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Robust finite-time stability of uncertain neutral nonhomogeneous fractional-order systems with time-varying delays 时变时滞不确定中立型非齐次分数阶系统的鲁棒有限时间稳定性
IF 0.7 Q3 Engineering Pub Date : 2020-01-01 DOI: 10.2298/tam2000016l
M. Lazarevic, Darko Radojevic, Stjepko Pisl, G. Maione
This article addresses the problem of finite-time stability for uncertain neutral nonhomogeneous fractional-order systems with time-varying delays where a stability test procedure is suggested. Based on the extended form of the generalized Gr?nwall inequality, a new sufficient condition for robust finite-time stability of such systems is established. Finally, a numerical example is given to show the effectiveness of the obtained result.
本文研究了一类具有时变时滞的不确定中立型非齐次分数阶系统的有限时间稳定性问题,并给出了稳定性检验方法。基于广义Gr?利用Nwall不等式,建立了该类系统鲁棒有限时间稳定的一个新的充分条件。最后,通过数值算例验证了所得结果的有效性。
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引用次数: 2
A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials 声子晶体和声学超材料中元adamping的分数阶演算方法
IF 0.7 Q3 Engineering Pub Date : 2020-01-01 DOI: 10.2298/tam200117003c
Milan Cajić, Danilo Karličić, Stepa Paunović, S. Adhikari
Research on phononic and acoustic materials and structures emerged in the recent decade as a result of switching from theoretical physics to applications in various engineering fields. Periodicity is the main characteristic of the phononic medium stemming from periodic material phases, geometry or the boundary condition with wave propagation properties analysed through frequency band structure. To obtain these characteristics, the generalized Bloch theorem is usually applied to obtain the dispersion relations of viscously damped resonant metamaterials. Here we develop a novel analytical approach to analyse the fractionally damped model of phononic crystals and acoustic metamaterials introduced through the fractional-order Kelvin–Voigt and Maxwell damping models. In the numerical study, the results obtained using the proposed models are compared against the elastic cases of the phononic crystal and locally resonant acoustic metamaterial, where significant differences in dispersion curves are identified. We show that the fractional-order Maxwell model is more suitable for describing the dissipation effect throughout the spectrum due to the possibility of fitting both, the order of fractional derivative and the damping parameter.
声子和声学材料和结构的研究是近十年来从理论物理转向各种工程领域应用的结果。周期性是声子介质的主要特征,由周期性的物质相位、几何形状或边界条件引起,通过频带结构分析了声子介质的传播特性。为了获得这些特性,通常采用广义布洛赫定理来获得粘滞阻尼谐振超材料的色散关系。本文提出了一种新的分析方法来分析分数阶Kelvin-Voigt和Maxwell阻尼模型引入的声子晶体和声学超材料的分数阶阻尼模型。在数值研究中,利用所提出的模型得到的结果与声子晶体和局部共振声学超材料的弹性情况进行了比较,两者的色散曲线存在显著差异。由于分数阶导数阶数和阻尼参数都可以拟合,分数阶麦克斯韦模型更适合描述整个谱的耗散效应。
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引用次数: 6
On the stability and instability criteria for circulatory systems: A review 循环系统稳定性和不稳定性标准的研究进展
IF 0.7 Q3 Engineering Pub Date : 2020-01-01 DOI: 10.2298/tam201021013b
M. Bulatovic
A survey of the selected published criteria ? expressed by the properties of the system matrices ? for the stability and instability of linear mechanical systems subjected to potential and circulatory forces is presented. In particular, recent generalizations of the well-known Merkin instability theorem are reported. Several simple numerical examples are used to illustrate the usefulness of the presented criteria and also to compare them.
对选定的已公布标准进行调查?用系统矩阵的性质来表示吗?给出了在势力和循环力作用下线性机械系统的稳定性和不稳定性。特别地,报告了著名的默金不稳定性定理的最新推广。用几个简单的数值例子来说明所提出的准则的有效性,并对它们进行比较。
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引用次数: 2
Size effects associated with skew symmetric burgers tensor 与偏对称汉堡张量相关的尺寸效应
IF 0.7 Q3 Engineering Pub Date : 2020-01-01 DOI: 10.2298/tam191125001b
A. Borokinni, O. Fadodun, O. Layeni, A. Akinola, B. Olokuntoye
. This paper investigates size effect phenomena associated with the divergence of the transpose of plastic distortion in plastically deformed isotropic materials. The principle of virtual power, balance of energy, second law of thermodynamics, and codirectionality hypothesis are used to formulate the governing microforce balance and thermodynamically consistent constitutive relations for dissipative microscopic stresses associated with the plastic distortion and skew part of the Burgers tensor. It is obtained that the defect energy through the strictly skew Burgers tensor is converted to the defect energy via the divergence of the plastic distortion. The presence of material length scales in the obtained flow rule indicates that it is possible to appre- hend size effects associated with the skew part of the Burgers tensor during the inhomogeneous plastic flow of solid material. Finally and amongst other things, it is shown that the dependency of the microscopic stress vector on the divergence of plastic distortion rate leads to weakening and strengthening effects in the flow rule.
