Numerical solutions of the problem of salt-transfer in soils

Yusupov, Maksudbek; Rahkmankulova, Barna; Aynakulov, Sharafidin

doi:10.1051/e3sconf/20199705024

Cited by 6 publications

(5 citation statements)

References 2 publications

(1 reference statement)

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“…The system (3) is solved by methods based on the quadrature formula [7][8][9][10][11][12][13]. Integrating the system (3) twice by t, at the interval [0; t] we have: In the latter system, replacing the integrals with quadrature trapezoid formulas to determine the displacement of the load from the static equilibrium position / = / , / = / , / = / CD) / = / ?…”

Section: Results and Conclusionmentioning

confidence: 99%

Vibrations of high-rise buildings under seismic impact taking into account physical nonlinearity

Mirzaev

Yusupov

Rakhmankulova

et al. 2022

J. Phys.: Conf. Ser.

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Analytical description of vibration loads of the complex construction structure is considered as a system of masses connected by means of viscoelastic springs. To take into account the rheological properties of the spring material, the Boltzmann-Volterra principle is used. A mathematical model of the problem under consideration has been developed, which boils down to the solution of a system of nonlinear integro-differential equations. A solution method based on the use of quadrature formulas has been developed and a computer program has been compiled on its basis. The results are shown as graphs. Influence of nonlinear and rheological properties of spring on amplitude and phase of mass oscillations is investigated.

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Section: Results and Conclusionmentioning

confidence: 99%

Vibrations of high-rise buildings under seismic impact taking into account physical nonlinearity

Mirzaev

Yusupov

Rakhmankulova

et al. 2022

J. Phys.: Conf. Ser.

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“…The system of integro-differential equations (1) with initial conditions (2) is solved by a method based on the use of the quadrature formula [9][10][11][12][13][14]. Integrating twice by t system (1) in the interval [0; t] and assuming ‫ݐ‬ = ‫ݐ‬ = ݊ • ‫,ݐ∆‬ ݊ = 0,1,2,3, … (∆t -step in time) we have:…”

Section: Methods Of Solutionmentioning

confidence: 99%

Numerical modeling of nonlinear viscoelastic vibrations of vehicles

2023

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Nonlinear viscoelastic oscillations of a vehicle in a vertical direction excited by static imbalance are considered. When taking into account the rheological properties of the suspension material and spring, the Boltzmann-Volterra principle was used. Mathematical models of the problem under consideration are obtained, which are described by systems of nonlinear integro-differential equations. A solution method based on quadrature formulas has been developed, and a computer program has been compiled on its basis. The results obtained are reflected in graphs. The influence of the material's rheological properties and the nonlinear characteristics of the suspension and spring on the amplitude and frequency of vertical vibrations of vehicles was investigated.

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“…is solved by the differential sweep method [10,11], according to which the solution is sought in the form:…”

Section: Methodsmentioning

confidence: 99%

Numerical modeling of the salt-transfer problem in soils

et al. 2021

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The article discusses the urgent problem associated with solving the problems of salt transfer in soils and is devoted to numerical modelling of the transference and diffusion of salts in soils, in which the total porosity of the soil is divided by the fraction of “through” and “dead-end” pores with the corresponding concentration of the solution. A brief review of scientific publications devoted to this problem is given. To study and predict the process of the spread of harmful substances, a mathematical model and a numerical algorithm for computer experimentation have been developed. The solution was obtained using a method based on the use of quadrature formulas in combination with the differential sweep method for a system of ordinary second-order differential equations with arbitrary linear boundary conditions. The concentrations of salts in the “through” and “dead-end” pores, respectively, were studied at various values of the filtration process. The results are shown in the graphs.

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Numerical solutions of the problem of salt-transfer in soils

Cited by 6 publications

References 2 publications

Vibrations of high-rise buildings under seismic impact taking into account physical nonlinearity

Vibrations of high-rise buildings under seismic impact taking into account physical nonlinearity

Numerical modeling of nonlinear viscoelastic vibrations of vehicles

Numerical modeling of the salt-transfer problem in soils

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