Phenomenological model of interaction of plate with a~flow

V. A. Samsonov ; Yu. D. Seliutski

Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 7, pp. 43-62

Résumé

In the present paper, a finite dimensional phenomenological model of unsteady interaction of a rigid plate with a flow is proposed. It is assumed that the plate performs translational motion across the flow. The internal dynamics of the flow is modeled by the attached second order dynamical system. It is shown that the model allows satisfactory agreement with experimental data. With the developed model an inverse problem of dynamics is examined for the situation, where the plate performing uniform translational motion at some moment begins uniform deceleration and finally stops. It is shown that for sufficiently large value of the plate acceleration for some time range the flow does not resist the motion of the plate, but “accelerates” it. It is shown also that the equations of motion in the context of the proposed model can be reduced to the integro-differential form, and comparison with the known model of S. M. Belotserkovsky is performed. Structural resemblance of the motion equations for body in flow in both models is marked. The domain of applicability of the quasi-stationary model is examined.