A dynamic stiffness element for free vibration analysis of composite beams and its application to aircraft wings

The dynamic stiffness matrix of a composite beam that exhibits both geometric and material coupling between bending and torsional motions is developed and subsequently used to investigate its free vibration characteristics. The formulation is based on Hamilton’s principle leading to the governing differential equations of motion in free vibration, which are solved in closed analytical form for harmonic oscillation. By applying the boundary conditions the frequency dependent dynamic stiffness matrix that relates the amplitudes of loads to those of responses is then derived. Finally the Wittrick-Williams algorithm is applied to the resulting dynamic stiffness matrix to compute the natural frequencies and mode shapes of an illustrative example. The results are discussed and some conclusions are drawn. The theory can be applied for modal analysis of high aspect ratio composite wings and can be further extended to aeroelastic studies.     

Qualitative models of seat discomfort including static and dynamic factors

Judgements of overall seating comfort in dynamic conditions sometimes correlate better with the static characteristics of a seat than with measures of the dynamic environment. This study developed qualitative models of overall seat discomfort to include both static and dynamic seat characteristics. A dynamic factor that reflected how vibration discomfort increased as vibration magnitude increased was combined with a static seat factor which reflected seating comfort without vibration. The ability of the model to predict the relative and overall importance of dynamic and static seat characteristics on comfort was tested in two experiments. A paired comparison experiment, using four polyurethane foam cushions (50, 70, 100, 120 mm thick), provided different static and dynamic comfort when 12 subjects were exposed to one-third octave band random vertical vibration with centre frequencies of 2.5 and 5.5 Hz, at magnitudes of 0.00, 0.25 and 0.50 m.s^-2 rms measured beneath the foam samples. Subject judgements of the relative discomfort of the different conditions depended on both static and dynamic characteristics in a manner consistent with the model. The effect of static and dynamic seat factors on overall seat discomfort was investigated by magnitude estimation using three foam cushions (of different hardness) and a rigid wooden seat at six vibration magnitudes with 20 subjects. Static seat factors (i.e. cushion stiffness) affected the manner in which vibration influenced the overall discomfort: cushions with lower stiffness were more comfortable and more sensitive to changes in vibration magnitude than those with higher stiffness. The experiments confirm that judgements of overall seat discomfort can be affected by both the static and dynamic characteristics of a seat, with the effect depending on vibration magnitude: when vibration magnitude was low, discomfort was dominated by static seat factors; as the vibration magnitude increased, discomfort became dominated by dynamic factors.     

新型光学动态靶标结构刚度有限元分析

为了更好的对光电经纬仪进行室内检测,提出了一种新型光学动态靶标,并对其优点和结构进行分析。基于材料力学原理建立靶标三维实体造型,以有限元分析软件NXNastran为辅助工具,对新型动态靶标的结构刚度进行分析,得出各个部件在靶标工作过程中的变形量,并计算靶标整体精度。结果表明,新型靶标结构形式合理、刚度良好,其俯仰角误差3.18″、方位角误差2.98″,能够初步满足光电经纬仪动态测角性能检测的需要。     

The influence of text modality on learning with static and dynamic visualizations

In this study we investigated the influence of text modality on learning with static and dynamic visualizations in a dynamic domain, namely the physical principles underlying fish locomotion. A 2 × 2-design with type of visualization (static vs. dynamic) and text modality (spoken vs. written) as independent variables was used. Concerning learning outcomes, it was hypothesized that (1) learners presented with dynamic visualizations would outperform learners presented with static visualizations, (2) learners presented with spoken text would outperform learners presented with written text, and (3) an interaction between type of visualization and modality would occur: the superiority of dynamic over static visualizations was expected to be more pronounced for spoken compared to written text. Subjective cognitive load measures were assessed and expected to mirror the aforementioned pattern of learning outcomes in accordance with Cognitive Load Theory (i.e., higher extraneous cognitive load (ECL) related to lower learning outcomes). For transfer tasks, the first two hypotheses could be confirmed. However, there was no interaction. Moreover, ECL was rated higher by subjects when learning with static compared to dynamic visualizations, but there were no differences for ECL with respect to the text modality. The results are discussed within the framework of Cognitive Load Theory.     

