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The brachistochronic motion of a vertical disk rolling on a horizontal plane without slip 无滑移的垂直圆盘在水平面上滚动的腕部慢性运动
IF 0.7 Q4 MECHANICS Pub Date : 2017-01-01 DOI: 10.2298/tam171002015o
A. Obradović, S. Šalinić, R. Radulović
This paper deals with the brachistochronic motion of a thin uniform disk rolling on a horizontal plane without slip. The problem is formulated and solved within the frame of the optimal control theory. The brachistochronic motion of the disk is controlled by three torques. The possibility of the realization of the brachistochronic motion found in presence of Coulomb dry friction forces is inspected. Also, the influence of values of the coefficient of dry friction on the structure of the extremal trajectory is analyzed. Two illustrative numerical examples are provided.
本文研究了均匀薄圆盘在水平面上无滑移滚动的臂慢运动。该问题是在最优控制理论的框架内表述和求解的。盘的臂慢运动由三个力矩控制。考察了在库仑干摩擦力作用下实现臂慢运动的可能性。分析了干摩擦系数的取值对极值轨迹结构的影响。给出了两个说明性的数值算例。
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引用次数: 5
Plane strain problem in a rotating microstretch thermoelastic solid with microtemperatures 旋转微拉伸热弹性固体的平面应变问题
IF 0.7 Q4 MECHANICS Pub Date : 2017-01-01 DOI: 10.2298/TAM170102003A
P. Ailawalia, S. K. Sachdeva, D. Pathania
A two-dimensional problem in an infinite microstretch thermoelastic solid with microtemperatures subjected to a mechanical source is studied. The medium is rotating with a uniform angular velocity Ω⃗. The normal mode analysis is used to obtain the exact expressions for the component of normal displacement, microtemperature, normal force stress, microstress tensor, temperature distribution, heat flux moment tensor and tangential couple stress. The effect of microrotation and stretch on the considered variables are illustrated graphically.
研究了在机械源作用下无限微拉伸热弹性固体的二维问题。介质以匀速角速度Ω / l旋转。通过法向模态分析,得到了法向位移分量、微温度分量、法向力应力分量、微应力张量分量、温度分布分量、热流矩张量分量和切向偶应力分量的精确表达式。微旋转和拉伸对所考虑的变量的影响用图形说明。
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引用次数: 3
Billiards on constant curvature spaces and generating functions for systems with constraints 常曲率空间上的台球及约束系统的生成函数
IF 0.7 Q4 MECHANICS Pub Date : 2017-01-01 DOI: 10.2298/TAM170523005J
B. Jovanović
In this note we consider a method of generating functions for systems with constraints and, as an example, we prove that the billiard mappings for billiards on the Euclidean space, sphere, and the Lobachevsky space are sympletic. Further, by taking a quadratic generating function we get the skew-hodograph mapping introduced by Moser and Veselov, which relates the ellipsoidal billiards in the Euclidean space with the Heisenberg magnetic spin chain model on a sphere. We define analogous mapping for the ellipsoidal billiard on the Lobachevsky space. It relates the billiard with the Heisenberg spin model on the light-like cone in the Lorentz–Poincare–Minkowski space.
在这篇文章中,我们考虑了一种有约束系统的生成函数的方法,作为一个例子,我们证明了欧几里得空间、球面和Lobachevsky空间上的台球映射是辛的。进一步,利用二次生成函数,我们得到了由Moser和Veselov引入的将欧几里得空间中的椭球球与球面上的Heisenberg磁自旋链模型联系起来的斜矢图映射。我们定义了Lobachevsky空间上椭球台球的类似映射。它将台球与洛伦兹-庞加莱-闵可夫斯基空间中类光锥上的海森堡自旋模型联系起来。
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引用次数: 4
Variational model of scoliosis 脊柱侧凸变分模型
IF 0.7 Q4 MECHANICS Pub Date : 2017-01-01 DOI: 10.2298/TAM170818012P
Igor Popov, N. Lisitsa, Y. Baloshin, M. Dudin, S. Bober
. Scoliosis, being one of the most widespread spinal diseases among children, has been studied extensively throughout the history of medicine, yet there is no clear understanding of its initiating factors and the mechanogenesis of the monomorphic three-dimensional deformation due to its polyetiological nature. We present a novel mathematical model of the process of emergence of the three-dimensional deformation of the human spine based on variational principles. Typical scoliosis geometry is assumed to be described as minimal curves of a particular energy functional, which are shown to closely resemble actual scoliosis. We investigate the numerical properties of the first stage of scoliosis, which is shown to have the highest influence on the development of the disease.
