A mathematical model for the propulsive thrust of the thin elastic wing harmonically oscillating in a flow of non-viscous incompressible fluid

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.