Open AccessDynamics of viscoelastic orthotropic shallow shells of variable thickness
Author(s) -
Bakhodir Normuminov,
Rustamkhan Abdikarimov,
B. Kh. Éshmatov,
Davron Yulchiyev
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/883/1/012214
Subject(s) - orthotropic material , viscoelasticity , nonlinear system , statics , galerkin method , correspondence principle (sociology) , shell (structure) , dynamic relaxation , parametric statistics , variable (mathematics) , relaxation (psychology) , mathematical analysis , materials science , mathematics , geometry , structural engineering , classical mechanics , physics , engineering , composite material , finite element method , psychology , social psychology , statistics , quantum mechanics , economics , market economy
Thin-walled structural elements such as plates, panels, and shells of variable thickness are widely used at present in engineering, machine-building, and construction. Modern technologies allow creating any structural elements of a given shape, material, and the law of thickness variation. Therefore, the solution to the problems of the statics and dynamics of plates, panels, and shells of variable thickness, considering the real properties of the material, is relevant. Nonlinear parametric oscillations of viscoelastic orthotropic shallow shells of variable thickness are considered in the paper. Using the Kirchhoff-Love hypothesis, a mathematical model of the problem is constructed in a geometrically nonlinear statement. To describe the viscoelastic properties of a shallow shell, the hereditary Boltzmann-Volterra theory with the Koltunov-Rzhanitsyn relaxation kernel is used. To obtain resolving equations of the problem, the Bubnov-Galerkin method was used in combination with the numerical method. The effects of various physico-mechanical and geometrical parameters of a shallow shell of variable thickness were investigated.