Modal transmission-line theory of three-dimensional periodic structures with arbitrary lattice configurations

The scattering of waves by multilayered periodic structures is formulated in three-dimensional space by using Fourier expansions for both the basic lattice and its associated reciprocal lattice. The fields in each layer are then expressed in terms of characteristic modes, and the complete solution is found rigorously by using a transmission-line representation to address the pertinent boundary-value problems. Such an approach can treat periodic arbitrary lattices containing arbitrarily shaped dielectric components, which may generally be absorbing and have biaxial properties along directions that are parallel or perpendicular to the layers. We illustrate the present approach by comparing our numerical results with data reported in the past for simple structures. In addition, we provide new results for more complex configurations, which include multiple periodic regions that contain absorbing uniaxial components with several possible canonic shapes and high dielectric constants.     

Forbidden gaps in periodic anisotropic layered media

The general case of obliquely incident plane-wave propagation in periodic anisotropic layered media is presented. Arbitrary permittivity tensors of the two alternating anisotropic layers are considered. An immersion model is used with the assumption that each layer is embedded between two isotropic regions that have the same index of refraction as the isotropic medium of incidence and a thickness that is set equal to zero. Then explicit relations are presented for normally incident plane waves in periodic structures that consist of alternating biaxial layers of arbitrary principal-axis orientation. Specific cases of alternating isotropic and biaxial layers are also considered. Unit cell translation matrices are presented for both traveling directions, from the left to the right and vice versa. Dispersion relations that contain information regarding the propagation bands and the forbidden gaps in periodic anisotropic structures are presented.     

Non—Local Analysis of Forming Limits of Ductile Material Considering Void Growth

The current study performed a finite element analysis of the strain localization behavior of a voided ductile material using a non-local plasticity formulation in which the yield strength depends on both an equivalent plastic strain measurement (hardening parameter) and Laplacian equivalent. The introduction of gradient terms to the yield function was found to play an important role in simulating the strain localization behavior of the voided ductile material. The effect of the mesh size and characteristic length on the strain localization were also investigated. An FEM simulation based on the proposed non-local plasticity revealed that the load-strain curves of the voided ductile material subjected to plane strain tension converged to one curve, regardless of the mesh size. In addition, the results using non-local plasticity also exhibited that the dependence of the deformation behavior of the material on the mesh size was much less sensitive than that with classical local plasticity and could be successfully eliminated through the introduction of a large value for the characteristic length.     

带限位倒摆的实验与数值研究

设计研制一个带限位的倒摆实验系统,建立 该系统的力学模型,通过实验与数值分析的研究,讨论周期与随机激励情况下的各种响应,证实所建立模型的正确性,揭示该系统存在复杂的非线性动力学行为,并指出噪声对系统非线性动力学行为的影响。研究结果将为带有间隙结构的设计和间隙结构动力学分析提供参考。     

Linear array arrangement using composite right-/left-handed transmission lines for magnetic resonance imaging

Array coils for magnetic resonance imaging have been used to improve field uniformity, improve signal-to-noise ratios, and increase imaging speed. Alternative radio frequency (RF) coils that use metamaterials, such as loop or microstrip coils, have recently been proposed and are expected to provide better performance than the traditional RF array coils. Transmission lines (TLs) based on metamaterials are known as composite right- and left-handed (CRLH) TLs, which are artificially created by adding inductances and capacitances to a common TL. CRLH TLs have a zero-order resonance mode, wherein wave propagation is independent of the TL's electrical length. Decoupling between array elements is important for obtaining the benefits of parallel imaging. In this study, we analyze the decoupling properties between two CRLH TLs. In addition, we design a linear array of four CRLH TLs to obtain a uniform magnetic (|B₁|)-field in the axial- and longitudinal-direction at 7T for the corresponding frequency of 300 MHz.     

