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Mathematical simulation of nonlinear oscillations of viscoelastic pipelines conveying fluid

APPLIED MATHEMATICAL MODELLING 2019年 66卷 662-679页

作者： Khudayarov, B. A. Turaev, F. Zh Tashkent Inst Irrigat & Agr Mechanizat Engineers Dept Higher Math Str Kari Niyazova 39 Tashkent 100000 Uzbekistan

A mathematical model of the problem of nonlinear oscillations of a viscoelastic pipeline conveying fluid is developed in the paper. The Boltzmann-Volterra integral model with weakly singular kernels of heredity is used to describe the processes of pipeline strain. Using the Bubnov-Galerkin method, the mathematical model of the problem is reduced to the study of a system of ordinary integro-differential equations, where time is an independent variable. The solution of integro-differential equations is determined by a numerical method based on the elimination of the singularity in the relaxation kernel of the integral operator. Using the numerical method for unknowns, a system of algebraic equations is obtained. To solve a system of algebraic equations, the Gauss method is used. A computational algorithm is developed to solve the problems of the dynamics of viscoelastic pipelines with a flowing fluid. The algorithm of the proposed method makes it possible to investigate in detail the effect of rheological parameters on the character of vibrational strength of viscoelastic pipelines with a fluid flow, in particular, in the study of free oscillations of pipelines based on the theory of ideally elastic shells. On the basis of the computational algorithm developed, a set of applied computer programs has been created, which makes it possible to carry out numerical studies of pipeline oscillations. The influence of singularity in the heredity kernels and the geometric parameters of the pipeline on the vibrations of structures possessing viscoelastic properties is numerically investigated. It is shown that an account of viscoelastic properties of pipeline material leads decrease in the amplitude and frequency of oscillation. It is established that to reveal the influence of viscoelastic properties of structure material on the pipeline oscillations, it is necessary to use the Abel-type weakly singular kernels of heredity. The obtained results of numerical simulation can be us

关键词： Mathematical model Simulation viscous-elasticity lntegro-differential equations Numerical algorithm Pipeline Fluid Cylindrical shell Oscillatory process Relaxation kernel

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Non-linear evolution of P-waves in viscous-elastic granular saturated media

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TRANSPORT IN POROUS MEDIA 2008年第2期73卷 125-140页

作者： Nikolaevskiy, Victor N. Russian Acad Sci Inst Earth Phys Moscow 123995 Russia

The Frenkel-Biot P-wave of the first type is a seismic longitudinal wave observed in rocks fully saturated with oil, water or high-pressure gas. The P-wave of the second type is observed in unsaturated soils and other porous media saturated with gas of low pressure. Their models include properties of the skeleton, that is, its elastic modules and its own viscosity. If the non-linear terms are accounted for, the asymptotic analysis, usual for weak non-linear waves, might be applied to get the wave spectrum evolution. The wetness of grains contacts in soils and such components of oil as tars or bitumen, which attached to the skeleton, can be described by generalized viscous-elastic stress-strain connections. The latter are nominated in such a way that creates the narrow frequency interval of wave of negative dissipation where the non-linear terms begin to play the main role besides the neutral stability for waves of zero wave number. The corresponding case, relevant to single continuum model, was analyzed in the literature. Here it is shown that the interpenetrating continua with interaction of the Darcy type provide the dissipation sink in the wave evolution equation. This generalization, (Tribelsky, M.I.: Phys. Rev. Lett. (2007, submitted)), can stabilize the asymptotic solution of the evolution equation, where the dispersion terms are omitted. The asymptotic solution of the equation is invariant to initial conditions and it means a transformation of initial wave spectra to unique one while wave is spreading in the viscous-elastic medium under consideration. This explains the phenomenon, observed in wave tests at marine beach, when any dynamics action (impact, explosion, and ultrasound action) created at some distance a wave of a single frequency (similar to 25 Hz).

