Nonlinear Model Reduction to Temporally Aperiodic Spectral Submanifolds
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911830396370944 |
|---|---|
| author | Haller, George Kaundinya, Roshan S. |
| author_facet | Haller, George Kaundinya, Roshan S. |
| contents | We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and control problems. The time-dependent SSMs we construct under these assumptions are normally hyperbolic and hence will persist for larger forcing and faster time dependence that are beyond the reach of our precise existence theory. For this reason, we also derive formal asymptotic expansions that, under explicitly verifiable nonresonance conditions, approximate SSMs and their aperiodic anchor trajectories accurately for stronger, faster or even temporally discontinuous forcing. Reducing the dynamical system to these persisting SSMs provides a mathematically justified model reduction technique for non-autonomous physical systems whose time dependance is moderate either in magnitude or speed. We illustrate the existence, persistence and computation of temporally aperiodic SSMs in mechanical examples under chaotic forcing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05355 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear Model Reduction to Temporally Aperiodic Spectral Submanifolds Haller, George Kaundinya, Roshan S. Dynamical Systems Chaotic Dynamics Pattern Formation and Solitons We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and control problems. The time-dependent SSMs we construct under these assumptions are normally hyperbolic and hence will persist for larger forcing and faster time dependence that are beyond the reach of our precise existence theory. For this reason, we also derive formal asymptotic expansions that, under explicitly verifiable nonresonance conditions, approximate SSMs and their aperiodic anchor trajectories accurately for stronger, faster or even temporally discontinuous forcing. Reducing the dynamical system to these persisting SSMs provides a mathematically justified model reduction technique for non-autonomous physical systems whose time dependance is moderate either in magnitude or speed. We illustrate the existence, persistence and computation of temporally aperiodic SSMs in mechanical examples under chaotic forcing. |
| title | Nonlinear Model Reduction to Temporally Aperiodic Spectral Submanifolds |
| topic | Dynamical Systems Chaotic Dynamics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2404.05355 |