. 研究了塑性变形各向同性材料中与塑性变形转置散度有关的尺寸效应现象。利用虚力原理、能量平衡、热力学第二定律和共向性假设,建立了与Burgers张量的塑性变形和偏曲部分相关的耗散微观应力的控制微力平衡和热力学一致的本构关系。得到了通过严格偏态Burgers张量的缺陷能量通过塑性畸变的散度转化为缺陷能量。在得到的流动规律中存在材料长度尺度表明,在固体材料的非均匀塑性流动过程中,有可能理解与Burgers张量的偏态部分相关的末端尺寸效应。结果表明,细观应力矢量对塑性变形率散度的依赖性导致了流变规律的弱化和强化效应。
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引用次数: 0
Classification of left invariant metrics on 4-dimensional solvable Lie groups 四维可解李群上左不变度量的分类
IF 0.7 Q3 Engineering Pub Date : 2020-01-01 DOI: 10.2298/tam200826014s
T. Šukilović
In this paper the complete classification of left invariant metrics of arbitrary signature on solvable Lie groups is given. By identifying the Lie algebra with the algebra of left invariant vector fields on the corresponding Lie group ??, the inner product ??,?? on g = Lie G extends uniquely to a left invariant metric ?? on the Lie group. Therefore, the classification problem is reduced to the problem of classification of pairs (g, ??,??) known as the metric Lie algebras. Although two metric algebras may be isometric even if the corresponding Lie algebras are non-isomorphic, this paper will show that in the 4-dimensional solvable case isometric means isomorphic. Finally, the curvature properties of the obtained metric algebras are considered and, as a corollary, the classification of flat, locally symmetric, Ricciflat, Ricci-parallel and Einstein metrics is also given.
本文给出了可解李群上任意签名左不变度量的完全分类。用相应李群上的左不变向量场的代数来识别李代数?,内积?? ??on g = Lie g唯一地扩展到一个左不变度规??在李群里。因此,分类问题被简化为被称为度量李代数的对(g, ??,??)的分类问题。尽管两个度量代数可以是等距的,即使对应的李代数是非同构的,但本文将证明在四维可解的情况下,等距意味着同构。最后,考虑了所得到的度量代数的曲率性质,并作为推论,给出了平面、局部对称、Ricciflat、Ricci-parallel和Einstein度量的分类。
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引用次数: 2
A brief survey of the spectral numbers in floer homology 花同源性中的谱数综述
IF 0.7 Q3 Engineering Pub Date : 2020-01-01 DOI: 10.2298/tam200831012k
J. Katić, D. Milinkovi'c, Jovan Nikolic
We give a brief introduction and a partial survey of some of the results about spectral numbers in symplectic topology that we are aware of. Without attempting to be comprehensive, we will select just some of the constructions and ideas that, according to our personal taste and our point of view, give a flavor of this fast developing theory.
本文对辛拓扑中关于谱数的一些已知结果作了简要介绍和部分综述。我们将根据自己的个人品味和观点,选择一些结构和思想,以呈现这一快速发展的理论。
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引用次数: 0
Evolution equations of translational-rotational motion of a non-stationary triaxial body in a central gravitational field 中心引力场中非定常三轴体平移旋转运动的演化方程
IF 0.7 Q3 Engineering Pub Date : 2020-01-01 DOI: 10.2298/tam191130007m
M. Minglibayev, A. Prokopenya, O. Baisbayeva
. The translational-rotational motion of a triaxial body with constant dynamic shape and variable size and mass in a non-stationary Newtonian central gravitational field is investigated. Differential equations of motion of the triaxial body in the relative coordinate system with the origin at the center of a non-stationary spherical body are obtained. The axes of the Cartesian coordinate system fixed to the non-stationary triaxial body are coincident with its principal axes and their relative orientation is assumed to remain unchanged in the course of evolution. An analytical expression for the force function of the Newtonian interaction of the triaxial body of variable mass and size with a spherical body of variable size and mass is obtained. Differential equations of translational-rotational motion of the non-stationary triaxial body are derived in Jacobi osculating variables and are studied with the perturba- tion theory methods. The perturbing function is expanded in power series in terms of the Delaunay–Andoyer elements up to the second harmonic element inclusive. The evolution equations of the translational-rotational motion of the non-stationary triaxial body are obtained in the osculating elements of Delaunay–Andoyer.
