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THE EFFECT OF THE AXIAL AND SHEAR STIFFNESSES ON ELASTIC ROD’S STABILITY 轴向刚度和剪切刚度对弹性杆稳定性的影响
Q4 Engineering Pub Date : 2022-12-28 DOI: 10.22337/2587-9618-2022-18-4-62-70
D. Kuznetsova, V. Lalin, N. Malkov
This article is about the nonlinear problems of the theory of elastic Cosserat – Timoshenko’s rods in the material (Lagrangian) description. The variational definition for the problem as finding the stationary point of the Lagrangian functional and differential formulation of static problems were given. The exact stability functional and stability equations of the plane problem for physically linear elastic rods taking into account the axial, shear and bending stiffnesses were received. The exact value of the critical load was obtained taking into account the axial, shear and bending deformations in the problem of the stability of a rod compressed by an axial force. In the present paper the stability of classical simplified rod’s models such as the Timoshenko beam and the Euler–Bernoulli beam was investigated. Also, the stability of third simplified rod’s model, based on beam’s axial and bending stiffnesses, was explored. The stability functionals, the stability equations and critical loads formulations for this three types of simplified models were derived as a particular case of the general theory. There were made the comparisons of described solutions which regards all the rod’s stiffnesses and solutions, based on simplified models. The effect of the axial and shear stiffnesses on rod’s stability was analyzed.
本文讨论了弹性coserat - Timoshenko棒理论在材料(拉格朗日)描述中的非线性问题。给出了求拉格朗日泛函驻点问题的变分定义和静态问题的微分形式。得到了考虑轴向刚度、剪切刚度和弯曲刚度的物理线弹性杆平面问题的精确稳定泛函方程和稳定方程。在轴向力压缩杆的稳定性问题中,考虑轴向、剪切和弯曲变形,得到了临界载荷的精确值。本文对Timoshenko梁和Euler-Bernoulli梁等经典简化杆模型的稳定性进行了研究。同时,对基于梁的轴向刚度和弯曲刚度的第三种简化杆模型的稳定性进行了探讨。作为一般理论的特例,导出了这三种简化模型的稳定性泛函、稳定性方程和临界荷载表达式。将考虑杆的所有刚度的解与基于简化模型的解进行了比较。分析了轴向刚度和剪切刚度对杆体稳定性的影响。
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引用次数: 0
EXPERIMENTAL METHOD FOR STRUCTURAL CONCRETE DAMPING PROPERTIES EVALUATION 结构混凝土阻尼性能评价的实验方法
Q4 Engineering Pub Date : 2022-12-28 DOI: 10.22337/2587-9618-2022-18-4-14-22
V. Smirnov, M. Smolyakov
This article proposes a solution for structural materials such as concrete and cement mortars dynamic properties investigation using experimental modal analysis technique. The studied dynamic characteristics of structural materials include the dynamic modulus of elasticity and the loss factor or its derivatives: the logarithmic oscillation decrement or the relative damping coefficient. Closed expressions are presented for determining the loss factor of mechanical vibrations, obtained on the basis of solving the differential equation for vibrations of a single-mass dynamic system. A method for calculating the loss factor based on the analysis of the spectrum of the transfer function of an oscillatory system loaded with an impulsive dynamic force is presented, in which the results of measuring accelerations at various points of the sample are used as a response. The experiments were carried out on short and long samples made from samples of structural materials - cement mortars with a density of 1500 - 1900 kg/m3 with special aggregates. Based on the solution of the equation of oscillations of a beam with distributed masses, a formula is presented for determining the dynamic modulus of elasticity of the beam material.
