset of 12,000 samples for predicting vibration patterns based on plate geometries. A harmonic force excites the plates, causing them to vibrate. The vibration patterns of the plates are obtained through numerical simulation. Diverse architectures are evaluated on the dataset. Right: Beadings are indentations and used in many vibrating technical systems. Here, on an oil filter, a washing machine and a disk drive. They increase the structural stiffness and alter the vibration.
• Figure 2: Process of the finite element solution in frequency domain in order to compute the velocity field at each frequency query.
• Figure 3: Dataset analysis. (a) shows two discretized plate geometries with their corresponding frequency response, the red crosses mark the detected peaks. (b) shows the mean plate design and frequency response. (c) shows number of peaks in different dataset settings. (d) shows the distribution of the peaks over the frequencies.
• Figure 4: Frequency-Query Operator method. The geometry encoder takes the mesh geometry and the scalar properties as input. The resulting feature volume along with a frequency query is passed to the query decoder, that either predicts a velocity field or directly a frequency response. The velocity field is aggregated to arrive at the frequency response at the query frequency $f$.
• Figure 5: Results. (b) to (d) show the velocity field at one frequency and prediction for the plate geometry in (a) from FQO-UNet. (e) shows the test MSE for training two methods with reduced numbers of samples from V-5000. (f) shows effects of different data generation strategies. The blue line is an isoconture for a fixed compute budget of 150,000 data points, with varying number of frequencies per plate geometry. The green star represents using a larger dataset at 15 frequencies per plate (half of V-5000). The red cross represents a model trained on V-5000. Training with fewer frequencies per plate is more efficient.