Problems of nonlinear vibrations of products lying on a viscoelastic layer are considered. A mathematical model was constructed in the form of systems of nonlinear integro-differential equations. The main quadratic theory of hereditary viscoelasticity of Ilyushin-Ogibalov was used as a physical relationship between forces and displacements. The rheological properties of the layer are taken into account using the Boltzmann-Volterra integral model with the Koltunov-Rzhanitsyn relaxation kernel. To solve problems, a numerical method is proposed, based on the use of quadrature formulas, eliminating singularities in the relaxation kernel. The influence of the rheological properties of the layer on the vertical and angular movements of the product was studied.
| Mualliflar | Yusupov, M., Юсупов, М. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashriyot | Тошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази |
| ISSN | 2181-8460, 2181-046X |
| Nashr sanasi | 2024-07-19 |
| Son | 3 |
| Betlar | 106-113 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| Indeksga qo‘shilgan | 2026-08-27 |
relaxation kernel, integro-differential equation, frequency, amplitude, viscoelasticity, vibration protection, stress, strain, integral operator, ядро релаксации, интегро-дифференциальное уравнение, частота, амплитуда, вязкоупругость, виброзащита, напряжение, деформация, интегральный оператор
| APA | Yusupov, M., & Юсупов, М. (2024). Mathematical modeling of nonlinear vibrations of vibration proof products laying on a viscoelastic layer. Ҳисоблаш ва амалий математика муаммолари, (3), 106-113. https://journals.airi.uz/index.php/pvpm/article/view/26 |
|---|---|
| GOST (OAK) | Yusupov, M., Юсупов, М. Mathematical modeling of nonlinear vibrations of vibration proof products laying on a viscoelastic layer // Ҳисоблаш ва амалий математика муаммолари. – 2024. – № 3. – P. 106-113. |
| MLA | Yusupov, M., and Юсупов, М. “Mathematical modeling of nonlinear vibrations of vibration proof products laying on a viscoelastic layer.” Ҳисоблаш ва амалий математика муаммолари, (3), 106-113, 2024. https://journals.airi.uz/index.php/pvpm/article/view/26 |
| Chicago | Yusupov, M., and Юсупов, М. “Mathematical modeling of nonlinear vibrations of vibration proof products laying on a viscoelastic layer.” Ҳисоблаш ва амалий математика муаммолари, (3), 106-113 (2024). https://journals.airi.uz/index.php/pvpm/article/view/26 |
| Harvard | Yusupov, M., and Юсупов, М (2024) ‘Mathematical modeling of nonlinear vibrations of vibration proof products laying on a viscoelastic layer’, Ҳисоблаш ва амалий математика муаммолари, (3), 106-113. https://journals.airi.uz/index.php/pvpm/article/view/26 |
| BibTeX | @article{yusupovm2024,
title = {Mathematical modeling of nonlinear vibrations of vibration proof products laying on a viscoelastic layer},
author = {Yusupov, M. and Юсупов, М.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2024},
number = {3},
pages = {106-113},
url = {https://journals.airi.uz/index.php/pvpm/article/view/26}
} |
Boshqa maqola uchun iqtibos tayyorlash
This article presents a numerical solution to the boundary inverse problem for the equation of relaxation filtration in porous media under elastic conditions. To solve the problem, the marching method of De Sousa was…
The article covers the theoretical and practical aspects of the mathematical model for predicting the movement and level of underground water based on the studied literature. An improved mathematical model based on…
A mathematical model for calculating the vibrations of three-layer rods under spatial loading is developed in the article. Variations of kinetic and potential energies and the work of external forces, substituted into…
The problem of the impact of a longitudinal wave on a system consisting of successively located wells and pipelines of finite length, interacting with soil by elastic-viscous law is considered in the article. The ends…
A related conjugate problem is to ensure that industrial facilities are optimally located throughout a region, taking into account global and local sanitary standards. The main parameters for the spread of harmful…
This paper investigates the qualitative properties of self-similar solutions of a nonlinear cross-diffusion system with nonlinear boundary conditions and a source. A self-similar solution of the cross-diffusion problem…
Computer virology and its formalization began seventy years ago with the work of Alan Turing. The work and results of von Neumann, Fred Cohen, Leonard Adleman, and others who followed them were groundbreaking. They…
In this article, the numerical simulation of a boundary value problem for a fourth order inhomogeneous differential equation with a small parameter at the highest deriva tive is carried out using the preliminary…
This article presents a numerical model and calculation algorithm for solving the problem of two-dimensional oil filtration in a porous medium, in which the change in permeability value when changing reservoir pressure…
Today it is much more difficult to imagine life without computers. There is not a single area that a computer cannot penetrate. Everyday life is rapidly digitizing and unfortunately, more and more people among us are…
Ҳисоблаш ва амалий математика муаммолари — barcha maqolalar · 2024-yil arxivi
This article presents the results of 2018-2023, such as biological diversity, inter-landscape distribution characteristics, density,and number of straggly insects identified from natural and anthropogenic areas of…
This article observational data on the species composition, distribution, population, density, and seasonal damage caused causedby herbivorus bugs. Observationes were carried out in April and September 2021. When…
In the article, the research fields of some species belonging to Paeonia, their significance in human life, adaptation features tovarious ecological conditions are highlighted, and the ecologist groups and other…
This article studies the number of species, population density of terrestrial mollusks of the Topalangdarya basin, located in theSurkhandarya region of Uzbekistan, in various altitudinal regions and biotopes and…
This article sheds light on changes in biomass formation and antimicrobial activity against test pathogenic strains under theinfluence of epigenetic modifiers and elicitors of the endophytic fungus Penicillium…
Shahimardonsoy covered issues such as the soil in the river basin and measures to increase its condition, salinity and fertility, theflora and fauna present in the basin landscape and their conservation.