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Unsteady aerodynamic theory of lifting surfaces and thin elastic bodies undergoing arbitrary small motions in a supersonic flow field. (English) Zbl 0625.73053

This paper deals with a formulation of the unsteady aerodynamic theory of lifting surfaces that undergo arbitrary small motions in a supersonic flow environment. In its approach, the expression correlating (in the time domain) the pressure distribution to the downwash distribution is established and some properties of the associated kernel function are derived. Further introduction into the analysis of the concept of generalized disturbances (used in conjunction with the mathematical theory of generalized functions) enables one to approach the case of arbitrary motions starting from rest at a certain instant \(t=t_ 0\). As a natural application of these results, the aeroelastic response of thin panels placed in a supersonic flow and subjected in addition to a prescribed forcing field is considered and a solution to this problem is proposed.
The paper is intended to bring new elements both in the unsteady aerodynamic theory of supersonic lifting surfaces and the modelling of their associated aeroelastic response problems.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
45L05 Theoretical approximation of solutions to integral equations
76J20 Supersonic flows
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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