Rectilinear Segment Research Articles

Equations for the Inductance of a Rectilinear Segment of a Round Conductor

Equations for the Inductance of a Rectilinear Segment of a Round Conductor

ANALYTICAL SOLUTION OF THE DIFFERENTIAL EQUATION OF FORCED OSCILLATIONS OF A VIBRATION PROTECTION SYSTEM WITH A PIECEWISE LINEAR STATIC FORCE CHARACTERISTIC UNDER HARMONIC KINEMATIC EXCITATION OF BASE DISPLACEMENTS

The need to protect operators of mobile machines from vibrations determines the relevance of the development of mathematical models for studying the dynamic processes of forced vibrations of the vibration-protected mass of the seat with the operator. Analytical solutions have the advantage of being the most accurate. For the design scheme of a vibration protection system with one degree of freedom in the form of a linear oscillator with kinematic excitation, an analytical solution to the problem of forced harmonic oscillations was obtained for the given values of the parameters: the initial absolute displacements and speed of the vibration-protected mass, the initial phase of the given harmonic oscillations of the seat base. At the same time, the expression of the static power characteristic of the vibration protection system was a straight line with a vertical displacement, which made it possible to break the transient process into separate time intervals, within which the local coordinate, showing the deformation of the vibration protection mechanism, is within a separate rectilinear segment of the piecewise linear static characteristic. The results of the comparative analysis showed a significant discrepancy between the piecewise analytical solution and the solution obtained by the numerical integration method.

Behaviour and Analysis of Horizontally Curved Steel Box-Girder Bridges

Various theories and analytical formulations were implemented and exploited in the 1980s and 1990s for the design of bridge beams or decks curved in the horizontal plane and subjected to out-of-plane loads. Nowadays, the Finite Element Method (FEM) is a valid tool for the analysis of structures with complex geometries and, therefore, the development of sophisticated analytical formulations is not needed anymore. However, they are still useful for the validation of FE models. This paper presents the case study of an existing viaduct built in North Italy, aiming to compare analytical approaches and numerical modelling. The bridge is characterized by an axis curved in two directions and a rectilinear segment. The global analysis of the viaduct is carried out with special attention to the attributes that cause torque action and bending moment. The theoretical developments focus on a deeper understanding of the torsional response under different constraint and loading conditions and aspire to raise awareness of the mutual interaction of flexural and torsional behaviour, that are always present in these complex curved systems. The examination of the case study is also obtained by comparing the response of isostatic and hyperstatic curvilinear steel box-girders.

Deformation of a pipeline element under cyclic loading by internal pressure

An experimental study of the strain of a rectilinear segment of a pipeline Du 200 made of steel 20 under cyclic loading by internal pressure was carry out. The tests were performed on a pneumohydraulic stand under conditions of flat stress, normal temperatures, and load cycle asymmetry with registration of circular and axial elastic-plastic strain. The aim of the work was to test an experimental technique for studying the effect of ratcheting (unilateral accumulation of plastic deformations) on real structural elements when changing the modes of cyclic loading. According to the results of the study, curves of cyclic deformation (ratcheting) of the pipe in the circular and axial direction on the basis 100 cycles were obtained.

Structures based on elliptical arcs in the problems of designing trajectories and creating mechanical systems

Abstract. An experimental study of the strain of a rectilinear segment of a pipeline Du 200 made of steel 20 under cyclic loading by internal pressure was carry out. The tests were performed on a pneumohydraulic stand under conditions of flat stress, normal temperatures, and load cycle asymmetry with registration of circular and axial elastic-plastic strain. The aim of the work was to test an experimental technique for studying the effect of ratcheting (unilateral accumulation of plastic deformations) on real structural elements when changing the modes of cyclic loading. According to the results of the study, curves of cyclic deformation (ratcheting) of the pipe in the circular and axial direction on the basis 100 cycles were obtained.