A systematic mapping study on the combination of static and dynamic quality assurance techniques

Context

A lot of different quality assurance techniques exist to ensure high quality products. However, most often they are applied in isolation. A systematic combination of different static and dynamic quality assurance techniques promises to exploit synergy effects, such as higher defect detection rates or reduced quality assurance costs. However, a systematic overview of such combinations and reported evidence about achieving synergy effects with such kinds of combinations is missing.

Objective

The main goal of this article is the classification and thematic analysis of existing approaches that combine different static and dynamic quality assurance technique, including reported effects, characteristics, and constraints. The result is an overview of existing approaches and a suitable basis for identifying future research directions.

Method

A systematic mapping study was performed by two researchers, focusing on four databases with an initial result set of 2498 articles, covering articles published between 1985 and 2010.

Results

In total, 51 articles were selected and classified according to multiple criteria. The two main dimensions of a combination are integration (i.e., the output of one quality assurance technique is used for the second one) and compilation (i.e., different quality assurance techniques are applied to ensure a common goal, but in isolation). The combination of static and dynamic analyses is one of the most common approaches and usually conducted in an integrated manner. With respect to the combination of inspection and testing techniques, this is done more often in a compiled way than in an integrated way.

Conclusion

The results show an increased interest in this topic in recent years, especially with respect to the integration of static and dynamic analyses. Inspection and testing techniques are currently mostly performed in an isolated manner. The integration of inspection and testing techniques is a promising research direction for the exploitation of additional synergy effects.     

Applicability of a static model in a dynamic context in group-screening decision making

When good items have to be separated from bad ones, significant reduction in costs can be achieved by screening the items in groups rather than individually. In this regard, the selection of an efficient group size is crucial. For several decades, a model from Robert Dorfman was the de facto standard to determine the optimal group size. However, more recently, it has been pointed out that the model from Dorfman is a static one, i.e., it postulates that a predetermined large number of items have to be screened that are all present from the beginning, whereas the practical context is usually not static but dynamic: items are not all present initially, they arrive at random moments in time, and in groups of variable sizes.In this paper, we investigate under which circumstances the optimal group size in the static model from Dorfman remains correct in a dynamic context. This is of crucial importance since, although dynamic models and analyses are available now, these are much harder to implement and the processing time is slow due to the numerical work that is involved, such as repeatedly calculating zeroes of functions and solving sets of equations. Static models are much easier to use, and therefore it is important for practitioners to comprehend when they can rely on static results in a dynamic context.The second major contribution of this paper is that we develop efficient heuristics and algorithms for those cases in which results from static models cannot be relied on. These lead to a tremendous reduction in time complexity.     

Virtual optimisation of car passenger seats: Simulation of static and dynamic effects on drivers’ seating comfort

The virtual investigation of static and dynamic effects on seating comfort requires the application of an adequate human model. An appropriate seat model considering static and dynamic properties of the structure, the foam and the trim is needed to perform an optimisation for a lower load level on the driver. The evaluation of the seating comfort must be divided into a static and a dynamic part. For the computation of the relevant physical quantities with the human model CASIMIR and a detailed seat model, the finite-element solver ABAQUS (ABAQUS Inc., http://www.abaqus.comwww.abaqus.com) is used.

To reflect a real driving situation, in the first step the human model is adapted to the right posture, which is given by the inclination of the cushion and the backrest. The seating process is then computed by the load due to gravity. The static comfort is mainly evaluated by the seat pressure distribution. Results such as the H-point and the meat-to-metal value can give additional important informations for the ergonomic and structural design of the seat. As the model reflects the nonlinear properties and the finite-element solver considers the effects out of finite displacements and contact, a good correlation with measurement is achieved.

The dynamic simulation is carried out by a unit excitation of the seat slides at the clamping points. To consider frequency-dependent properties of foam, structure and the human body, the computation uses an implicit solver. Therefore the model is linearised after the nonlinear static seating process.

Dynamic comfort is evaluated by the seat-transfer function. The presented numerical method leads to a good correlation with the measurements. Superposing the results with real excitation signals enables the estimation of the dynamic loads as muscle or intervertebral disc forces on the driver.

Altogether this method, in an early state of the development enables the user to optimise a car passenger seat structure due to the static and dynamic comforts. Considering boundary conditions as higher load amplitudes and accelerations, the advantages of virtual development can also be applied for construction vehicle seats.

