Modeling of supersonic nonlinear flutter of plates on a visco-elastic foundation

Numerical study of the flutter of a plate on a viscoelastic foundation is carried out in the paper. Critical velocity of the flutter of a plate on an elastic and viscoelastic foundation is determined. The mathematical model for the investigation of viscoelastic plates is based on the Marguerre\'s theory applied to the study of the problems of strength, rigidity and stability of thin-walled structures such as aircraft wings. Aerodynamic pressure is determined in accordance with the A.A. Ilyushin\'s piston theory. Using the Bubnov - Galerkin method, the basic resolving systems of nonlinear integro-differential equations (IDE) are obtained. At wide ranges of geometric and physical parameters of viscoelastic plates, their influence on the flutter velocity has been studied in detail.