The flutter velocities of viscoelastic plates are determined. It is shown that the viscoelastic characteristics reduce them Keywords: viscoelastic plate, nonlinear flutter, Bubnov-Galyorkin method, numerical method, flatter velocityComposite materials are increasingly used in aviation structures. In this connection, methods and algorithms for design of aircraft elements made of composites are of importance [1-3, 5, 7-9, 13-15].In this paper, we will address the flutter of viscoelastic plates interacting with the environment. A supersonic gas flow with an unperturbed velocity V is past one side of a plate of thickness h. Aerodynamic pressure is defined by Ilyushin piston theory [6]. Vibrations are described by integral partial differential equations. The Bubnov-Galerkin method based on the polynomial approximation of deflections reduces the problem to a system of ordinary integro-differential equations (IDEs) where time is an independent variable. The IDEs are solved by the numerical method proposed in [3]. This method is algorithmized. The influence of physical, geometrical, and rheological parameters on the flutter of plates and the influence of acoustic and static differential pressures on the flutter velocities are analyzed.Let us analyze the nonlinear flutter of a viscoelastic plate, taking into account acoustic and static differential pressures. The plate with sides a and b and thickness h is hinged on all sides. There is a pressurized cavity in the bottom portion of the plate, and a supersonic gas flow is past the upper face of the plate. Under the assumption adopted in [4,12], the vibration equation of the plate is
Nonlinear vibrations of viscoelastic elements of aviation structures are studied. A method and an algorithm for the numerical solution of integrodifferential equations are proposed. The critical velocity of the flow past viscoelastic plates is determined.In the present paper, the effect of the viscoelastic properties of structural materials on the nonlinear vibrations of cylindrical panels in a gas flow is studied. Use is made of the nonlinear equations of Marguerre's shallow thin shell theory [1-3], from which von Kármán's equations [4] are derived as a particular case.
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