. 研究了非稳态牛顿中心引力场中具有恒定动态形状、变尺寸和变质量的三轴物体的平移-旋转运动。得到了以非定常球面为中心的三轴体在相对坐标系中的运动微分方程。固定在非静止三轴体上的笛卡儿坐标系各轴与三轴的主轴重合,并假定它们的相对方位在演化过程中保持不变。得到了变大小变质量的三轴体与变大小变质量的球面体的牛顿相互作用的力函数的解析表达式。推导了非定常三轴体在雅可比接触变量下的平移-旋转运动微分方程,并用摄动理论方法进行了研究。扰动函数以Delaunay-Andoyer元的幂级数展开,直至包含二次谐波元。得到了非定常三轴体在Delaunay-Andoyer耦合单元中平移-旋转运动的演化方程。
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引用次数: 1
Free vibrations of planar serial frame structures in the case of axially functionally graded materials 轴向功能梯度材料情况下平面串联框架结构的自由振动
IF 0.7 Q3 Engineering Pub Date : 2020-01-01 DOI: 10.2298/tam2000017o
A. Obradović, S. Šalinić, A. Tomović
This paper considers the problem of modal analysis and finding the closed-form solution to free vibrations of planar serial frame structures composed of Euler?Bernoulli beams of variable cross-sectional geometric characteristics in the case of axially functionally graded materials. Each of these beams is performing coupled axial and bending vibrations, where coupling occurs due to the boundary conditions at their joints. The numerical procedure for solving the system of partial differential equations, after the separation of variables, is reduced to solving the two-point boundary value problem of ordinary linear differential equations with nonlinear coefficients and linear boundary conditions. In this case, it is possible to transfer the boundary conditions and reduce the problem to the Cauchy initial value problem. Also, it is possible to analyze the influence of different parameters on the structure dynamic behavior. The method is applicable in the case of different boundary conditions at the right and left ends of such structures, as illustrated by an appropriate numerical example.
本文研究了由欧拉?轴向功能梯度材料中变截面几何特性的伯努利梁。这些梁中的每一个都执行耦合的轴向和弯曲振动,其中耦合是由于其结合处的边界条件而发生的。将分离变量后求解偏微分方程组的数值过程简化为求解具有非线性系数和线性边界条件的常线性微分方程的两点边值问题。在这种情况下,可以将边界条件转化为柯西初值问题。此外,还可以分析不同参数对结构动力性能的影响。该方法适用于这种结构的左右两端不同边界条件的情况,并通过适当的数值算例加以说明。
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引用次数: 0
An analytical mechanics approach to the first law of thermodynamics and construction of a variational hierarchy 热力学第一定律的分析力学方法和变分层次结构的构造
IF 0.7 Q3 Engineering Pub Date : 2019-08-06 DOI: 10.2298/tam200315011s
H. Said
A simple procedure is presented for the study of the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically, a second-order quasi-linear wave equation. An immediate implication of this procedure is the formation of a least action principle for the balance of energy with dissipation. The corresponding action functional enables us to establish a complete analytic mechanics for thermomechanical systems: a Lagrangian?Hamiltonian theory, integrals of motion, bracket formalism, and Noether?s theorem. Furthermore, we apply our procedure iteratively and produce an infinite sequence of interlocked variational principles, a variational hierarchy, where at each level or iteration the full implication of the least action principle can be shown again.
给出了一维连续介质力学中带耗散的能量守恒方程的一个简单方法。利用该方法将非线性演化扩散方程转化为双曲偏微分方程;具体来说,二阶拟线性波动方程。这个过程的直接含义是形成能量与耗散平衡的最小作用原理。相应的作用泛函使我们能够建立一个完整的热力系统解析力学:拉格朗日?哈密顿理论,运动积分,托架形式论,还有诺特?年代定理。此外,我们迭代地应用我们的过程,并产生一个连锁变分原理的无限序列,一个变分层次结构,在每个层次或迭代中,最小作用原理的全部含义可以再次显示。
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引用次数: 0
Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere 多维橡胶鲁思球的哈密顿化、测度保存和第一积分
IF 0.7 Q3 Engineering Pub Date : 2019-01-30 DOI: 10.2298/TAM190130004G
Luis C. Garc'ia-Naranjo
We consider the multi-dimensional generalisation of the problem of a sphere, with axi-symmetric mass distribution, that rolls without slipping or spinning over a plane. Using recent results from Garc?a-Naranjo [21] and Garc?a-Naranjo and Marrero [22], we show that the reduced equations of motion possess an invariant measure and may be represented in Hamiltonian form by Chaplygin?s reducing multiplier method. We also prove a general result on the existence of first integrals for certain Hamiltonisable Chaplygin systems with internal symmetries that is used to determine conserved quantities of the problem.
我们考虑一个具有轴对称质量分布、在平面上滚动而不滑动或旋转的球体问题的多维推广。根据Garc?a-Naranjo[21]和Garc?a-Naranjo和Marrero[22],我们证明了运动约简方程具有不变测度,并且可以用Chaplygin?S减乘法。我们还证明了一类具有内对称的可哈密顿Chaplygin系统第一积分存在性的一般结果,用于确定问题的守恒量。
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引用次数: 12
期刊
Theoretical and Applied Mechanics
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