01/03/2022
O ciclo de palestras do Programa de Verão 2022 - PGMAC/UEL convida a todos para o Webnário que será ministrado pelo Prof. Dr. Justin Thomas Webster, na próxima sexta-feira (04/03/2022) às 14h00.
TÍTULO: Cantilever Flutter in Piezo-electric Energy Harvesting Applications
RESUMO: Flutter is a self-excitation instability of an elastic structure in a surrounding fluid flow. Instances of flutter in aerospace applications are of great interest in engineering. Here, motivated by piezoelectric energy harvesting considerations, we necessarily consider the large deflections of a 1D elastic cantilever. Mathematically, there is little by way of rigorous analysis of recent PDE models. For the large deflections of a cantilever (rather than a fully restricted structure), we have nonlinear restoring forces coming through an inextensibility constraint, rather than local stretching. This leads to both nonlinear inertia and stiffness terms, introducing nonlocality and quasilinearity. We begin with an overview on the well-posedness and long-time behavior of simplified cantilever large deflection models. Then, we derive the inextensible cantilever model at hand through Hamilton's principle. The existence and uniqueness of strong solutions for the quasilinear problem is demonstrated through a Galerkin procedure, and we focus specifically on the complications introduced by the nonlocal inertial terms which preclude a natural weak formulation without the addition of Kelvin-Voigt structural damping. Global existence is obtained for small data through stabilization type multiplier analysis. Time permitting, we discuss recent models for 2D large deflection cantilevers, and compare with the established von Karman plate theory.
DOCENTE RESPONSÁVEL: Justin Thomas Webster - University of Maryland, Baltimore County - US
DATA: 04/03/2022
HORÁRIO: 14h00
