Аннотация:
The article is dedicated to computer modeling of a viscoelastic based plate flutter in design of
aeronautical structures in sustainable mechanical engineering. The mathematical model of the
flutter problem for viscoelastic plates with viscoelastic base is presented. Using the BubnovGalerkin method, discrete models of the flutter problem for viscoelastic plates streamlined by
the supersonic gas jet are deduced. A numerical method is developed for solving nonlinear
integro-differential equations for the viscoelasticity hereditary theory problem with weakly
singular kernels. According to the above numerical method with respect to unknowns, a system
of algebraic equations is obtained. To solve the system of algebraic equations, the Gauss method
is used. An application program package has been developed to enable modeling and studying
of the nonlinear dynamic problems for the hereditary viscoelasticity theory with weakly
singular kernels. Based on the proposed model, numerical method and algorithm, nonlinear
problems for the viscoelastic plates flutter with a viscoelastic base are investigated. The critical
flutter velocity of the viscoelastic plates is determined for solving the stability problem in design
of aircraft structures.