本文提出了一种利用试验模态分析技术进行混凝土、水泥砂浆等结构材料动力特性研究的解决方案。所研究的结构材料的动力特性包括动态弹性模量和损耗因子或其导数:对数振荡减量或相对阻尼系数。在求解单质量动力系统振动微分方程的基础上,提出了确定机械振动损失因子的封闭表达式。本文提出了一种计算损耗因子的方法,该方法基于对加载脉冲动力的振荡系统的传递函数谱的分析,将样品各点的加速度测量结果作为响应。实验是用结构材料样品——密度为1500 - 1900 kg/m3的水泥砂浆和特殊骨料制成的短样品和长样品进行的。在求解分布质量梁的振动方程的基础上,提出了确定梁材料动力弹性模量的公式。
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引用次数: 1
DYNAMIC MODEL OF BEAM DEFORMATION WITH CONSIDER NONLOCAL IN TIME ELASTIC PROPERTIES OF THE MATERIAL 考虑材料非局部时间弹性特性的梁变形动力学模型
Q4 Engineering Pub Date : 2022-12-28 DOI: 10.22337/2587-9618-2022-18-4-124-131
V. Sidorov, E. Badina, R. Tsarev
In this paper, the problem of numerical dynamic calculation of a beam made of composite material with a developed internal structure is considered.  The elastic properties are assumed to be nonlocal in time. A short review of the existing methods for mathematical modeling of the dynamic behavior of elements with a developed internal structure was carried out. A non-local in time model of dynamic deformation of a bending beam is constructed. Since the finite element analysis (FEA) is the most demanded numerical method for mechanical systems analysis, a non-local dynamic deformation model is integrated into the algorithm of this method. The equilibrium equation of the structure in motion is solved by an explicit scheme. The damping matrix is obtained from the condition of stationarity of the total deformation energy of a moving mechanical system. A one-dimensional non-local in time model was implemented in the MATLAB software package.
本文考虑了具有发达内部结构的复合材料梁的数值动力计算问题。假定弹性性质在时间上是非局部的。简要回顾了现有的具有发达内部结构的单元动力行为数学建模方法。建立了弯曲梁动态变形的非局部时间模型。由于有限元分析是机械系统分析中最常用的数值方法,因此将非局部动态变形模型集成到该方法的算法中。用显式格式求解了运动结构的平衡方程。根据运动机械系统总变形能的平稳条件,得到阻尼矩阵。在MATLAB软件包中实现了一维非局域时间模型。
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引用次数: 0
MODEL OF THERMOMECHANICAL VIBRATIONS OF CURRENT-CARRYING CONDUCTORS 载流导体的热机械振动模型
Q4 Engineering Pub Date : 2022-12-28 DOI: 10.22337/2587-9618-2022-18-4-39-48
A. Danilin, E. Onuchin, Valery Feldshteyn
In the operation practice of overhead power transmission lines (OHL), the phenomenon of "galloping" of conductors is well known – vibrations with frequencies of ~ 1 Hz and with amplitudes of the order of the static sag [1, 2]. This phenomenon is observed, as a rule, when the symmetry of the conductor section is violated due to icy deposits, which gives the conductor some aerodynamic efficiency. However, this model does not explain all the observed cases of galloping. In this regard, it is advisable to pay attention to the little-known experience of Academician Abram F. Ioffe, who experimentally discovered the self-excitation of a current-carrying conductor – a stretched string that heats up when connected to an electrical circuit. Solving this issue can significantly expand the understanding of the nature of conductor galloping and open up new ways to fend off this phenomenon, which poses a danger to the stability of the functioning of energy systems. This requires a mathematical model of the OHL conductor describing the interaction of mechanical and thermal processes. The purpose of this work is to construct the simplest version of this model, on the basis of which the condition of self-excitation of thermomechanical self-excitation of real OHL conductors can be justified.
