Analytical modeling of the binary dynamic circuit motion

The binary dynamic circuit, which can be a design scheme for a number of technical systems is considered in the paper. The dynamic circuit is characterized by the kinetic energy of the translational motion of two masses, the potential energy of these masses’ elastic interaction and the dissipative function of energy dissipation during their motion. The free motion of a binary dynamic circuit is found according to a given initial phase state. A mathematical model of the binary dynamic circuit motion in the canonical form and the corresponding characteristic equation of the fourth degree are compiled. Analytical modeling of the binary dynamic circuit is carried out on the basis of the proposed particular solution of the complete algebraic equation of the fourth degree. A homogeneous dynamic circuit is considered and the reduced coefficients of elasticity and damping are introduced. The dependence of the reduced coefficients of elasticity and damping is established, which provides the required class of solutions to the characteristic equation. An ordered form of the analytical representation of a dynamic process is proposed in symmetric determinants, which is distinguished by the conservatism of notation with respect to the roots of the characteristic equation and phase coordinates.

Observability, controllability and stability analysis of discrete time engineering dynamic systems by means of Lagrangian, Hamiltonian and dissipative functions in discrete forms

Purpose The purpose of this paper is to analyze the dynamical state of a discrete time engineering/physical dynamic system. The analysis is performed based on observability, controllability and stability first using difference equations of generalized motion obtained through discrete time equations of dissipative generalized motion derived from discrete Lagrange-dissipative model [{L,D}-model] for short of a discrete time observed dynamic system. As a next step, the same system has also been analyzed related to observability, controllability and stability concepts but this time using discrete dissipative canonical equations derived from a discrete Hamiltonian system together with discrete generalized velocity proportional Rayleigh dissipation function. The methods have been applied to a coupled (electromechanical) example in different formulation types. Design/methodology/approach An observability, controllability and stability analysis of a discrete time observed dynamic system using discrete equations of generalized motion obtained through discrete {L,D}-model and discrete dissipative canonical equations obtained through discrete Hamiltonian together with discrete generalized velocity proportional Rayleigh dissipation function. Findings The related analysis can be carried out easily depending on the values of classical elements. Originality/value Discrete equations of generalized motion and discrete dissipative canonical equations obtained by discrete Lagrangian and discrete Hamiltonian, respectively, together with velocity proportional discrete dissipative function are used to analyze a discrete time observed engineering system by means of observability, controllability and stability using state variable theory and in the method proposed, the physical quantities do not need to be converted one to another.

SYSTEM REPRESENTATIONS OF DYNAMIC PROCESSES IN MECHANICAL OSCILLATORY SYSTEMS WITH SPECIAL FEATURES

Рассматриваются подходы в формировании методологического базиса системного анализа колебательных структур на примере упруго-диссипативных механических систем с двумя степенями свободы. Целью исследования является разработка метода оценки свойств механических колебательных систем с учетом сил вязкого трения на основе частотных функций и функции демпфирования в зависимости от коэффициентов форм связности. Для построения математических моделей используется формализм Лагранжа, матричные методы, элементы теории функций комплексной переменной. Представлены понятия частотной функции и функции демпфирования, отражающие особенности соотношения потенциальной, кинетической энергии системы с учетом сил вязкого трения, представленных диссипативной функцией. Разработан метод построения частотной функции и функции демпфирования, отражающих динамические особенности свободных движений с учетом сил трения в зависимости от коэффициента форм связности. На основе полученных общих аналитических выражений частотных функций и функций демпфирования проведен анализ особенных вариантов механических колебательных систем, представляющих интерес на начальном этапе исследования. Разработанный метод построения частотной функции и функции демпфирования может быть использован для отображения динамических форм связности движений механических колебательных систем. Предложенный метод построения частотной функции и функции демпфирования может быть обобщен на механические колебательные системы, рассматриваемые в различных системах координат. Approaches to the formation of a methodological basis for the system analysis of oscillatory structures on the example of elastic-dissipative mechanical systems with two degrees of freedom are considered. The aim of the study is to develop a method for evaluating the properties of mechanical oscillatory systems with account for viscous friction forces based on frequency functions and damping functions depending on the coefficients of connectivity forms. To build mathematical models, we use Lagrange formalism, matrix methods, and elements of the theory of functions of a complex variable. The concepts of the frequency function and the damping function are presented, which reflect the features of the ratio of the potential and kinetic energy of the system, taking into account the viscous friction forces represented by the dissipative function. A method is developed for constructing the frequency function and damping function that reflect the dynamic features of free movements, taking into account the friction forces depending on the coefficient of connectivity forms. Based on the obtained General analytical expressions of frequency functions and damping functions, special variants of mechanical oscillatory systems that are of interest at the initial stage of research are analyzed. The developed method for constructing the frequency function and the damping function can be used to display dynamic forms of connectivity of movements of mechanical oscillatory systems. The proposed method for constructing the frequency function and the damping function can be extended to mechanical oscillatory systems considered in different coordinate systems.