ПРО КРАЙОВІ ЗАДАЧІ ДЛЯ РІВНЯННЯ ПУАССОНА У БАГАТОЛИСТІЙ ОБЛАСТІ, СКЛАДЕНІЙ ІЗ РІЗНИХ КРУГОВИХ СЕГМЕНТІВ

The non-classical boundary problem of the mathematical physics for the two-dimensional Poisson equation is considered. As the area, in which the solution is sought, the area, made up of different circular segments, folded into a multi-sheet plate of a book structure, is taken. All sheets are different from each other, both in their physical properties and in geometric dimensions, and are interconnected by a chord common to all sheets. The problem statement is given and its exact solution is obtained.The solution to the problem is considered in bipolar coordinate systems, each of which is associated with one of the segments. In this case, all coordinate systems have a common parameter - the length of the rectilinear segment boundary. As a method for solving the problem, the classical method of separation of variables is used – the Fourier method. Although the Dirichlet problem is considered as a basic one, however, the proposed method can be applied in the case when conditions of other types are given on the arcs of separate circles: Neumann or the third main problem.The statement of the considered problem differs from the classical one in that the conjugation conditions of fields on the line of connection of segments are added to the traditional boundary conditions. These conditions represent the equality of the values of the functions and the equality to zero of the sum of linear combinations of their normal derivatives. The solution is constructed (selected) in such a way that the first of the field conjugation conditions is fulfilled automatically for any choice of unknown functions. The boundary conditions on the segments and the second conjugation condition make it possible to determine all the unknown functions of the problem. To apply the Fourier method, it is necessary that all boundary functions are equal to zero at the corner points of the segments. If this condition is violated, a modification of the method that allows one to obtain an exact solution in this case is proposed. As an application, such problems are considered: a) on the torsion of a composite rod, the cross-section of which is two different segments; b) the stationary heat conductivity problem for two glued half-segment with sources of heat inside the area. Exact analytical solutions to these new problems have been obtained.

Aeolian Processes in Forest-Steppe Landscapes in the Upper Angara Region in the Holocene

Presented are the results from investigating the aeolian sand massifs in the Belaya river valley. The Belaya, Kholmushino and Usolye massifs with the area of 2, 1.4 and 269 km, respectively, are singled out. They are differentiated by the degree and magnitude of manifestation of aeolian processes, and by the morphology of landforms. The Belaya massif is characterized by narrow gully‒low ridge topography. The initial fluvial relief is moderately modified because of the isolated location of the area in the spur of the incised meander and its boundedness by the slope of the narrow segment of the valley. In the Kholmushino massif located in the zone of contact of the segment of the incised channel and the broadening of the valley, aeolian forms were able to evolve fully but they occur only along narrow terraced surfaces of the rectilinear segment of the valley. The more favorable conditions emerged for the evolution of the Usolye massif. The broad-floodplain type of Belaya channel promoted accumulation of significant volumes of sandy material and its free transport in the process of aeolian morphogenesis. The most intense aeolian accumulation was observed in the lower reaches of the Belaya at the interface of the Late Glacial and Holocene (from 13.1 kyr BP) and was proceeding throughout the Early Holocene until 8.9 kyr BP when there occurred a decrease in activity of the aeolian processes and an intense soil formation began. The landscape-climatic conditions of the Atlantic period were favorable for the attenuation of aeolian activity and for a gradual fixation of sands by vegetation. The intensification phases of the aeolian processes were replaced by stages of a decrease in activity of the aeolian morphogenesis and soil formation in the intervals 9.3‒8.6; 6.7‒6; 3.5‒2.6 and 1.2‒0.9 kyr BP. The pedogenesis stages coincided with an increase in heat and moisture availability. Analysis of the findings suggests the rhythmic behavior in the evolution of the region’s natural environment in the Late Glacial with the manifestation of aeolian phases every 4‒5 ka and phases of intense soil formation every 1.9‒2.5 ka.

