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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.23306 |
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| _version_ | 1866915519257378816 |
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| author | Deliyianni, Maria Lasiecka, Irena Webster, Justin T. |
| author_facet | Deliyianni, Maria Lasiecka, Irena Webster, Justin T. |
| contents | We consider a canonical flow-structure system modeling airflow over a cantilevered beam. Flow-beam interactions arise in flight systems as well as alternative energy technologies, such as piezoelectric energy harvesters. A potential flow, given through a hyperbolic equation, captures the airflow interacting with a beam clamped on one end and free on the other. The dynamic coupling occurs through an impermeability condition across the beam; in the wake the Kutta-Joukowski flow condition is imposed. Several challenges arise in the analysis, including the unboundedness of the flow domain, lack of interface trace regularity, and flow conditions which give rise to a dynamic and mixed boundary value problem. Additionally, we consider a recent nonlinear model capturing the cantilever large deflections through the effects of inextensibility. We produce a viable underlying semigroup for the model's linearization, which includes a flow regularity theory. Then, exploiting higher regularity nonlinear estimates for the beam, we utilize a semigroup perturbation to obtain local-in-time strong solutions for the nonlinear dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23306 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large Deflections of A Flow-Driven Cantilever with Kutta-Joukowski Flow Conditions Deliyianni, Maria Lasiecka, Irena Webster, Justin T. Analysis of PDEs 74F10, 74K10, 35L51, 35M33, 35D30 We consider a canonical flow-structure system modeling airflow over a cantilevered beam. Flow-beam interactions arise in flight systems as well as alternative energy technologies, such as piezoelectric energy harvesters. A potential flow, given through a hyperbolic equation, captures the airflow interacting with a beam clamped on one end and free on the other. The dynamic coupling occurs through an impermeability condition across the beam; in the wake the Kutta-Joukowski flow condition is imposed. Several challenges arise in the analysis, including the unboundedness of the flow domain, lack of interface trace regularity, and flow conditions which give rise to a dynamic and mixed boundary value problem. Additionally, we consider a recent nonlinear model capturing the cantilever large deflections through the effects of inextensibility. We produce a viable underlying semigroup for the model's linearization, which includes a flow regularity theory. Then, exploiting higher regularity nonlinear estimates for the beam, we utilize a semigroup perturbation to obtain local-in-time strong solutions for the nonlinear dynamics. |
| title | Large Deflections of A Flow-Driven Cantilever with Kutta-Joukowski Flow Conditions |
| topic | Analysis of PDEs 74F10, 74K10, 35L51, 35M33, 35D30 |
| url | https://arxiv.org/abs/2509.23306 |