关键词： non-linear dynamics viscous-elasticity wave evolution soils fragmented rocks fluid saturation continuum Biot waves Darcy law stabilization

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MECHANICAL STUDIES OF RUBBER MICRO- AND NANOCOMPOSITES PROMISING FOR THE TIRE INDUSTRY. UNIAXIAL AND BIAXIAL TESTS

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MATERIALS PHYSICS AND MECHANICS 2019年第4期42卷 445-454页

作者： Garishin, O. K. Shadrin, V. V. Kornev, Yu, V Inst Continuous Media Mech UB RAS Academician Korolev St 1 Perm Russia Perm State Natl Res Univ Bukireva St 15 Perm Russia Inst Appl Mech RAS Leningradsky Prt 7 Moscow Russia

Complex studies of the mechanical properties of composites based on rubber vulcanizates with various micro and nanofillers (which are already used or intended to be used in the tire industry) were carried out. Testing of composites for uniaxial stretching to rupture allowed us to determine the reinforcing effects of the input of fillers, as well as materials strength and deformability. Cyclic tests for biaxial loading in two mutually perpendicular directions were also carried out. As a result, the effects of softening and the occurrence of induced mechanical anisotropy in filled elastomers under the action of a biaxial load were studied. It was shown that there are no hysteresis losses in the unfilled elastomer, and there is no induced anisotropy. For a filled elastomer, the value of hysteresis and induced anisotropy depend on the type of filler, its concentration and particle size.

关键词： rubber mineral fillers strength ultimate strain biaxial loading viscous-elasticity softening induced mechanical anisotropy

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Mathematical Simulation of Deformational and Relaxation Process in Capillary-porous Materials 11

Mathematical Simulation of Deformational and Relaxation Proc...

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PERSPECTIVE TECHNOLOGIES AND METHODS IN MEMS DESIGN MEMSTECH

作者： Sokolovskyi, Ja Mokrytska, O. Krishtapovich, V. Natl Univ Forestry & Wood Technol Ukraine Gen Chuprynky Str 103 UA-79057 Lvov Ukraine

ISBN: (纸本)9786176078081

Within mechanics of heterogeneous media there was developed a mathematical model of stress-deformable - state of wood as a three-phase system consisting of solid (wood material), liquid and air-vapor mixture phases. Defining relation allow to describe elastic, viscoelastic, residual strain deformations and deformations caused by mechanism of mechanical and sorption creep. The object-oriented software was created to implement the mathematical model of viscoelastic deformation of capillary-porous materials using the finite element method.

关键词： simulation creep viscous-elasticity capillaries-porous materials moisture deformation

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Numerical Calculation of viscous-Elastic Fluid Flooding Residual Oil Film in the Complex Pore

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Open Journal of Fluid Dynamics 2013年第3期3卷 147-151页

作者： Lili Liu Chao Yu Lihui Wang Lu Liu Daqing Petroleum Equipment Group Daqing China Department of Petroleum Engineering Northeast Petroleum University Daqing China

In order to analyze the stress and deformation of different permeability of residual oil film in the complex pore, which are affected by the viscous-elasticity of the fluid, the hydrodynamic displacement mechanism is explored from the stand-point of hydrodynamics, that is, the residual oil film displaced by alternating injection of different concentrations of the polymer solution, viscous-elastic fluid flow equation is established in the complex pore by choosing continuity equation, motion equation and the upper convected Maxwell constitutive equation. The flow field is computed by using the method of numerical analysis. Not only the stress and deformation of residual oil film on the different permeability of micro pores, but also the analysis of the flooding mechanism of alternating injection of different concentrations of the polymer solution is got. The results show that the larger the viscous-elasticity of polymer solution is, the bigger the normal deviatoric stress acting on the residual oil film is;the distribution of normal deviatoric stress has the abrupt change. The stronger the viscous-elasticity of the polymer solution is, the bigger the horizontal stress difference acting on the residual oil film is and the more obvious the deformation is;the high-concentration polymer solution is suitable for high-permeability micro pores. Low-concentration polymer solution is suitable for medium and low-permeability micro pores. Alternating injection of polymer solution can improve Volumetric Sweep Efficiency and increase the deformation of residual oil film, which is conducive to enhancing oil recovery.

关键词： Complex Pore Residual Oil Film Deformation viscous-elasticity Permeability

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