Use of eye tracking device to evaluate the driver’s behaviour and the infrastructures quality in relation to road safety

Eye tracking allows to obtain important elements regarding the drivers’ behaviour during their driving activity, by employing a device that monitors the movements of the eye and therefore of the user’s observation point. In this paper it will be explained how analysing the behaviour of the drivers through the eye movements permits to evaluate the infrastructures quality in terms of road safety.Driver behaviour analysis have been conducted in urban areas, examining the observation target (cars, pedestrians, road signs, distraction elements) in quantitative terms (time of fixing each singular target). In particular, roundabout intersections and rectilinear segment of urban arterials have been examined and the records related to seven drivers’ behaviour were collected, in order to have a significant statistical variability. Only young people has considered in this study.The analyses carried out have made it possible to assess how different types of infrastructure influence the behaviour of road users, in terms of safety performance given by their design.In particular, quantitative analyzes were carried out on driving times dedicated to observing attention rather than distraction targets. From a statistical point of view, the relationship that exists between the characteristics of the driver, weather conditions and infrastructure, with driving behavior (traveling speed and attention / inattention time) was analyzed by ANOVA method.

Singular behavior of harmonic maps near corners

For a harmonic map transforming the contour of an angle of the boundary into a rectilinear segment of the boundary , the behavior near the vertex of the specified angle is investigated. The behavior of the inverse map near the preimage of the vertex is investigated as well. In particular, we prove that if ϕ is the value of the angle at which a ray is issued from the vertex, and θ is the value of the angle at which its image leaves the vertex's, then the dependence of θ on ϕ is described by a discontinuous function. Thus, such a behavior of the harmonic map qualitatively differs from the behavior of the corresponding conformal map: for the latter one, the dependence is described by a linear function.

Effect of the blade loading distribution on hydrodynamic performance of a centrifugal pump with cylindrical blades

The effect of the blade loading distribution on head, radial force and pressure pulsation of a low specific-speed centrifugal pump with cylindrical impeller blades were investigated in the present study. Blade shapes were obtained by adopting the 1D inverse design method, impellers with different blade loading curves were obtained while the distribution of the blade loading was carefully tailored. Threedimensional URANS simulation method based on the Shear stress transport (SST) k-ω turbulence model was employed for the analyzation of flow patterns. Numerical results including the pressure distribution and velocity profile were validated by comparing with the available experimental data, and an acceptable agreement was obtained. Three typical parameters of the blade loading curve, including the location of the fore-loading point (mpre), location of the aft-loading point (mpost) and slope of the rectilinear segment (K), were analyzed. Results showed that the well-designed blade loading curve, such as the fore-loading impeller, can effectively reduce the pressure pulsation amplitude and the radial force. The significant effect of the variation of the aft-loading point on pump hydrodynamic performance was also investigated. Meanwhile, pressure and velocity distributions at different slopes of the blade loading curves show that the fore-loading impeller produces more uniform flow issuing from the impeller than that of the pump with aft-loading impeller, thus reduces the radial force and pressure pulsation of the pump.

Guaranteed strategies for escaping encirclement

This paper considers a conflict situation on the plane as follows. A fast evader E has to break out the encirclement of slow pursuers P j1,...,j n = {P j1,..., P jn }, n ≥ 3, with a miss distance not smaller than r ≥ 0. First, we estimate the minimum guaranteed miss distance from E to a pursuer P a , a ∈ {j 1,..., j n }, when the former moves along a given straight line. Then the obtained results are used to calculate the guaranteed estimates to a group of two pursuers P b,c = {P b , P c }, b, c ∈ {j 1,..., j n }, b ≠ c, when E maneuvers by crossing the rectilinear segment P b P c , and the state passes to the domain of the game space where E applies a strategy under which the miss distance to any of the pursuers is not decreased. In addition, we describe an approach to the games with a group of pursuers P j1,... jn , n ≥ 3, in which E seeks to break out the encirclement by passing between two pursuers P b and P c , entering the domain of the game space where E can increase the miss distance to all pursuers by straight motion. By comparing the guaranteed miss distances with r for all alternatives b, c ∈ {j 1,..., j n }, b ≠ c, and a ∉ {b, c}, it is possible to choose the best alternative and also to extract the histories of the game in which the designed evasion strategies guarantee a safe break out from the encirclement.

