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

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.