# Doctoral Dissertation Defense: Maria Deliyianni

## Advisor: Dr. Justin Webster

Friday, April 22, 2022

11:00 AM – 1:00 PM

11:00 AM – 1:00 PM

Mathematics/Psychology : 401

**Title:**

*Modeling and PDE Theory for The Large Deflections of Elastic Cantilevers*

**Abstract**

Flutter is defined as a self-excitation of a thin structure where a surrounding flow destabilizes its natural elastic modes. Cantilevers are particularly prone to flutter, and it has been shown that this instability can induce large displacements from which mechanical energy can be captured via piezoelectric laminates. To effectively harvest energy in this manner, one must have viable models that describe the behavior of the cantilever's large deflections after the onset of flutter.

In this talk we focus on the modeling and the mathematical analysis for large deflections for elastic cantilevers. In the first part, we introduce a recent PDE model for an inextensible cantilevered beam and demonstrate theoretical results that are centered around the existence, uniqueness, and decay of strong solutions. Secondly, we focus on cantilevered plates and discuss various modeling hypotheses which lead to several different systems of equations of motion for 2D large deflections. Following this, we visit the linear (Kirchhoff-Love) cantilevered plate and develop a semigroup argument that addresses its well-posedness. Lastly, we introduce a system that couples a linear cantilevered beam with a full potential flow given by a perturbed wave equation. The resulting flow-beam system has mixed interface conditions of Kutta-Joukowsky type, and we discuss recent work on semigroup well-posedness and stability.