Mathematical modeling of a whipping instability of an electrically charged liquid jet

Recent experiments have demonstrated that a fundamental mechanism of the electrospinning process is the rapid whipping of an electrically charged liquid jet. This article focuses on the mathematical modeling of such a whipping, also called a bending, instability of the electrically charged liquid jet, which is created from a polymer solution by electrospinning. The ideal rectilinear segment of the electrically charged jet, the so-called “viscoelastic dumbbell”, is a key attribute of the mathematical model presented herein. We have formulated governing equations which can be used to describe the physical properties and dynamics of this segment in a three-dimensional Cartesian coordinate system. We developed a multi-threaded computer application that allows us to simulate the electrospinning process. This application is the algorithmization of a numerical discretization. Using three-dimensional computer graphics we are able to visualize the results of the computer simulations of paths of the jet as well as the depositions of electrospun nanofiber. These theoretical results are in agreement with previously published laboratory experiments.

Möbius bilipschitz homogeneous arcs on the plane

A mobius bilipschitz mapping is an η-quasimobius mapping with the linear distortion function η(t) = Kt. We show that if an open Jordan arc γ ⊂ C with distinct endpoints a and b is homogeneous with respect to the family F K of mobius bilipschitz automorphisms of the sphere C with K specified then γ has bounded turning RT(γ) in the sense of Rickman and, consequently, γ is a quasiconformal image of a rectilinear segment. The homogeneity of γ with respect to F K means that for all x, y ∈ γ {a, b} there exists f ∈ F K with f(γ) = γ and f(x) = y. In order to estimate RT(γ) from above, we introduce the condition BR(δ) of bounded rotation of γ, and then the explicit bound depends only on K and δ.

A Geometric Extension of Schwarz’s Lemma and Applications

Abstract Let f be a holomorphic function of the unit disc , preserving the origin. According to Schwarz’s Lemma, |f'(0)| ≤ 1, provided that . We prove that this bound still holds, assuming only that f() does not contain any closed rectilinear segment [0, eiϕ], ϕ ∊ [0, zπ], i.e., does not contain any entire radius of the closed unit disc. Furthermore, we apply this result to the hyperbolic density and give a covering theorem.

Improving of the aerodynamic characteristics of turbine transonic nozzle vane cascades

A detailed experimental investigation of two transonic turbine nozzle vane cascades aimed at improving their characteristics is carried out. The initial cascades had a convex suction side in the outlet area between the throat and trailing edge with skew angles equal to 11° and 15°. Only the shape of this suction side part was modernized. Different approaches to modernizing the cascades were used: in the first cascade with the flow outlet angle equal to around 17° and with the reduced flow outlet velocity λ1 = 1, a rectilinear segment with the skew angle decreased to 9° was formed on the suction side near the trailing edge, and in the second cascade with the flow outlet angle equal to around 23° and λ1 = 1.11, inverse concavity was formed in the same zone of cascade outline. A smaller flow over-expansion degree downstream of the throat was obtained in both cascades, the point of maximum velocity shifted toward the trailing edge, and lower flow velocity was obtained near the trailing edge. The study results confirmed that owing to the modernization, the profile loss coefficient at 0.9 = λ1 = 1.1 has decreased by 0.4–0.6%.