多圆盘转子系统的周期运动及其稳定性分析

采用短轴承理论方法 ,把油膜力作为转子系统的约束力加入到转子的动力学方程中 ,分析了多圆盘转子系统在非线性油膜力作用下的周期性运动及稳定性。对转子系统的周期运动 ,使用近似级数表达形式 ,对于非线性的油膜力 ,根据周期运动的特点 ,采用周期级数展开形式 ,求解了非线性动力学方程 ,得到了转子的周期运动轨道。在分析周期运动的稳定性时 ,采用谐波平衡方法 ,得到转子周期运动的稳定条件 ,为工程设计提供了一定的依据。最后对刚性非平衡对称支承单圆盘的周期运动及稳定性进行了数值模拟 ,证明了本文方法的有效性     

Creation of spatial structure by an electric field applied to an ionic cubic autocatalator system

The effects of applying electric fields to a reactor with kinetics based on an ionic version of the cubic autocatalator are considered. Three types of boundary condition are treated, namely (constant) prescribed concentration, zero flux and periodic. A linear stability analysis is undertaken and this reveals that the conditions for bifurcation from the spatially uniform state are the same for both the prescribed concentration and zero-flux boundary conditions, suggesting bifurcation to steady structures, whereas, for periodic boundary conditions, the bifurcation is essentially different, being of the Hopf type, leading to travelling-wave structures. The various predictions from linear theory are confirmed through extensive numerical simulations of the initial-value problem and by determining solutions to the (non-linear) steady state equations. These reveal, for both prescribed concentration and zero-flux boundary conditions, that applying an electric field can change the basic pattern form, give rise to spatial structure where none would arise without the field, can give multistability and can, if sufficiently strong, suppress spatial structure entirely. For periodic boundary conditions, only travelling waves are found, their speed of propagation and wavelength increasing with increasing field strength, and are found to form no matter how strong the applied field.     

Shear stiffness prediction of Reissner–Mindlin plates with periodic microstructures

In this article, an intuitionistic interpretation of the new numerical implementation of asymptotic homogenization for effective bending stiffness of in-plane periodic plate structures is presented. Based on this interpretation, a two-step method of effective shear stiffness prediction for their Reissner–Mindlin model is developed. An equivalent displacement field of linear curvature is applied to a unit cell in the first step; in the second step, a new unit cell problem is constructed and solved, and the effective shear stiffness is obtained through energy equivalence. This method can be easily implemented in commercial software and several examples are given to demonstrate its validity.     

Characterization of edge effects of composite lattice structures

To analyze the mechanical behaviors of composite lattice structures with finite sizes and strengthened edges, periodic expansion method was developed to get the corresponding equivalent infinite periodic structures. Finite element method was also adopted to testify the theoretical predictions. The strengthened edges greatly influence the properties of composite lattice structures made up of only several layers of unit cells. Reductions of the specific stiffness and strength of the lattice composites in most cases stem from the mass enhancement. Made up of more than 10–20 unit cell layers, the lattices possess nearly identical properties of the intact composite lattice structures and the edge effect is small enough. Compared with the weak edges, the major advantage of strong edges is that they distribute loads more extensively and evenly and greatly decrease the localization of strains and stresses on the boundaries under concentrated loads.     

FFT-based analysis of periodic structures in microacoustic devices

Periodic structures utilized as transducer or reflector elements play an important role in microacoustic wave devices. Such structures can be described using approximate analytical models. However, to obtain the accuracy required for reliable device simulation, numerical methods have to be employed. In this contribution, we present an efficient numerical approach to calculate the dispersion curves associated with microacoustic modes propagating in periodic structures; the method is demonstrated for the case of Love wave modes. The computational efficiency is related to the utilization of the FFT algorithm in a hybrid Method of Moments (MoM)/Mode-Matching analysis. From the obtained dispersion curves, characteristic parameters such as the stopband width can be obtained which can be used in a coupling-of-modes (COM) model of the structure.     

