Abstract
This paper describes the analyses of the nonlinear vibrations and dynamic stability of an airfoil on hereditary-deformable suspensions. The model is based on two-degree-of-freedom structure in geometrically nonlinear statements. It provides justification for the choice of the weakly singular Abelian type kernel, with rheological parameters. To solve problems of viscoelastic system with weakly singular kernels of relaxation, a numerical method has been used, based on quadrature formulae. With a combination of the Galerkin and the presented method, problems of nonlinear vibrations and dynamic stability in viscoelastic two-degree-of-freedom structure have been solved. A comparison of the results obtained via this method is also presented. In all problems, the convergence of the Galerkin method has been investigated. The implications of material viscoelasticity on vibration and dynamic stability are presented graphically.
Highlights
At recent years, the mechanics of composite materials has great impact to the development of the aerospace industry
There are many problems such as deformation, durability, vibrations, and dynamic stability of the structures made from composite materials
Interest in problems of deformation, durability, vibrations, and dynamic stability of structures made of composite material is prompted by the fact that they are the main load-bearing elements in, etc
Summary
The mechanics of composite materials has great impact to the development of the aerospace industry. There are many problems such as deformation, durability, vibrations, and dynamic stability of the structures made from composite materials. Badalov on the basis of quadrature rules, it is possible to solve the system of nonlinear integrodifferential equations with weakly singular kernels of the Abel and other types This method provides results of a reasonably high accuracy and is universal. According to the numerical method [14] and [15] based on quadrature formulas; it is possible to solve the system of nonlinear integro-differential equations with weakly singular kernels. This method provides a high accuracy of results
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