Issue |
E3S Web Conf.
Volume 110, 2019
International Science Conference SPbWOSCE-2018 “Business Technologies for Sustainable Urban Development”
|
|
---|---|---|
Article Number | 01045 | |
Number of page(s) | 11 | |
Section | Energy Efficiency in the Construction | |
DOI | https://doi.org/10.1051/e3sconf/201911001045 | |
Published online | 09 August 2019 |
Nonlinear parametric oscillations of a viscoelastic shallow shell of variable thickness
1 Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, Kary-Niyazov 39, 100000 Tashkent, Uzbekistan
2 Tashkent University of Information Technologies, Amir Temur 108, 100200 Tashkent, Uzbekistan
3 Moscow State University of Civil Engineering, 129337, 26, Yaroslavskoye Shosse, Moscow, Russia
4 Moscow Region State University, 105005, Radio str, 10A, Moscow, Russia
* Corresponding author: dhodjaev@mail.ru
The problem of parametric oscillations of an isotropic viscoelastic shallow shell of variable thickness under periodic load is considered. It is believed that under the influence of specified load, the shallow shell allows displacements (in particular, deflections), commensurate with its thickness. In a geometrically nonlinear statement, taking into account the viscoelastic properties of material, a mathematical model of the problem has been developed using the classical Kirchhoff-Love hypothesis. Using the Bubnov-Galerkin method based on the polynomial approximation of the deflections, the problem is reduced to the study of the system of integro-differential equations, where time is the independent variable. The solution of the system of integrodifferential equations is determined by the proposed numerical method. Based on this method, a numerical solution algorithm is described. The Koltunov-Rzhanitsyn kernel with three different rheological parameters is chosen as a weakly singular kernel. At the same time, the effect of geometric nonlinearity, viscoelastic properties of material, as well as other physicomechanical and geometric parameters and factors (rheological parameters, thickness, initial shape imperfections, aspect ratios, boundary conditions, excitation coefficient) on the area of dynamic instability is taken into account. The results obtained in this study are in good agreement with the results and data obtained by other authors.
© The Authors, published by EDP Sciences, 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.