Computer Modeling of Nonlinear Flutter of Viscoelastic Based Plate as a Sustainable Mechanical Engineering Approach in Aircraft Structures’ Design

Abstract

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.