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A mathematical model for the propulsive thrust of the thin elastic wing harmonically oscillating in a flow of non-viscous incompressible fluid
Institution:1. Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA;2. Department of Mechanical Engineering, University of Massachusetts, Lowell, MA, USA;3. Department of Mechanical, Materials, and Aerospace Engineering, Illinois Institute of Technology, IL, USA;1. Department of Mathematics, Modelling and Scientific Computing (MOX) – Politecnico di Milano, Via Bonardi 9, I-20133 Milan, Italy;2. Fondazione CEN, Piazza Leonardo da Vinci, 32, I-20133 Milan, Italy;3. Department of Mathematical Sciences (DISMA) “G.L. Lagrange” – Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy;1. Faculty of Mathematics, Al. I. Cuza University of Iaşi, 700506 Iaşi, Romania;2. Octav Mayer Mathematics Institute, Romanian Academy, 700505 Iaşi, Romania;3. Università della Calabria, Via Pietro Bucci, 87036 Arcavacata di Rende (CS), Italy;1. Department of Mathematics and Computer Science, University of Messina, Viale F. Stagno d’Alcontres 31, Messina 98166, Italy;2. Department of Mathematics, Computer Science and Economics, University of Basilicata, Viale dell’Ateneo Lucano 10, Potenza 85100, Italy
Abstract:In the present paper there is proposed an analytical approach to study vibration of a rectangular elastic wing in the stationary stream of non-viscous fluid. We first develop a basic two-dimensional integral equation. Then a series expansion along the short coordinate is applied. This reduces the problem to an infinite set of one-dimensional integral equations which is studied asymptotically with respect to the large aspect ratio parameter. An example of optimization of thickness of the wing is demonstrated, to test the efficiency of the proposed method in applications.
Keywords:Elastic wing oscillation  Integral equation  Thrust  Optimization
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