Damping of Magnetoelastic Waves

A general method for constructing a model of the dissipative function describing the relaxation processes induced by the damping of coupled magnetoacoustic waves in magnetically ordered materials has been developed. The obtained model is based on the symmetry of the magnet and describes both exchange and relativistic interactions in the crystal. The model accounts for the contributions of both the magnetic and elastic subsystems to the dissipation, as well asthe relaxation associated with the magnetoelastic interaction. The dispersion law for coupled magnetoelastic waves is calculated in the case of a uniaxial ferromagnet of the “easy axis” type. It is shown that the contribution of the magnetoelastic interaction to dissipative processes can play a significant role in the case of magnetoacoustic resonance.

Functional analysis of thermal conductivity and viscosity of quasi-solid capillary-porous bodies under varying air environment conditions during museum storage

Fundamental analysis of the thermal conductivity and viscosity of quasi-solid capillary-porous bodies (CPBs), which are museum exhibits’ materials, is presented. The air environment parameters change leads to a temperature gradient in the CPBs. Non-uniform heating of the solid medium, in particular, quasi-solid CPB, is not accompanied by convection, and heat transfer is carried out only due to the mechanism of thermal conductivity. In order to create a mathematical model of this process in CPB, a system of partial differential equations in time and space coordinates is obtained. The resulting system adequately describes the thermal conductivity process in quasi-solid CPBs. The anisotropy of CPB’s thermal parameters, especially, its coefficients of thermal expansion and thermal conductivity, is also taken into account. Theoretically, the deformation process during motion in quasi-solid CPB is taken as reversible. In real conditions, the process is thermodynamically reversible only when it occurs at an infinitesimal speed. Then at each point in time, the CPB is able to establish a thermodynamic equilibrium state. Real motion occurs at a finite velocity, the CPB is not in an equilibrium state at any given moment, so there are endogenous processes that try to get it into a balanced condition. The occurrence of these processes causes the irreversibility of motion, which acts, in particular, through the dissipation of mechanical energy, which eventually turns into heat. The energy dissipation is caused by irreversible processes of thermal conductivity and processes of internal friction or viscosity. The dissipative function for isotropic and anisotropic cases was determined in order to analyze the viscosity of quasi-solid CPBs. The viscosity in the equations of motion can be considered by replacing the stress tensor with a tensor, which additionally takes into account the "dissipative" stress tensor.

PRESTRESS EFFECT ON THE THERMOMECHANICAL RESPONSE OF VISCOELASTIC CIRCULAR CYLINDRICAL SHELL UNDER HARMONIC LOADING

The problem of forced resonant vibrations and dissipative heating of a hinged viscoelastic elastomeric circular cylindrical shell is considered. The problem statement is based on the use of Kirchhoff–Love hypotheses and the concept of complex modules used to describe the cyclic reaction of a viscoelastic material to a harmonic loading. In the axisymmetric setting, it is assumed that there is a membrane force as a consequence of the applied tensile or prestress. The problem is solved in two stages: first the problem of mechanics is solved, and then for the found amplitudes of kinematic and force characteristics the dissipative function is constructed and both the steady-state and transient thermal problem is solved. As a result of solving the steady-state thermal problem, the amplitude-frequency and temperature-frequency curves are built.

The Peculiarities of Oil Displacement in the Process of Oscillating Injection of Polymer Solution into the Bed with Layered Heterogeneity

