Bladed Disk Vibration Dynamics
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Abstract
Abstract
We prove the existence of spectral submanifolds in nonlinear partial differential equations (PDEs) describing forced-damped continuum vibrations. Our results cover structural vibrations subject to generalized structural damping. Based on these results, backbone curves and forced response curves can be rigorously extracted from PDEs, without a priori discretization. On two examples involving an elastic beam and a thin plate, we show that backbone and forced response curves can even be calculated by hand directly from the PDEs.
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@article{Buza2026Spectral,
title = {Spectral submanifold reduction for PDEs describing nonlinear continuum vibrations},
author = {Gergely Buza and George Haller},
journal = {arXiv (Cornell University)},
year = {2026},
doi = {10.48550/arxiv.2607.10675},
url = {https://doi.org/10.48550/arxiv.2607.10675}
}FAQ
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