在架空输电线路(OHL)的运行实践中,导体的“驰骋”现象是众所周知的-频率为~ 1hz的振动,其振幅为静态垂降的数量级[1,2]。当导体截面的对称性由于冰沉积而被破坏时,通常会观察到这种现象,这给了导体一些空气动力学效率。然而,这个模型并不能解释所有观察到的奔跑情况。在这方面,我们应该注意一下鲜为人知的艾布拉姆·f·约夫院士的经验,他通过实验发现了载流导体的自激作用——一根被拉伸的绳子在连接到电路中时会发热。解决这一问题可以极大地扩展对导体驰骋本质的理解,并开辟新的方法来抵御这种对能源系统功能稳定性构成威胁的现象。这需要一个描述机械和热过程相互作用的OHL导体的数学模型。本工作的目的是建立该模型的最简单版本,在此基础上可以证明实际OHL导体的热力自激的条件。
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引用次数: 0
ON THE CALCULATIONS FOR THE STABILITY OF BEAMS, FRAMES, AND CYLINDRICAL SHELLS IN THE ELASTO-PLASTIC STAGE 梁、框架和圆柱壳在弹塑性阶段的稳定性计算
Q4 Engineering Pub Date : 2022-09-30 DOI: 10.22337/2587-9618-2022-18-3-25-36
G. Manuylov, S. Kosytsyn, M. Begichev
The problems of stability of some beams, Π-shaped frames and cylindrical shells with the elasto-plastic material are considered. The possibility of modeling bars using finite elements of various types is studied. Plate elements and even one-dimensional beam finite elements can be used for modelling compressed rods with geometric and physical nonlinearity. For the problem of stability of a circular cylindrical shell is given the comparison of the authors' results obtained using the FEM with the experimental results of V.G. Sazonov and the calculations of A.V. Karmishin.
考虑了弹塑性材料作用下的梁、Π-shaped框架和圆柱壳的稳定性问题。研究了用不同类型的有限元对杆件进行建模的可能性。板单元甚至是一维梁有限元都可以用来模拟具有几何和物理非线性的压缩杆。对于圆柱壳的稳定性问题,给出了作者的有限元计算结果与v.g.s azonov的实验结果和a.v.k armishin的计算结果的比较。
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引用次数: 0
MODELING OF SEISMIC WAVES STRESSES IN A HALF-PLANE WITH A VERTICAL CAVITY FILLED WITH WATER (THE RATIO OF WIDTH TO HEIGHT IS ONE TO TEN) 半平面内垂直充水腔内地震波应力的模拟(宽高比为1:10)
Q4 Engineering Pub Date : 2022-09-30 DOI: 10.22337/2587-9618-2022-18-3-114-125
V. Musayev
The problem of mathematical modeling of unsteady seismic waves in an elastic half-plane with a ver-tical rectangular cavity filled with water is considered. The problem of modeling problems of the transition peri-od is an actual scientific problem. A quasi-regular approach is proposed to solve a system of linear ordinary dif-ferential equations of the second order in displacements with initial conditions and to approximate the region un-der study. The method is based on the schemes: a point, a line and a plane. An algorithm and a set of programs for solving flat (two-dimensional) problems that allow obtaining a stress-strain state in complex objects have been developed. To assess the reliability of the developed methodology, algorithm and software package, the problem of the effect of a plane longitudinal wave in the form of a Heaviside function on an elastic half-plane was solved. The numerical solution corresponds quantitatively to the analytical solution. The problem of mathe-matical modeling of unsteady elastic stress waves in a half-plane with a cavity filled with water (the ratio of width to height is one to ten) under seismic influence is solved. A system of equations consisting of 8016008 un-knowns is solved. Contour stresses and components of the stress tensor are obtained in the characteristic areas of the problem under study. A cavity filled with water, with a width-to-height ratio of one to ten, reduces the amount of elastic contour stress.
