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arXiv · 2509.23306

Large Deflections of A Flow-Driven Cantilever with Kutta-Joukowski Flow Conditions

Maria Deliyianni·Irena Lasiecka·Justin T. Webster
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Abstract

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.

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Maria Deliyianni, Irena Lasiecka, Justin T. Webster. 2025-09-27. Large Deflections of A Flow-Driven Cantilever with Kutta-Joukowski Flow Conditions. https://arxiv.org/abs/2509.23306

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