On Fractional PI λ Controllers: Some Tuning Rules for Robustness to Plant Uncertainties

The objective of this work is to find out optimum settings for a fractional PI ^λ controller in order to fulfill three different robustness specifications of design for the compensated system, taking advantage of the fractional order, λ. Since this fractional controller has one parameter more than the conventional PI controller, one more specification can be fulfilled, improving the performance of the system and making it more robust to plant uncertainties, such as gain and time constant changes. For the tuning of the controller an iterative optimization method has been used, based on a nonlinear function minimization. Two real examples of application are presented and simulation results are shown to illustrate the effectiveness of this kind of unconventional controllers.     

Extraction-condensation method for solving large sets of equations in FE analysis

In static and dynamic analysis of a large complex structure, one may merely be interested in the stresses and displacements at some important locations. A new solution technique for structural analysis with FEM is proposed in this paper by which those important unknowns are separated from the rest. In static analysis the important unknows can be found directly. In dynamic analysis all mass and exciting forces can be condensed onto a small number of predetermined points in order to make the dynamic analysis much simplified. A large scale problem can be solved with a small capacity computer quickly.     

Finite element analysis of a bimaterial interface crack

In this investigation, the enriched element method developed by Benzley was extended to treat the stress analysis problem involving a bimaterial interface crack. Unlike crack problems in isotropic elasticity, where the stress singularity at the crack tip is of the inverse square root type, the interface crack contains an additional oscillatory singularity. Although the effect of this oscillatory characteristic is confined to a region very close to the crak tip, it nevertheless requires proper treatment in order to obtain accurate predictions on the stress intensity factors. Using appropriate crack tip stress and displacement expressions, the enriched element method can model the stress singularity for an interface crack exactly. The finite element implementation of this method has been made on the code APES. Stress intensity factor results predicted by the modified APES program compare favorably with those available in the literature. This indicates tha the enriched element technique provides an accurate and efficient numerical tool for the analysis of bimaterial interface crack problems.     

Solvent-aided phase separation in hydrogel towards significantly enhanced mechanoresponsive strength

Understanding working principles and thermodynamics behind phase separations, which have significant influences on condensed molecular structures and their performances, can inspire to design and fabricate anomalously and desirably mechanoresponsive hydrogels. However, a combination of techniques from physicochemistry and mechanics has yet been established for the phase separation in hydrogels. In this study, a thermodynamic model is firstly formulated to describe solvent-aided phase and microphase separations in the hydrogels, which present significantly improved mechanoresponsive strengths. Flory–Huggins theory and interfacial energy equation have further been applied to model the thermodynamics of concentration-dependent and temperature-dependent phase separations. An intricately detailed phase map has finally been formulated to explore the working principle. The thermodynamic methodology of phase separations, combined with the constitutive stress–strain relationships, has a great potential to explore the working mechanisms in mechanoresponsive hydrogels.

Graphic abstract

     

A phenomenological theory for elastic superconductors

The purpose of the present study is to develop a phenomenological theory for elastic superconductors that is based on a rigorous thermodynamical internal variable theory in which the concept of complex internal variable is introduced to include the phase effect of quantum mechanics. Two phenomena of superconductivity, i.e., perfect conductivity and perfect diamagnetism, can be explained in the formulation. In the equilibrium state, this theory can be reduced to the well-known Ginzburg-Landau (GL) theory. Upon linearizing the field equations, boundary conditions and constitutive equations, the governing equations of the rigid-body state and the perturbed state are obtained. These equations then serve to analyze the effect of the hydrostatic deformation on the penetration depth, the GL coherence length and the critical field.     

二维弹性接触问题中随机边界元法与可靠性分析

发展了二维弹性接触问题中的随机边界元法，推导并建立了相应的随机边界元基本方程，并将所发展的方法用于静强度的可靠性分析，讨论了其数值解技术。通过算例分析表明，本文发展的方法是可行的。     

Natural convection in a partitioned enclosure heated from below

Cubic spline collection numerical method has been developed to determine two dimensional natural convection in a partitioned enclosure heated from below. The both sides of impermeable partition are considered to have continuity in heat flux and temperatures. The governing equations are solved with aid of the SADI procedure. Parametric studies of the effects of the partition and Rayleigh number on the fluid flow and temperature fields have been performed. Results show that the location of the partition and Rayleigh number have a significant influence on the flow and heat transfer characteristics.

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Freie Konvektion in einem von unten beheizten, unterteiltem Hohlraum

Zusammenfassung Eine numerische dreidimensionale SplineMethode zur Berechnung der zweidimensionalen Naturkonvektion in einem von unten beheizten, unterteiltem Hohlraum wird vorgestellt. Der Wärmestrom und die Temperatur auf beiden Seiten der undurchlässigen Trennwand werden als konstant betrachtet. Mit Hilfe der SADI-Prozedur werden die beschreibenden Gleichungen gelöst. Über den Einfluß der Unterteilung und der Rayleigh-Zahl auf die Strömung des Fluids und das Temperaturfeld wird eine Parameter-Studie durchgeführt. Die Ergebnisse zeigen, daß die Anordnung der Unterteilung und die Rayleigh-Zahl einen entscheidenden Einfluß auf das Wärmeübertragungsverhalten haben.

