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Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia最新文献

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Liquid oscillation in a cylindrical-conical shell under the action of vertical and horizontal excitation 圆柱-锥形壳体在垂直和水平激励作用下的液体振荡
V. Y. Kylynnyk, D. Kriutchenko, Y. Naumenko
Vibrations of an ideal incompressible fluid in shells of revolution have been considered. The shells of revolution under consideration include cylindrical and conical parts. It is assumed that the shell is subjected to vertical and horizontal excitations. The liquid in the shells is supposed to be an ideal and incompressible one. The fluid flow is the irrotational. Therefore the velocity potential that satisfies the Laplace equation exists. The non-penetration conditions are applied to the wetted surfaces of the shell and the kinematic and dynamic conditions on the free surface have been considered. The liquid pressure as the function of the velocity potential is defined using the Bernoulli equation. The problem of determining the fluid pressure is reduced to solving a singular integral equation. The numerical solution of the equation has been obtained by the method of discrete singularities. The method of simulating the free and forced oscillations of the fluid in the shells of revolution has been developed.
考虑了理想不可压缩流体在旋转壳体中的振动。所考虑的旋转壳体包括圆柱形和圆锥形部件。假设壳受到垂直和水平的激励。壳体中的液体被认为是理想的不可压缩液体。流体的流动是无旋的。因此满足拉普拉斯方程的速度势是存在的。将非侵彻条件应用于壳体的湿表面,并考虑了自由表面的运动学和动力学条件。用伯努利方程定义了液体压强作为速度势的函数。确定流体压力的问题被简化为求解一个奇异积分方程。用离散奇异点法得到了方程的数值解。提出了一种模拟旋转壳体中流体自由振荡和强迫振荡的方法。
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引用次数: 0
Liquid vibration modeling in prismatic tanks with quarter baffles 带四分之一挡板的棱柱形槽内液体振动模型
Free vibrations of liquid in a rigid prismatic tank with vertical cross partitions are considered. These partitions divide the tank into four compartments. The partitions make it possible to reduce the amplitude of liquid sloshing in the tank under suddenly applied external loads due to earthquakes, terrorist attacks, emergencies, etc. It is assumed that the fluid is perfect and incompressible, and its motion is vortex-free. Under these conditions, there is a velocity potential that satisfies the Laplace equation. A non-leak condition is applied on the sides, bottom and partitions of the tank. On a free surface, kinematic and dynamic conditions are set. The kinematic condition is that the points of fluid that are on the free surface at the initial moment will remain on that surface for the entire subsequent motion. The dynamic condition is the equality of the fluid pressure on the free surface to the atmospheric pressure. An analytical solution of the boundary value problem for the Laplace equation is obtained for the case of the tank with a square bottom. The free surface oscillations have been found to be symmetrical. It should be noted that the oscillation patterns in each compartment are the same. The frequencies of free oscillations of the fluid in the tank with the cross partitions are increased in comparison with similar frequencies of oscillations of the prismatic tank without partitions. The frequencies obtained and the modes of natural oscillations of the fluid free surface allow us to solve the boundary value problem in case of sudden external loads. In this case, the velocity potential and the function describing the behaviour of the free surface are represented as the series according to the modes of natural fluctuations of the fluid free surface. Therefore it is possible to prevent the unwanted resonant frequencies at exploitation and transportation by designing prismatic tanks in a particular way.
