Description:

Title: Large Deflections of Inextensible Beams and Plates

Speaker: Maria Deliyianni, PhD Student, University of Maryland Baltimore County

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 capture the behavior of the cantilever's large deflections after the onset of flutter. In this talk, we discuss a recent PDE model that derives the equations of motion for an inextensible cantilevered beam via Hamilton's principle. Our theoretical results are centered around the existence, uniqueness, and decay of strong solutions for the derived equations. Following this, we move to a two dimensional rectangular domain and derive the equations of motion for an inextensible cantilevered plate, while discussing various modeling hypotheses that can be employed during this process. Lastly, we see how the cantilever's mixed boundary conditions impose challenges in the analysis of the plate, even in the entirely linear case.

**Please note, this event will be held online via Zoom at the following link: https://northwestern.zoom.us/j/97555366197

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