The authors study the filtration flow of polyethylene oxide (PEO) water solutions of molecular weights 4∙106 and 6∙106 within the concentration range from 0 to 0.05% when exposed to an oscillating hydrodynamic field. Photographs characterizing the displacement of oil (with a viscosity of 10 to 50 mPa. s) with PEO water solutions from model porous formations with layered heterogeneity have been obtained. They have made it possible to specify the effectiveness of different oil displacement modes. It is shown that pumping a polymer solution into porous heterogeneous strata, while exposing it to oscillating hydrodynamic field, proved to yield a higher oil displacement ratio, as compared with a stationary oil displacement mode. The authors find out the conditions providing the positive influence on elastic deformations effects in the process of enhanced oil recovery by using polymer solutions. If elastic deformations take place, the filtration flow of polymer solutions should be carried out in the oscillating mode, whereas the frequency of the oscillating effect on the filtration flow should correspond to the dissipative function maximum. The stated results of the polymer solution flow research, under model conditions of a porous bed, have confirmed the nonlinearity mechanism of the polymer solutions filtration flow. In essence, the molecular and macromolecular non-linearity mechanism of the polymer solutions filtration flow means that in a porous medium under the influence of quasi-regular longitudinal velocity gradients, there arise self-sustained oscillations of reversible macromolecular deployment; the deployed macromolecules, in turn, influence the structure of the filtration flow, both on the molecular and macromolecular levels. Deformation oscillations of macromolecules and dissolubility of dynamic macromolecular structures formed under the influence of tensile currents result in the energy dissipation increase and the filtration flow nonlinearity. The nonlinearity of polymer solutions filtration flow ensures the alignment of the frontal advance of the polymer solutions within a porous bed with a layered heterogeneity and, consequently, higher oil displacement efficiency.

Multi-objective optimization of the dimple/protrusion channel with pin fins for heat transfer enhancement

PurposeThe purpose of this paper is to investigate the optimal geometry parameters in a dimple/protrusion-pin finned channel with high thermal performance.Design/methodology/approachThe BSL turbulence model is used to calculate the flow structure and heat transfer in a dimple/protrusion-pin finned channel. The optimization algorithm is set as Non-dominated Sorting Genetic Algorithm II (NSGA-II). The high Nusselt number and low friction factor are chosen as the optimization objectives. The pin fin diameter, dimple/protrusion diameter, dimple/protrusion location and dimple/protrusion depth are applied as the optimization variables. An in-house code is used to generate the geometry model and mesh. The commercial software Isight is used to perform the optimization process.FindingsThe results show that the Nusselt number and friction factor are sensitive to the geometry parameters. In a pin finned channel with a dimple, the Nusselt number is high at the rear part of the dimple, while it is low at the upstream of the dimple. A high dissipative function is found near the pin fin. In the protrusion channel, the Nusselt number is high at the leading edge of the protrusion. In addition, the protrusion induces a high pressure drop compared to the dimpled channel.Originality/valueThe originality of this paper is to optimize the geometry parameters in a pin finned channel with dimple/protrusion. This is good application for the heat transfer enhancement at the trailing side for the gas turbine.

Modulation Instability in Two Component Bose-Einstein Condensate with Dissipation

In this paper, we consider the dynamic evolution of a binary mixture of a Bose-Einstein condensate taking into account the presence of dissipation inside the components. Using the introduction of the dissipative function, the modified Gross-Pitaevskii equations are obtained. These equations, in contrast to the usual Gross-Pitaevskii equations for two-component condensate, allow us to take into account the dissipation in the system. The influence of dissipative processes on the development of modulation instability in a spatially homogeneous two-component Bose-Einstein condensate is investigated. In contrast to the one-component Bose-Einstein condensate, in which modulation instability arises only when there are forces of attraction between atoms, in a two-component Bose-Einstein condensate nonlinear dynamics, leading to modulation instability is more complex. It essentially depends on the signs and values of the constant interaction of the components, which leads to a greater variety of possible scenarios for the development of modulation instability. The paper considers two cases. The first case is when repulsive forces act inside the components, and the second is when repulsive forces act in the first component, and in the second one - attractive forces. At the same time, the situation when there is a repulsion in the first component, and attraction between the particles in the second component differs significantly from the case of only positive interaction inside the components. The relations between the interaction constants that determine the development of the modulation instability turn out to be different. Given the relations between the interaction constants, taking into account dissipation processes, the occurrence of modulation instability in two-component Bose-Einstein condensates was studied, the maximum growth rate of oscillations was found, and the limits of the existence of modulation instability in the space of wave numbers were found. It is shown that the small effect of dissipation on the modulation instability in the Bose – Einstein condensate is explained not only by the smallness of the friction forces. For wave vectors corresponding to a mode with a maximum increment, the contribution of dissipation in the linear approximation with respect to the dissipative parameter is strictly zero. Thus, the condition for the development of the most rapidly growing mode of oscillations, which determines the beginning of the modulation instability, remains the same as in the nondissipative case.