。脊柱侧凸是儿童中最常见的脊柱疾病之一,在整个医学史上进行了广泛的研究,但由于其多形态的性质,对其起始因素和单形态三维变形的机制发生尚不清楚。我们提出了一种基于变分原理的人体脊柱三维变形出现过程的数学模型。典型的脊柱侧凸几何被认为是描述为一个特定的能量函数的最小曲线,这显示出与实际的脊柱侧凸非常相似。我们调查的数值性质的第一阶段的脊柱侧凸,这是显示对疾病的发展影响最大。
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引用次数: 2
Small oscillations of an ideal liquid contained in a vessel closed by an elastic circular plate, in uniform rotation 由弹性圆板封闭的容器中理想液体的均匀旋转的小振荡
IF 0.7 Q4 MECHANICS Pub Date : 2017-01-01 DOI: 10.2298/TAM160123002E
H. Essaouini, B. El, P. Capodanno
Abstract. The problem of the small oscillations of an ideal liquid contained in a vessel in uniform rotation has been studied by Kopachevskii and Krein in the case of an entirely rigid vessel [3]. We propose here, a generalization of this model by considering the case of a vessel closed by an elastic circular plate. In this context, the linearized equations of motion of the system plateliquid are derived. Functional analysis is used to obtain a variational equation of the small amplitude vibrations of the coupled system around its equilibrium position, and then two operatorial equations in a suitable Hilbert space are presented and analyzed. We show that the spectrum of the system is real and consists of a countable set of eigenvalues and an essential continuous spectrum filling an interval. Finally the existence and uniqueness theorem for the solution of the associated evolution problem is proved by means the semigroups theory.
摘要Kopachevskii和Krein在完全刚性容器[3]的情况下,研究了均匀旋转容器中理想液体的小振荡问题。我们在这里提出,通过考虑由弹性圆板封闭的容器的情况下,这个模型的推广。在这种情况下,导出了系统的线性化运动方程。利用泛函分析得到耦合系统在平衡位置附近的小振幅振动的变分方程,并在合适的Hilbert空间中给出了两个操作方程。我们证明了系统的谱是实数的,由一个可计数的特征值集合和一个填充区间的基本连续谱组成。最后利用半群理论证明了关联进化问题解的存在唯一性定理。
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引用次数: 0
The Routh Theorem for Mechanical Systems with Unknown First Integrals 具有未知第一积分的机械系统的劳斯定理
IF 0.7 Q4 MECHANICS Pub Date : 2017-01-01 DOI: 10.2298/TAM170512008K
A. V. Karapetyan, Alexander S. Kuleshov
In this paper we discuss problems of stability of stationary motions of conservative and dissipative mechanical systems with first integrals. General results are illustrated by the problem of motion of a rotationally symmetric rigid body on a perfectly rough plane. Application of the Routh–Salvadori theorem and its generalizations [1–4] for investigation of stability of stationary motions of mechanical systems with first integrals U0 = c0, U1 = c1, . . . , Uk = ck is reduced to study the type of stationary value of U0 (here U0 can be also a nonincreasing along system trajectories function) for fixed values of U1, . . . , Uk. The effective method of such investigation is proposed in [5]. This method does not take into account equations of motion of the considered system however it is supposed that all first integrals are known explicitly. On the other hand using results by I. M. Mindlin and G. K. Pozharitskii [6] it is possible to distinguish the systems [7] for which the stability analysis does not require the explicit form of all first integrals U1 = c1, . . . , Uk = ck, except U0 = c0. Let equations of motion of a mechanical system have the following form (here T means transposition): (1) d dt (︁∂K ∂?̇? )︁ = ∂K ∂q +G?̇? − ∂W ∂q − Γ ∂W ∂p ,
本文讨论了具有第一积分的守恒和耗散力学系统的稳态运动的稳定性问题。一般结果由一个旋转对称刚体在完美粗糙平面上的运动问题来说明。应用Routh-Salvadori定理及其推广[1-4]研究具有第一积分U0 = c0, U1 = c1,…的机械系统静止运动的稳定性,将Uk = ck约简为研究U0的定值类型(这里U0也可以是沿系统轨迹的非递增函数)。,英国。在b[5]中提出了这种调查的有效方法。该方法不考虑所考虑系统的运动方程,但假定所有的第一积分都是显式已知的。另一方面,利用i.m. Mindlin和g.k. Pozharitskii[6]的结果,可以区分出稳定性分析不需要所有第一积分的显式形式(U1 = c1,…)的系统[7]。,除U0 = c0外,Uk = ck。设一个机械系统的运动方程有如下形式(这里T表示转置):(1)d dt(︁∂K∂?︁=∂K∂q +G?−∂W∂q−Γ∂W∂p,
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引用次数: 1
Bertolino-Baksa stability at nonlinear vibrations of motor vehicles 汽车非线性振动下Bertolino-Baksa稳定性
IF 0.7 Q4 MECHANICS Pub Date : 2017-01-01 DOI: 10.2298/TAM171128019K
L. Kudrjavceva, M. Mićunović, D. Miloradović, A. Obradović
Research of vehicle response to road roughness is particularly important when solving problems related to dynamic vehicle stability. In this paper, unevenness of roads is considered as the source of non-linear vibrations of motor vehicles. The vehicle is represented by an equivalent spatial model with seven degrees of freedom. In addition to solving the response by simulating it within a numerical code, quasi-linearization of nonlinear differential equations of motion is carried out. Solutions of quasi-linear differential equations of forced vibrations are determined using the small parameter method and are indispensable for the study of spatial stability of the vehicle. An optimal stabilization for a simplified two-dimensional model was performed. Spatial stability and internal resonance are considered briefly.
