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 |
| Nashr sanasi | 2025-01-03 |
| Son | 4/2 |
| Betlar | 134-141 |
| Til | Rus |
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
A multidimensional mathematical model of simultaneous heat and moisture transfer processes in inhomogeneous porous bodies is proposed, considering internal heat and moisture release, heat and moisture exchange with the…
The approximate solution of linear Fredholm integral equations of the second kind is one of the pressing problems in the field of computational mathematics today. Most researchers offer various approximate methods for…
A numerical study of the non-stationary technological process of filtering lowconcentration solutions through a porous medium, proceeding in accordance with Darcy’s law taking into account the phenomena of colmatation…
This paper investigates the construction of an optimal quadrature formula for Fourier integrals of ????(????) function using the method of ????-functions. The function ????(????) belongs to the Hilbert space, which…
In this work, a mathematical model of the thermo-electro-magnetic-elastic deformation process of thin plates with a complex shape was developed and calculation experiments were carried out using the…
In the present article, the problem of constructing the optimal quadrature formula in the sense of Sard is discussed for numerical integration of the weighted integrals in the Hilbert space of real-valued functions…
Using the Duhamel-Neumann relationship and the equations of motion, the Saint-Venant compatibility conditions, are written as a system of six dynamic equations with respect to strains. It is shown that, unlike the…
One of the classical problems in computational mathematics is to construct an interpolation formulas from a countable set of data. This paper demonstrates the problem of construction of optimal interpolation formulas…
To solve elliptic equations, iterative methods are mainly used, the number of iterations in which is often very large. For this reason, it is of interest to develop high-precision direct oriented methods for solving…
This paper presents the construction of an optimal quadrature formula in Sobolev space for integrals with power-logarithmic kernels. Formulas are derived for calculating the coefficients of the optimal quadrature…