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Nomenclature A aspect ratio=L/H - g gravitational acceleration - H enclosure height - H₁ distance between the top wall of enclosure and the partition - H₂ distance between the bottom wall of enclosure and the partition - k thermal conductivity of fluid - L enclosure length - m number of vertical grid lines - n number of horizontal grid lines - Nu Nusselt number - P pressure - Pr Prandtl number - Q heat transfer across enclosure - Ra Rayleigh number based onH - t time - T dimensional temperature - T _H temperature of warm horizontal wall - T _L temperature of cold horizontal wall - T ₀ average temperature=T(_H+T_L)/2 - T temperature difference between the hot and cold wall =T _H–T_L - u, U dimensional and dimensionless horizontal velocity - , V dimensional and dimensionless vertical velocity - x, X dimensional and dimensionless horizontal coordinate - y, Y dimensional and dimensionless vertical coordinate - fluid thermal diffusivity - coefficient of thermal expansion - viscosity - kinematic viscosity=/g9 - density - , dimensional and dimensionless stream function - dimensionless temperature - , dimensional and dimensionless vorticity - dimensionless time     

板结构功率流的参数研究

板以及肋板结构在工程中有着广泛的应用，其振动嗓声问题一直受到理论和工程领域的关注。本文在板结构功率流理论的基础上￣［１］，对板的损耗因子和不同加肋形式对其功率流的影响进行了分析和测量。     

ANALYSIS OF FRICTION INDUCED VIBRATION UNDER THE ACTIVE DISTURBANCE REJECTION CONTROL FRAMEWORK 1)

自抗扰控制(active disturbance rejection control, ADRC)是一种具有两自由度控制结构的工程化方法, 由于其能够直观有效地处理多种扰动, 近些年来在许多机电系统上得到了成功应用. 当采用ADRC对带有摩擦力的机电系统进行调节时, 可能会产生极限环振动. 目前, 还没有ADRC框架下摩擦力振动精确分析的相关工作. 因此, 本文采用非线性动力学系统的分析工具对这一问题进行研究. 首先, 考虑两种典型摩擦力模型, 静态切换模型和动态LuGre 模型, 对一类二阶运动系统设计不同阶次的ADRC, 得到控制器的等效形式, 并揭示出与比例积分微分(proportional-integral-derivative, PID)控制之间的联系. 然后, 采用打靶法结合拟弧长延拓方法求解系统中的极限环, 并根据Floquet理论判断极限环的稳定性、可能出现的分岔以及分岔类型. 此外, 通过雅克比矩阵和近似数值方法对系统平衡点集的局部稳定性进行了分析. 最后, 通过数值计算研究了摩擦力模型和参数、ADRC阶次和参数对极限环和平衡点集的影响. 计算结果表明, 决定摩擦力Stribeck效应负斜率的参数$\beta$作用较大. 当$\beta>1$时, 两种摩擦力模型下的闭环系统呈现出相同的特性, 极限环会出现环面折叠分岔(cyclic fold bifurcation, CFB)且平衡点集是局部稳定的. 然而当$\beta<1$时, 两种闭环系统呈现出完全不同的特性. 此外, 不同阶次的ADRC在极限环的存在性和稳定性、平衡点集的稳定性上面的结论是相同的, 而低阶次的ADRC能够更好地解决摩擦力补偿和稳定鲁棒性之间的矛盾问题. 这些结论对实际现象的理解、ADRC阶次的选择以及参数整定提供了一定指导.     

Modulus, Fracture Strength, and Brittle vs. Plastic Response of the Outer Shell of Arc-grown Multi-walled Carbon Nanotubes

The fracture strengths and elastic moduli of arc-grown multi-walled carbon nanotubes (MWCNTs) were measured by tensile loading inside of a scanning electron microscope (SEM). Eighteen tensile tests were performed on 14 MWCNTs with three of them being tested multiple times (3×, 2×, and 2×, respectively). All the MWCNTs fractured in the “sword-in-sheath” mode. The diameters of the MWCNTs were measured in a transmission electron microscope (TEM), and the outer diameter with an assumed 0.34 nm shell thickness was used to convert measured load-displacement data to stress and strain values. An unusual yielding before fracture was observed in two tensile loading experiments. The 18 outer shell fracture strength values ranged from 10 to 66 GPa, and the 18 Young's modulus values, obtained from a linear fit of the stress–strain data, ranged from 620 to 1,200 GPa, with a mean of 940 GPa. The possible influence of stress concentration at the clamps is discussed.