Molecular-dynamics study of dynamic vortex defects as the mechanism of relaxation in loaded solids

Processes in a loaded solid have been studied by the method of molecular dynamics. It is established that dynamic vortex structures can form both in the stage of active loading and in the stress relaxation stage. In the latter case, atomic displacements can result in the formation of a periodic system of correlated vortex threads. The lifetime of such dynamic defects may reach tens of nanoseconds, while their characteristic dimensions are on the nanometer scale. It is demonstrated that the system of vortex threads can change the sign of the angular velocity so that atomic displacements taking place within different time intervals virtually compensate each other. The formation of analogous dynamic vortexlike structures in the active stage of loading does not exhibit a periodic character.     

基于小波时频框架分解方法的滚动轴承故障诊断

损伤点通过其它元件时引起的周期性冲击是判断滚动轴承局部损伤故障的关键特征信息.针对滚动轴承的振动特点,设计了小波时频框架,利用框架分解方法在匹配信号特征结构,直接提取特征信息方面的优势,分析了滚动轴承的振动信号.根据框架分解结果,在时频联合域内清晰直观地提取了滚动轴承局部损伤故障的周期性冲击特征,识别了滚动体、内圈和外圈的单点缺陷,与小波变换的对比验证了框架分解在检测滚动轴承局部损伤故障方面的有效性.     

A perturbation solution for the steady heat flow around a thin circular insulating annulus on the surface of a conducting half-space

A constant temperature circular disc on the surface of a conducting half-space is surrounded by an insulating annulus. The remainder of the surface of the half space is maintained at zero temperature. The steady heat flow rate from the disc to the zero temperature surface is required. The mathematical problem, a three-part mixed boundary value problem can be reduced to integral equation form. Several alternative formulations are possible. The existing formulations do not readily yield solutions for the case in which the thickness-to-radius radio of the insulating annulus is small compared to unity. This case is considered here and a solution based on integral perturbation methods is obtained. An existing alternative integral equation formulation is also solved, by iteration, for cases in which the inner-to-outer radius ratio of the insulating annulus is small compared to unity. These two solutions are found to coalesce over an intermediate range of annulus thickness. Thus a composite solution is obtained which is valid for all cases. The solutions given here are also of practical interest in analogous problems in, e.g. the flow of fluids through porous media, and in elasticity theory.     

Cellular growth and dislocation structures in laser-nitrided titanium

Transmission electron microscopic observations were made of different dislocation structures in laser-nitrided titanium. Equidistant edge dislocations in the bulk and periodic surface structures exhibit a periodicity within the same order of magnitude. An analysis is presented in which both periodic phenomena are explained by cellular growth. This revised version was published online in November 2006 with corrections to the Cover Date.     

A generalised instantaneous non-active power theory for STATCOM

A generalised instantaneous non-active power theory is presented. Comprehensive definitions of instantaneous active and non-active currents, as well as instantaneous, average and apparent powers, are proposed. These definitions have flexible forms that are applicable to different power systems, such as single-phase or multi-phase, periodic or non-periodic and balanced or unbalanced systems. By changing the averaging interval and the reference voltage, various non-active power theories can be derived from this theory. The definitions of instantaneous active and non- active currents provide an algorithm for a STATCOM to calculate the non-active current in the load current. The theory is implemented by the STATCOM, and four cases (three-phase balanced RL load, three-phase unbalanced RL load, diode rectifier load and single-phase load) are tested. The experimental results show that the STATCOM can perform instantaneous non-active power compensation, and both the fundamental non-active component and the harmonics are eliminated from the utility so that nearly unity power factor can be achieved. The STATCOM also has a fast dynamic response for transients.     

A near row matching approach to prediction of multiple precipitation crystallography of compound precipitates and its application to a Mg/Mg<Subscript>2</Subscript>Sn system

