Abstract
In this paper the flutter of nonlinear viscoelastic plates in a supersonic flow is investigated. The basic direction of work is consisted in taking into account of viscoelastic material’s properties at supersonic speeds. Quasi-steady aerodynamic panel loadings are determined using piston theory. The vibration equations relatively of deflection are described by Integrо-differential equations in partial derivatives. The plate nonlinear partial integro-differential equation is transformed info a set of nonlinear ordinary IDE through a Bubnov-Galerkin’s approach. The resulting system of IDE is solved through the Badalov-Eshmatov integration method. Critical speeds for plate flutter are defined.
Highlights
There are much literature on the flutters, and the problem sufficiently is solved, though we need enough accordance between the theory and experiments for configuration and Mach number, In the [1,2 ] work Fung has analyzed the problem of the flutters
The stability of plates and shells in supersonic flow was considered in many works [4,5,6]
Integration of the system (8) of KoltunovRjanitsin kernel (R(t)=Aexp(-β t)tα -1, 0
Summary
There are much literature on the flutters, and the problem sufficiently is solved, though we need enough accordance between the theory and experiments for configuration and Mach number, In the [1,2 ] work Fung has analyzed the problem of the flutters. The analysis of the motion of structures under deterministic treatment of the problem is given in these works. The mathematical modeling is based on linear representation of elastic and aerodynamic forces. In the given work mathematical models of the problems of the viscous-elastic plates were constructed by taking account of the geometrical and aero dynamical non-linearity, aero dynamical damping, statically pressure dropping on the basis of the Kirchhoff-Love hypothesis. For the solution to the system was applied the problem was solved by the usual IDE based on flexure polynomial approximation by means of Bubnov-Galerkin’s method. The numerical method based on quatrature proposed by F.Badalov and. It was described the algorithm of the numerical solution on the basis of the method. Critical speeds of the viscous-elastic plate’s flutter moved by constant super sound speed were found in all parts of the problem
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