在解决与车辆动态稳定性相关的问题时,研究车辆对路面粗糙度的响应尤为重要。本文将道路的不平整度视为机动车非线性振动的来源。车辆由具有七个自由度的等效空间模型表示。除了在数值代码中模拟求解响应外,还对非线性运动微分方程进行了准线性化处理。采用小参数法确定受迫振动的准线性微分方程的解,是研究车辆空间稳定性不可缺少的方法。对一个简化的二维模型进行了最优镇定。简要地考虑了空间稳定性和内部共振。
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引用次数: 1
A note on the complete instability of linear non-conservative undamped systems 线性非保守无阻尼系统的完全不稳定性
IF 0.7 Q4 MECHANICS Pub Date : 2017-01-01 DOI: 10.2298/TAM170620010B
R. Bulatović
The note is concerned with the problem of determining the completely unstable linear non-conservative undamped (circulatory) dynamical systems. Several conditions that provide the complete instability for such systems are derived using the direct method of Lyapunov and the concept of controllability. The conditions are expressed directly via the matrices describing the dynamical system.
本文讨论了确定完全不稳定线性非保守无阻尼(循环)动力系统的问题。利用李亚普诺夫的直接方法和可控性的概念,导出了这种系统完全不稳定的几个条件。这些条件直接通过描述动力系统的矩阵表示出来。
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引用次数: 2
In)compressibility and parameter identification in phase field models for capillary flows 毛细管流动相场模型的可压缩性和参数辨识
IF 0.7 Q4 MECHANICS Pub Date : 2017-01-01 DOI: 10.2298/TAM170803009D
M. Dehsara, H. Fu, S. Mesarovic, D. P. Sekulic, M. Krivilyov
Phase field (diffuse interface) models accommodate diffusive triple line motion with variable contact angle, thus allowing for the no-slip boundary condition without the stress singularities. We consider two commonly used classes of phase field models: the compositionally compressible (CC) model with compressibility limited to the fluid mix within the diffuse interface, and the incompressible (IC) model. First, we show that the CC model applied to fluids with dissimilar mass densities exhibits the computational instability leading to the breakup of the triple line. We provide a qualitative physical explanation of this instability and argue that the compositional compressibility within the diffuse interface is inconsistent with the global incompressible flow. Second, we derive the IC model as a systematic approximation to the CC model, based on a suitable choice of continuum velocity field. Third, we benchmark the IC model against sharp interface theory and experimental kinetics. The triple line kinetics is well represented by the triple line mobility parameter. Finally, we investigate the effects of the bulk phase field diffusional mobility parameter on the kinetics of the wetting process and find that within a wide range of magnitudes the bulk mobility does not affect the flow.
相场(扩散界面)模型可以适应变接触角的扩散三线运动,从而允许无滑移边界条件而不存在应力奇点。我们考虑了两类常用的相场模型:可压缩性仅限于扩散界面内流体混合的组分可压缩(CC)模型和不可压缩(IC)模型。首先,我们表明CC模型应用于具有不同质量密度的流体表现出计算不稳定性,导致三线断裂。我们对这种不稳定性提供了定性的物理解释,并认为扩散界面内的组分可压缩性与整体不可压缩流动不一致。其次,在选择合适的连续速度场的基础上,我们推导出了作为CC模型的系统逼近的IC模型。第三,我们根据锐界面理论和实验动力学对集成电路模型进行了基准测试。三线迁移率参数很好地表示了三线动力学。最后,我们研究了体相场扩散迁移率参数对润湿过程动力学的影响,发现在很宽的量级范围内,体迁移率不影响流动。
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引用次数: 12
Compressible flow through solar chimneys with variable cross section - an exact solution 可压缩流通过可变截面的太阳能烟囱-一个精确的解决方案
IF 0.7 Q4 MECHANICS Pub Date : 2017-01-01 DOI: 10.2298/TAM170815014D
D. Djordjevic, S. A. Ćoćić
Buoyancy driven, adiabatic and compressible flow in relatively high solar chimneys is treated in the paper analytically by using one-dimensional model of flow. General equations written suitably in a non-dimensional form are used for a qualitative discussion pertaining to the mutual effects of gravity, viscosity and varying cross section of the chimney. It is shown that in case of low Mach number flow these equations possess exact solutions obtainable by ordinary mathematical methods for any given chimney shape. Also shown, and demonstrated on an example, is the procedure of evaluation of the chimney shape that satisfies a condition imposed beforehand upon the flow. For better insight into the role of various parameters the solutions are presented in the form of power series expansions.
本文采用一维流动模型对较高太阳烟囱内的浮力驱动、绝热和可压缩流动进行了分析。用适当的无量纲形式的一般方程定性地讨论了重力、粘度和烟囱截面变化的相互影响。结果表明,在低马赫数流动情况下,这些方程对任何给定的烟囱形状都具有精确解。文中还给出了烟囱形状是否满足预先设定的流场条件的评定过程,并通过实例进行了说明。为了更好地理解各种参数的作用,解以幂级数展开的形式呈现。
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引用次数: 0
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Theoretical and Applied Mechanics
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