研究了含水垂直矩形空腔的弹性半平面非定常地震波的数学建模问题。转型期问题的建模问题是一个现实的科学问题。提出了一种拟正则方法来求解具有初始条件的二阶位移线性常微分方程组并逼近所研究的区域。该方法是基于方案:一个点,一条线,一个平面。开发了一种求解平面(二维)问题的算法和一套程序,这些问题允许在复杂物体中获得应力-应变状态。为了评估所开发的方法、算法和软件包的可靠性,解决了以Heaviside函数形式存在的平面纵波在弹性半平面上的影响问题。数值解在数量上与解析解相对应。解决了地震作用下含水半平面(宽高比为1:10)非定常弹性应力波的数学建模问题。求解了一个由8016008个未知数组成的方程组。在所研究的问题的特征区域得到了轮廓应力和应力张量的分量。一个充满水的空腔,其宽高比为1:10,减少了弹性轮廓应力的量。
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引用次数: 0
ВЛИЯНИЕ ЖЕСТКОСТИ СВЯЗЕЙ СДВИГА НА НАПРЯЖЕННО-ДЕФОРМИРОВАННОЕ СОСТОЯНИЕ МНОГОЭТАЖНЫХ ЗДАНИЙ 多层建筑的应力变形状态
Q4 Engineering Pub Date : 2022-09-27 DOI: 10.22337/2587-9618-2022-18-3-37-43
Валерий Люблинский
В работе рассмотрены вопросы нелинейного поведения сдвиговых связей, влияющих на изменение распределения напряжений и деформаций в вертикальных конструкциях, а также сопоставление этих напряжений и деформаций с линейной постановкой решения задачи, в которой податливость связей постоянна. . В сложной многосвязной системе многоэтажного здания возникает новое перераспределение напряжений, не совпадающее с первоначальным распределением напряжений. Для корректировки значения жесткости связей использовались экспериментальные данные. Модуль секущей использовался для определения жесткости вертикальных швов. Загрузка производилась ступенчатым методом. На предельной стадии нагружения перераспределение напряжений в несущих элементах здания показало их значительное нивелирование. Требует обсуждения вопрос о предельных деформациях связей сдвига, ограничивающих процесс перераспределения напряжений и деформаций.
在工作中,讨论了影响垂直结构中应力和应变分布变化的非线性关系行为,并将这些应变和应变与线性解决问题的方法进行比较。在复杂的多层楼系统中,新的应力分布发生了,与最初的应力分布不一致。实验数据被用来校正连接强度的值。分叉模块用于检测垂直缝合线的硬度。下载是用阶梯方法完成的。在负载负荷的最后阶段,建筑承载单元的应力重新分配显示了相当大的水准。需要讨论这种转变耦合的极限变形,限制应力和应变的重新分配过程。
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引用次数: 0
NORMAL VIBRATIONS OF SAGGING CONDUCTORS OF OVERHEAD POWER LINES 架空电线下垂导线的正常振动
Q4 Engineering Pub Date : 2022-09-27 DOI: 10.22337/2587-9618-2022-18-3-147-158
A. Valiullin, A. Danilin, Valery Feldshteyn
The phenomenon of self-excitation of thermomechanical vibrations of current-carrying conductors, experimentally discovered by academician A.F. Ioffe, is of practical interest as a possible explanation of the phenomenon of galloping conductors of overhead power transmission lines (OHL) – low-frequency vibrations with frequencies of ~ 1 Hz and with amplitudes of the order of the static conductor sagging. To build the theoretical foundations of this phenomenon, as a special class of self-oscillating systems, it is necessary, first of all, a model of conductor vibrations in the OHL span. With regard to the most studied type of conductor vibrations, high-frequency aeolian vibration, excited by sign-alternating aerodynamic forces from the Karman vortex street, the classical model of a straight string is reasonably applied. However, to study low-frequency vibrations of the galloping type, it is necessary to take into account the effect of sagging of the conductor, the associated elastic tension and, in some cases, the nonlinear nature of the vibrations. The article presents two models for calculating the natural vibrations of sagging conductors (cables) within the framework of the technical theory of flexible threads, assuming the constancy of the tension force along the length. The first model describes linear oscillations of an elastic conductor in the sagging plane. For a system of equations with respect to the displacement components given in natural coordinates, an exact solution of the Sturm-Liouville problem with estimates of the frequency ranges arising is obtained. The second model describes nonlinear vibrations of an elastic conductor in the sagging plane and pendulum vibrations accompanied by an exit from it. The solution of the problem is based on the principle of possible displacements using the Ritz method. The structure of the frequency spectrum and the natural forms of transverse vibrations are studied. The developed models are intended for further investigation of thermomechanical vibrations of conductor and flexible cable systems.
