The nonlinear viscoelastic vibration protection system is considered, which consists of a vibration protection object installed on a platform, which, in turn, is installed on another platform, the lower platform is placed on a vibrating base. It is assumed that the characteristics of the viscoelastic elements of the system have a nonlinear cubic characteristic. A mathematical model is constructed in the form of systems of nonlinear integro-differential equations. The rheological properties of the suspension are taken into account with the Boltzmann-Volterra integral model with the Koltunov-Rzhanitsyn relaxation kernel. To solve the problems, a numerical method is proposed based on the use of quadrature formulas that eliminates the singularities in the relaxation kernel. The influence of the rheological properties of the suspension and the vibrating base on the oscillation modes with respect to the equilibrium position of the system is investigated.
| 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 | 2025-01-03 |
| Son | 4/2 |
| Betlar | 134-141 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| Indeksga qo‘shilgan | 2026-08-27 |
viscoelasticity, integral operator, relaxation kernel, integro-differential equations, trapezoid formula, quadrature formula, Boltzmann-Volterra principle, vibration protection system, вязкоупругость, интегральный оператор, ядро релаксации, интегро-дифференциальные уравнения, формула трапеции, квадратурная формула, принцип Больцмана-Вольтерры, виброзащитная система
| APA | Yusupov, M., & Юсупов, М. (2025). Study of Nonlinear Viscoelastic Vibration Protection System. Ҳисоблаш ва амалий математика муаммолари, (4/2), 134-141. https://journals.airi.uz/index.php/pvpm/article/view/70 |
|---|---|
| GOST (OAK) | Yusupov, M., Юсупов, М. Study of Nonlinear Viscoelastic Vibration Protection System // Ҳисоблаш ва амалий математика муаммолари. – 2025. – № 4/2. – P. 134-141. |
| MLA | Yusupov, M., and Юсупов, М. “Study of Nonlinear Viscoelastic Vibration Protection System.” Ҳисоблаш ва амалий математика муаммолари, (4/2), 134-141, 2025. https://journals.airi.uz/index.php/pvpm/article/view/70 |
| Chicago | Yusupov, M., and Юсупов, М. “Study of Nonlinear Viscoelastic Vibration Protection System.” Ҳисоблаш ва амалий математика муаммолари, (4/2), 134-141 (2025). https://journals.airi.uz/index.php/pvpm/article/view/70 |
| Harvard | Yusupov, M., and Юсупов, М (2025) ‘Study of Nonlinear Viscoelastic Vibration Protection System’, Ҳисоблаш ва амалий математика муаммолари, (4/2), 134-141. https://journals.airi.uz/index.php/pvpm/article/view/70 |
| BibTeX | @article{yusupovm2025,
title = {Study of Nonlinear Viscoelastic Vibration Protection System},
author = {Yusupov, M. and Юсупов, М.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2025},
number = {4/2},
pages = {134-141},
url = {https://journals.airi.uz/index.php/pvpm/article/view/70}
} |
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