Open AccessDynamic stability and vibrations of thin-walled structures considering heredity properties of the material
Author(s) -
B.A. Khudayarov,
Ф.Ж. Тураев,
Valizhon Vakhobov,
Otabek Gulamov,
Sa’dulla Shodiyev
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/869/5/052021
Subject(s) - galerkin method , mathematics , boundary value problem , nonlinear system , vibration , polynomial , partial differential equation , mathematical analysis , stability (learning theory) , quadrature (astronomy) , computer science , physics , quantum mechanics , machine learning , optics
Dynamic stability and vibrations of thin-walled structures, taking into account the heredity properties of the material are considered in the paper. Mathematical models were constructed in a two-dimensional statement, using the Karman theory of plane plate strains and A.A. Ilyushin aerodynamic theory. When realizing the physico-mechanical properties of the material of the object, the systems of integro-differential equations (IDE) in partial derivatives with the corresponding initial and boundary conditions are taken as mathematical models of the problems under consideration. The obtained nonlinear partial IDEs using the Bubnov-Galerkin method under considered boundary conditions are reduced to solving systems of nonlinear ordinary IDEs with constant or variable coefficients with respect to the time function. The integration of equations obtained using the polynomial approximation of the deflections was carried out by a numerical method based on the use of quadrature formulas. Based on this method, an algorithm for the numerical solution of the problem was developed suitable for all viscoelastic and elastic elements of thin-walled structures of plate type.