RG-Based Local Hopf Reduction and Slow-Manifold Reconstruction for Nonlinear Aeroelastic Systems
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| Format: | Preprint |
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2026
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| _version_ | 1866908987236024320 |
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| author | Chen, Gelin Song, Chen Yang, Chao |
| author_facet | Chen, Gelin Song, Chen Yang, Chao |
| contents | Self-excited limit-cycle oscillations (LCOs) from Hopf bifurcations are a key feature of nonlinear aeroelasticity and depend sensitively on structural and aerodynamic parameters. Classical center-manifold and normal-form theory describe this local behavior, but can be cumbersome to apply in large discretized models and standard reduced-order modeling (ROM) workflows. A renormalization-group (RG)-based reduction is developed that directly yields a Hopf-type amplitude equation on a local invariant manifold, specialized for polynomial nonlinearities in tensor-based discretizations and compatible with finite-element-type settings. The method provides explicit coefficients governing the Hopf threshold, criticality, and leading LCO amplitude/frequency trends, and admits a companion slow-manifold approximation with selected stable modes retained as static coordinates. Representative nonlinear-aeroelastic examples illustrate how the proposed framework supplies compact, parameter-aware Hopf/LCO descriptors suitable for local ROM construction near flutter. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_20753 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | RG-Based Local Hopf Reduction and Slow-Manifold Reconstruction for Nonlinear Aeroelastic Systems Chen, Gelin Song, Chen Yang, Chao Fluid Dynamics Systems and Control 37G15, 37M99, 70K50, 74H45, 93A30 Self-excited limit-cycle oscillations (LCOs) from Hopf bifurcations are a key feature of nonlinear aeroelasticity and depend sensitively on structural and aerodynamic parameters. Classical center-manifold and normal-form theory describe this local behavior, but can be cumbersome to apply in large discretized models and standard reduced-order modeling (ROM) workflows. A renormalization-group (RG)-based reduction is developed that directly yields a Hopf-type amplitude equation on a local invariant manifold, specialized for polynomial nonlinearities in tensor-based discretizations and compatible with finite-element-type settings. The method provides explicit coefficients governing the Hopf threshold, criticality, and leading LCO amplitude/frequency trends, and admits a companion slow-manifold approximation with selected stable modes retained as static coordinates. Representative nonlinear-aeroelastic examples illustrate how the proposed framework supplies compact, parameter-aware Hopf/LCO descriptors suitable for local ROM construction near flutter. |
| title | RG-Based Local Hopf Reduction and Slow-Manifold Reconstruction for Nonlinear Aeroelastic Systems |
| topic | Fluid Dynamics Systems and Control 37G15, 37M99, 70K50, 74H45, 93A30 |
| url | https://arxiv.org/abs/2604.20753 |