Sharp faceted interfaces are often observed between compound precipitates and matrix phases, which are remarkably different in their lattice parameters. Multiple orientation relationships (ORs) corresponding to various faceted interfaces tend to coexist in one alloy. A near row matching (NRM) approach is proposed for a systematic investigation of ORs corresponding to potential preferred interfaces. Unlike a common practice to search for misorientations corresponding to low sigma grain boundaries associated with matching periodicity in three dimensions (3D), this approach directly searches for ORs that permit local 2D periodic good matching structures in preferred interfaces. The calculation method consists of two simple steps to evaluate matching within and between rows of lattice points. The method has been applied to a Mg₂Sn/Mg system. Ten of the forty-four predicted facets agree with the experimental observations, for the cases that the preferred facets can be described (approximately) by low index planes of the precipitates. The predictions can cover all known observations, if limited high index planes are included as candidates. Each observed facet is characterized with a periodic pattern of good matching sites (GMSs) in localized regions. NRM is a necessary condition for the existence of a periodic GMS pattern. The agreement between the calculation results and experimental results confirms the important role of periodic matching in the development of preferred interfaces and their corresponding ORs. It also demonstrates the usefulness of geometric matching study for quantitative predictions of potential preferred interfaces.     

A complex variable solution of two-dimensional heat conduction of composites reinforced with periodic arrays of cylindrically orthotropic fibers

Problems of two-dimensional steady-state heat conduction for composites with doubly periodic arrays of cylindrically orthotropic fibers are dealt with. A new complex variable method is presented by introducing an appropriate coordinate transformation to convert the governing differential equation into a harmonic one, and the eigenfunction expansions of the field variables in a unit cell are derived. Then by using a generalized variational functional which absorbs the periodicity condition, an eigenfunction expansion–variational method based on a unit cell is developed to solve such problems. A convergence analysis and a comparison with finite element calculations are conducted to demonstrate the correctness and efficiency of the present method. A discussion is made about the effects of the cylindrical orthotropy of the fiber and the existence of the isotropic core in the fiber on the effective conductivity of the composite. An engineering equivalent parameter, which reflects the overall influence of the thermal conductivities of the matrix and fibers as well as the interfacial characteristic on the effective thermal conductivity of the composite, is found. It is shown that the present first-order approximation of the effective thermal conductivity of the composite can be written in a unified formula for different microstructural characteristics and possesses a good engineering accuracy.     

Wave finite element‐based superelements for forced response analysis of coupled systems via dynamic substructuring

The wave finite element (WFE) method is used for assessing the harmonic response of coupled mechanical systems that involve one‐dimensional periodic structures and coupling elastic junctions. The periodic structures under concern are composed of complex heterogeneous substructures like those encountered in real engineering applications. A strategy is proposed that uses the concept of numerical wave modes to express the dynamic stiffness matrix (DSM), or the receptance matrix (RM), of each periodic structure. Also, the Craig–Bampton (CB) method is used to model each coupling junction by means of static modes and fixed‐interface modes. An efficient WFE‐based criterion is considered to select the junction modes that are of primary importance. The consideration of several periodic structures and coupling junctions is achieved through classic finite element (FE) assembly procedures, or domain decomposition techniques. Numerical experiments are carried out to highlight the relevance of the WFE‐based DSM and RM approaches in terms of accuracy and computational savings, in comparison with the conventional FE and CB methods. The following test cases are considered: a 2D frame structure under plane stresses and a 3D aircraft fuselage‐like structure involving stiffened cylindrical shells. Copyright © 2015 John Wiley & Sons, Ltd.     

矩形RC桥墩变形能力概率模型

桥墩是桥梁抗侧力体系中的关键构件。为实现基于概率和性能的桥梁抗震设计的多级性能目标,有必要给出桥墩在不同性能极限状态下的概率能力。基于已有研究工作,将RC桥墩的抗震性能水平划分为五个等级,并定义了相应的性能极限状态。采用等效集中塑性铰理论,推导并建立了各性能极限状态下RC墩柱变形能力的确定性计算公式;基于183个矩形RC墩柱试件的拟静力试验结果,通过多元回归分析,确定了各计算公式中与轴压比、长细比和配箍特征值等设计参数相关的待定系数。基于确定性计算模型和拟静力试验结果,考虑认知不确定性,建立了矩形RC墩柱变形能力的概率模型。通过实例分析,表明该模型可用于基于概率和性能的桥梁抗震设计和抗震 评估。