Vibration analysis of airfoil on hereditary deformable suspensions

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.