研究了具有垂直横隔板的刚体柱槽中液体的自由振动。这些隔板把油箱分成四个隔间。隔板可以减少由于地震、恐怖袭击、紧急情况等突然施加的外部载荷下罐内液体晃动的幅度。假设流体是完美的、不可压缩的,它的运动是无涡的。在这些条件下,有一个满足拉普拉斯方程的速度势。在罐的侧面、底部和隔板上应用无泄漏条件。在自由曲面上,设定了运动学和动力学条件。运动学条件是,在初始时刻在自由表面上的流体点将在整个后续运动中保持在该表面上。动态条件是自由表面上的流体压力与大气压力相等。得到了方形底罐的拉普拉斯方程边值问题的解析解。发现自由表面振荡是对称的。应该注意的是,每个隔室的振荡模式是相同的。有交叉隔板的槽内流体的自由振荡频率比无隔板的棱柱形槽内流体的自由振荡频率增加。所得的频率和流体自由表面的固有振动模态使我们能够解决在突然外载荷情况下的边值问题。在这种情况下,速度势和描述自由表面行为的函数根据流体自由表面的自然波动模式表示为级数。因此,通过以特定的方式设计棱柱形储罐,可以防止在开采和运输时产生不必要的谐振频率。
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引用次数: 1
The method for calculating singular integrals in problems of axially symmetric Stokes flows 轴对称斯托克斯流奇异积分的计算方法
The flow of a viscous fluid at small Reynolds numbers (Stokes flow) in a three-dimensional formulation is investigated. In this case, the inertial terms in the equations of motion can be neglected. Such flows can occur in nanotubes that can be considered as inclusions in representative volume elements of nanomaterials. By using the fundamental solution of Ossen, an integral representation of the velocity is proposed. This representation is used to receive an integral equation for an unknown density. The solution of the resulting equation makes it possible to calculate the fluid pressure on the walls of the shell. The case of axially symmetric flows is investigated. For this, an integral representation of the unknown velocity in cylindrical coordinates is obtained. By integrating over the circumferential coordinate, the two-dimensional singular integral equation is reduced to one-dimensional one. It has been proved that the components of the kernels in singular operators are expressed in terms of elliptic integrals of the first and second kind. It has been proved that the singularities of the kernels of one-dimensional singular integral equations have a logarithmic character. To calculate elliptic integrals, the Gaussian algorithm based on the use of the arithmetic-geometric mean value is proposed. This procedure allows us to obtain logarithmic singular components with high accuracy, which makes it possible to use special quadrature formulas to calculate such integrals. An algorithm with usage of the boundary element method for the numerical solution of the obtained singular integral equations is proposed. The method for solving one-dimensional singular equations, where the kernels contain elliptic integrals with logarithmic singularities (i.e logarithmic singularity is not expressed explicitly) has been tested. The obtained numerical results have been compared with the well-known analytical solutions. The data obtained indicate the high efficiency of the proposed numerical method.
研究了粘性流体在小雷诺数下的三维流动(斯托克斯流)。在这种情况下,运动方程中的惯性项可以忽略。这种流动可以发生在纳米管中,可以被认为是纳米材料代表性体积元素中的内含物。利用Ossen的基本解,给出了速度的积分表示。这种表示用于接收未知密度的积分方程。所得方程的解使计算壳体壁面上的流体压力成为可能。研究了轴对称流动的情况。为此,得到了未知速度在柱坐标下的积分表示。通过在周坐标上积分,二维奇异积分方程化为一维积分方程。证明了奇异算子核的分量可以用第一类和第二类椭圆积分表示。证明了一维奇异积分方程核的奇异性具有对数性质。为了计算椭圆积分,提出了基于算术-几何均值的高斯算法。这个程序使我们能够高精度地得到对数奇异分量,这使得使用特殊的正交公式来计算这类积分成为可能。提出了一种利用边界元法对得到的奇异积分方程进行数值求解的算法。求解一维奇异方程的方法,其中核包含椭圆积分与对数奇点(即对数奇点不显式表示)已被测试。得到的数值结果与已知的解析解进行了比较。计算结果表明,所提出的数值方法具有较高的效率。
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引用次数: 0
Mathematical modeling and forecasting the dynamics of a segment of the river bed of Seversky Donets river 塞弗斯基-顿涅茨河河床段动力学的数学建模与预测
The flow in the section of the Seversky Donets river in Kharkiv region is studied based on long-term measurements of the channel profile in a 10 cm increments. The geometry of the studied channel section on the Earth's surface has been determined by hydrological maps, and the cross-section profiles have been reconstructed by splines from the measurement results. The analysis of the results has revealed the profile variability in accordance with the change in the bottom sediments and the current year rainfall. A mathematical model describing the flow parameters in dependence on the slope and profile of the river channel has been developed. The model allows calculating flow velocities, dynamic pressure and viscous friction, predicting the evolution of coastal channel lines, the presence of stagnant zones with slow circulation, and predicting the dynamics of bottom drifts and channel overgrowing. Based on the three-dimensional flow of water in the channel with given geometry, numerical calculations by the finite element method are carried out. The flow rates are calculated and the presence of separated stagnant zones with slow circulation in which the channel overgrowth and water quality deterioration could be amplified is shown. Calculations of dynamic pressure and viscous friction shows the presence of areas with increased pressure which, in time, can ruin the riverbanks, contribute to the formation of bottom sediments, and increase the area of ​​stagnant zones with slow circulation. Since there is a system of positive feedbacks in the river ecosystem, the resulting deterioration in circulation and water quality cannot be stopped naturally and require special engineering and hydrogeological measures. The developed model allows planning various specific measures to prevent river erosion and overgrowth, to improve circulation and water quality by introducing the changes into the original geometric model as well as quantifying the changes caused by hydrodynamic factors that affect the evolution of the river system.