Effect of Structural Relaxation on the In-Plane Electrical Resistance of Oxygen-Underdoped ReBa $$_2$$ 2 Cu $$_3$$ 3 O $$_{7-\delta }$$ 7 - δ (Re = Y, Ho) Single Crystals

The effect of jumpwise temperature variation and room-temperature storing on the basal-plane electrical resistivity \(\rho _{ab}\) of underdoped ReBa\(_2\)Cu\(_3\)O\(_{7-\delta }\) (Re = Y, Ho) single crystals is investigated. Reducing the oxygen content has been revealed to lead to the phase segregation accompanied by both, labile component diffusion and structural relaxation in the sample volume. Room-temperature storing of \({\text {YBa}}_2{\text {Cu}}_3{\text {O}}_{7-\delta }\) single crystals with different oxygen hypostoichiometries leads to a substantial widening of the rectilinear segment in \(\rho _{ab}(T)\) in conjunction with a narrowing of the temperature range of existence of the pseudogap state. It is established that the excess conductivity obeys an exponential law in a broad temperature range, while the pseudogap’s temperature dependence is described satisfactory in the framework of the BCS-BEC crossover theory. Substituting yttrium with holmium essentially effects the charge distribution and the effective interaction in CuO planes, thereby stimulating disordering processes in the oxygen subsystem. This is accompanied by a notable shift of the temperature zones corresponding to transitions of the metal-insulator type and to the regime of manifestation of the pseudogap anomaly.

Optimal synthesis of a path generator six-bar linkage

This paper presents the optimal dimensional synthesis of a six-bar linkage with rotational constraints in which a point on the second dyad generates the desired path. The aim of the synthesis is to bring the generated path as close to the given path as possible, the given path being a combination of a rectilinear segment and a circular arc. A large population of mechanisms is formed using the method of controlled decrease of allowed deviations and the differential evolution algorithm — DE within the optimization procedure. Establishing the initial boundaries of allowed deviations “far” enough leads to significant accumulation of generated paths around the given one. The path is given by a large number of precision points. The mechanisms realizing satisfactory motion are obtained by the method of controlled decrease of allowed deviations with the application of specific adaptation of algorithm DE.

A case of motional stability of railway wheel pair

Motion of the railway wheel pair along a rectilinear segment of track was considered within the Carter model of wheel-rail interaction with regard for the nonlinear part of the creep forces. The linear parts of these forces were modified by the integral Volterra operator characterizing the visco-elastic characteristics of the material. Stability of motion of the wheel pair with zero conicity was studied using the integro-differential equations.

A Boundary Integral Equations Method for Computing Inertial and Damping Characteristics of Arbitrary Contours in Deep Fluid

A modification of Yeung’s boundary-integral method of solving the linear boundary-value problem related to the frequency-domain hydrodynamic characteristics of arbitrary smooth contours intersecting the free surface of the fluid has been further developed. The modification relates to the integral equation’s discretization step and consists in substituting the orthodox one-point collocation with another collocation method satisfying the integral equation in the mean over each rectilinear segment in the polygonal approximation of the contour. Relatively complicated in fluence functions were evaluated analytically. Numerical tests demonstrate that the suggested method shows better accuracy at equal number of panels (segments) and is robust and reliable enough to be recommended for practical calculations.

A Model Problem of the Design and Aerodynamical Calculation of the Gliding Wing Airfoil of a Wing-in-Ground Vehicle

The problem of the design and aerodynamical calculation of a wing airfoil whose trailing edge glides over a plane horizontal surface is formulated and solved. The known airfoil undersurface is a rectilinear segment forming a given angle with the ground surface, while the upper surface is sought on the basis of a preassigned velocity distribution. This distribution is taken from a class of hydrodynamically advantageous distributions ensuring separationless flow around the airfoil within the framework of the mathematical flow model adopted. The problem is reduced to a mixed boundary value problem in a half-plane and solved analytically. For calculating the lift coefficient the assumption of a thin jetlet flowing between the horizontal region of the airfoil contour and the ground surface is introduced. The effect of the law of pressure decrease along the jetlet, from the stagnation to the exit value, on the lift coefficient is studied. On the basis of the calculations performed a conclusion is drawn concerning the influence of the rectilinear region slope on the airfoil shape; it is also shown how the slope and the value of the maximum velocity on the airfoil affect its shape and the lift coefficient.