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arXiv · 2607.10675

Spectral submanifold reduction for PDEs describing nonlinear continuum vibrations

Gergely Buza·George Haller
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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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Gergely Buza, George Haller. 2026-07-12. Spectral submanifold reduction for PDEs describing nonlinear continuum vibrations. https://arxiv.org/abs/2607.10675

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