# Flexural-torsional flutter of an aerrodynamic profile with irregular compaction

 1Safronov, AV, 1Semon, BY, 1Nedilko, AN1The National Defence University of Ukraine named after Ivan Cherniakhovsyi, Kyiv, Ukraine Space Sci. & Technol. 2019, 25 ;(2):12-21 https://doi.org/10.15407/knit2019.02.012 Publication Language: Ukrainian Abstract:  The article proposes one of the possible mathematical models for estimating the effect of shock waves on the value of the critical velocity head of a bending-torsional flutter of a direct aerodynamic profile in transonic air flow. The mathematical model is based on the traditional methods of classical (two-degree) flutter, on a joint analysis of the Bernoulli equations for compressible gas, on the characteristics of the supersonic gas flow in the Prandtl-Meier flow, and on the application of the “dynamic profile curvature” hypothesis.           On the basis of the linearization of the Bernoulli equations for a compressible gas, namely for air, the condition for the formation of shock waves on the airfoil surface in the transonic range of Mach numbers is obtained. Using this condition and the “dynamic profile curvature” hypothesis as a basis and taking into account the nature of changes in the parameters of the local supersonic flow when flowing around the diffuser part of the surface of an aerodynamic profile, approximate laws of interaction of shock waves with flexural-torsional oscillations of the airfoil are obtained. The patterns obtained are used to form mathematical models for estimating the values of destabilizing and perturbing forces and moments caused by the peculiarities of the interaction of shock waves with flexural-torsional oscillations of the airfoil.           The estimation of the critical velocity head of a flexural-torsional flutter of an aerodynamic profile with shock waves was performed by solving a system of two differential equations of the second order. The result of the estimation formed the basis for determining approximate analytical dependences of the values of the above mentioned critical velocity head. They were obtained both in uniform air flow and the flow with irregular seals. A comparison of the obtained results shows that the magnitude of the critical velocity head of a flexural-torsional flutter of typical aerodynamic profiles with shock waves is always less than the magnitude of the critical velocity head of the flexural-torsional flutter in uniform air flow. Keywords: aerodynamic profile, air compressibility, flexural-torsional flutter, Mach number, mathematical model, pressure, shock waves, transonic flow, velocity head
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