Ioffe院士在实验中发现的载流导体热机械振动的自激现象,可能解释架空输电线路(OHL)导线的驰动现象——频率为~ 1hz的低频振动,其振幅与静态导体下垂的数量级相当。为了建立这一现象的理论基础,作为一类特殊的自振荡系统,首先需要在OHL跨度中建立导体振动模型。对于研究最多的导体振动类型,即由卡门涡街的符号交替气动力激发的高频风成振动,可以合理地应用经典的直弦模型。然而,为了研究驰振型的低频振动,有必要考虑导体下垂的影响,相关的弹性张力,在某些情况下,振动的非线性性质。本文在软螺纹技术理论的框架下,提出了两种计算下垂导线(电缆)固有振动的模型,假设拉力沿长度方向恒定。第一个模型描述弹性导体在下垂平面上的线性振荡。对于一个以自然坐标给出的位移分量方程组,得到了Sturm-Liouville问题的精确解,并给出了频率范围的估计。第二个模型描述了弹性导体在下垂平面上的非线性振动和钟摆振动。该问题的解决是基于使用里兹方法的可能位移原理。研究了振动的频谱结构和横向振动的自然形式。所建立的模型是为了进一步研究导体和柔性电缆系统的热机械振动。
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引用次数: 0
MODELING OF THE MICROCLIMATE OF A RESIDENTIAL COURTYARD DURING RENOVATION 改造过程中住宅院落小气候的建模
Q4 Engineering Pub Date : 2022-09-27 DOI: 10.22337/2587-9618-2022-18-3-44-53
V. Telichenko, Yurii Sumerkin
The article provides an example of modeling the microclimate of a residential courtyard during renovation in conditions of high-density urban development. Modeling is carried out on the basis of a bioclimatic indicator - the environmental heat load index (TNS-index). The calculations are based on the method for analysis temperature radiation and determining the angel factors between a black glob temperature to the surrounding the given platforms of side of residential courtyard. The method shows a good reflection on changes in spatial planning, architectural and construction solutions, landscaping, aeration of the yard, etc. This allows to comprehensively assessing the degree of comfort of the microclimate of the courtyard for specific weather conditions.
本文以高密度城市发展条件下住宅院落改造过程中的小气候建模为例。建模是基于一个生物气候指标——环境热负荷指数(tns指数)。计算是基于分析温度辐射的方法,并确定黑球温度与周围给定的住宅院落侧面平台之间的角度因子。这种方法很好地反映了空间规划、建筑和施工方案、景观美化、庭院通风等方面的变化。这可以全面评估特定天气条件下庭院小气候的舒适程度。
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引用次数: 1
ON THE QHASI CLASS AND ITS EXTENSION TO SOME GAUSSIAN SHEETS 关于qhasi类及其在若干高斯表上的推广
Q4 Engineering Pub Date : 2022-09-27 DOI: 10.22337/2587-9618-2022-18-3-54-64
C. El-Nouty, D. Filatova
Introduced in 2018 the generalized bifractional Brownian motion is considered as an element of the quasi-helix with approximately stationary increment class of real centered Gaussian processes conditioning by parameters. This paper proves that the generalized bifractional Brownian motion is an element of the above mentioned class with no condition on parameters. The quasi-helix with approximately stationary increment class of real centered Gaussian processes is extended to two-dimensional processes as the fractional Brownian sheet, the sub-fractional Brownian sheet, and the bifractional Brownian sheet. This generalized presentation of the class of stochastic processes is used to augment the training samples for generative adversarial networks in computer vision problem.
2018年引入的广义双分数布朗运动被认为是准螺旋的一个元素,具有由参数调节的实中心高斯过程的近似平稳增量类。本文证明了广义双分数布朗运动是上述一类不带参数条件的元。将实中心高斯过程的近似平稳增量类拟螺旋推广到二维过程,即分数布朗片、次分数布朗片和双分数布朗片。这类随机过程的广义表示用于增强计算机视觉问题中生成对抗网络的训练样本。
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引用次数: 0
期刊
International Journal for Computational Civil and Structural Engineering
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