哈尔科夫地区塞弗斯基顿涅茨河河段的流量是基于对河道剖面的长期测量,以10厘米的增量进行研究的。通过水文图确定了所研究的地球表面河道断面的几何形状,并根据测量结果用样条法重建了断面剖面。对结果的分析揭示了剖面的变异与底层沉积物的变化和当年的降雨量有关。建立了一个描述水流参数与河道坡度和剖面关系的数学模型。该模型可以计算流速、动压力和粘性摩擦,预测沿海航道的演变、缓慢环流的停滞带的存在,以及预测底部漂移和河道过度生长的动力学。根据给定几何形状的沟道内的三维水流,采用有限元法进行了数值计算。计算了流速,发现存在分离的滞流区,循环缓慢,河道过度生长和水质恶化可能被放大。动压和粘性摩擦的计算表明,存在压力增大的区域,这些区域会及时破坏河岸,促进底部沉积物的形成,并增加缓慢循环的停滞带的面积。由于河流生态系统存在着一个正反馈系统,由此导致的循环恶化和水质恶化无法自然停止,需要采取特殊的工程水文地质措施。开发的模型允许规划各种具体措施,以防止河流侵蚀和过度生长,通过在原始几何模型中引入变化来改善循环和水质,并量化影响河流系统演变的水动力因素引起的变化。
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引用次数: 1
Infinity substitute in exactly minimizing total tardiness in tight-tardy progressive 1-machine scheduling by idling-free preemptions of equal-length jobs 在紧延迟渐进单机调度中,通过等长作业的无空转抢占来精确地最小化总延迟
A schedule ensuring the exactly minimal total tardiness can be found by the respective integer linear programming problem with infinities. In real computations, the infinity which shows that the respective states are either forbidden or impossible is substituted with a sufficiently great positive integer. An open question is whether the substitute can be selected so that the computation time would be decreased. The goal is to ascertain how the increment of the infinity substitute in the respective model influences the computation time of exact schedules. If the influence appears to be significant, then a recommendation on selecting the infinity substitute is to be stated in order to decrease the computation time. A pattern of generating instances of the job scheduling problem is provided. The instances of the job scheduling problem are generated so that schedules which can be obtained trivially, without the exact model, are excluded. Nine versions of the infinity substitute have been proposed. The increment of the infinity substitute in the model of total tardiness exact minimization rendered to solving an integer linear programming problem involving the branch-and-bound approach may have bad influence on the computation time of exact schedules. At least, the greater value of the infinity substitute cannot produce an optimal schedule faster in tight-tardy progressive 1-machine scheduling by idling-free preemptions of equal-length jobs. Roughly the best value of the infinity substitute is the maximal value taken over all the finite triple-indexed weights in the model and increased then by 1. The influence of the “max” infinity substitution is extremely significant. Compared to the case when the infinity is substituted with a sufficiently great integer, the “max” infinity substitution saves up to 50 % of the computation time. This saves hours and even days or months when up to 8 jobs of a few equal processing periods are scheduled for a few thousands of cycles or longer. Therefore, it is strongly recommended always to select the infinity substitute as less as possible in order to decrease the computation time.
通过求解相应的具有无穷大的整数线性规划问题,可以找到保证总延误精确最小的调度。在实际计算中,用一个足够大的正整数来代替表示各自状态被禁止或不可能的无穷大。一个悬而未决的问题是,是否可以选择替代,以减少计算时间。目的是确定各自模型中无穷代换的增量如何影响精确调度的计算时间。如果影响似乎是显著的,则建议选择无穷大代换,以减少计算时间。提供了一种生成作业调度问题实例的模式。生成了作业调度问题的实例,从而排除了在没有精确模型的情况下可以轻松获得的调度。已经提出了9种版本的无穷代换。用分枝定界法求解整型线性规划问题时,总时滞精确最小化模型中无穷代换的增量会对精确调度的计算时间产生不良影响。至少,无穷大代换的较大值不能更快地通过对等长度作业的无空转抢占而在紧延迟渐进单机调度中产生最优调度。粗略地说,无穷代入的最佳值是模型中所有有限的三索引权值的最大值,并将其增加1。“max”无穷代换的影响是非常显著的。与将无穷大替换为一个足够大的整数的情况相比,“max”无穷大替换可节省高达50%的计算时间。当为数千个周期或更长时间安排多达8个相同处理周期的作业时,这可以节省数小时甚至数天或数月的时间。因此,强烈建议总是尽量少地选择无穷代换,以减少计算时间。
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引用次数: 3
期刊
Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia
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