Relevance to Industry

The present method allows the evaluation of static and dynamic comforts in a virtual phase of seat development. Besides the reduction of time and costs, the application of the simulation enables the testing of new materials and ways of construction with low investment.     

Thick shells of revolution: Derivation of the dynamic stiffness matrix of continuous elements and application to a tested cylinder

This paper describes a procedure for calculating the dynamic stiffness matrix of tubular shells with free edge boundary conditions. Such an analysis forms the basis for the Continuous Element Method. The method is used to formulate a thick axisymmetric shell element which takes into account rotatory inertia, transverse shear deformation and non-axisymmetric loadings.     

球轴承非线性动态刚度特性及其复杂共振行为研究

滚动轴承由于其低阻尼、大过载和小体积等特点是航空发动机、铁路货车、舰船发动机等旋转机械的主要支承件.变柔度(varying compliance,VC)振动是由滚动体公转引起的一种不可避免的时变刚度参激振动.赫兹接触支承刚度给球轴承及其支承转子系统带来的滞后VC共振现象在相关研究中被大量发现.滞后突跳振动不但影响到转子系统的运行稳定性与安全性,而且其冲击作用也是轴承等系统元件裂纹及疲劳破坏的重要诱导因素.本文将通过分析球轴承动态时变刚度特性,拟提出一种采用系统动态固有频率估算球轴承VC共振区间的方法.在此基础上,探讨系统动态刚度特性与主共振区间复杂运动分岔行为的内在关联,发现当系统不同自由度方向上的固有频率值接近1〖DK〗∶2比例关系时,系统可能产生强烈的内共振,进而诱发响应的周期倍化分岔甚至准周期、混沌振动.该研究对球轴承复杂共振响应的控制具有潜在的理论意义和工程价值.     

基于有限元法的桥式起重机桥架结构刚度和强度仿真分析

桥架是桥式起重机的重要组成部分,用以支撑桥式起重机整机的机械、电气设备及被起升的重物,其强度及刚度的校核是桥式起重机设计和制造中的重要因素之一.通过理论计算和Marc有限元仿真方法对桥式起重机桥架结构进行静力学刚度和强度分析,得到桥架结构在极限工况下的承载应力大小及分布状况,对桥架进行强度及刚度校核,可为在役桥式起重机结构的安全性和可靠性评估提供理论支撑.     

Design and analysis of asymptotically optimal randomized tree embedding algorithms in static networks

The problem of dynamic tree embedding in static networks is studied in this paper. We provide a unified framework for studying the performance of randomized tree embedding algorithms which allow a newly created tree node to take a random walk of short distance to reach a processor nearby. In particular, we propose simple randomized algorithms on several most common and important static networks, including d-dimensional meshes, d-dimensional tori, and hypercubes. It is shown that these algorithms, which have small constant dilation, are asymptotically optimal for embedding healthy trees. Our analysis technique is based on random walks on static networks. Hence, analytical expressions for expected load on all the processors are available.     

Statical and dynamical behaviour of thin fibre reinforced composite laminates with different shapes

Based on the classical laminated plate theory, a variational approach for the study of the statical and dynamical behaviour of arbitrary quadrilateral anisotropic plates with various boundary conditions is developed. The analytical formulation uses the Ritz method in conjunction with natural coordinates to express the geometry of general plates in a simple form. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated using the Gram-Schmidt procedure. The algorithm developed is quite general and can be used to study fibre reinforced composite laminates with symmetric lay-ups, which may have general anisotropy and any combinations of clamped, simply supported and free edge support conditions. Various numerical applications are presented and some results are compared with existing values in the literature to demonstrate the accuracy and flexibility of the present method. New results were also determined for plates with different geometrical shapes, combinations of boundary conditions, several stacking sequences and various angles of fibre orientation.     

基于6DOF模型及动网格的动静压轴承刚度阻尼数值计算

针对传统雷诺方程求解三维油膜流场特性的局限性,提出基于6DOF模型及动网格的动静压轴承刚度阻尼计算方法.以具有典型结构形式的液体动静压轴承为例,通过加载6DOF自定义程序,采用非线性迭代方法计算外载荷作用下轴心轨迹的瞬态变化过程,得到轴颈在外载荷作用下的静平衡位置;通过嵌入UDF宏程序以动网格更新方法实现对轴颈在静平衡位置的扰动,求解Navier-Stokes方程得到轴颈扰动前后位置变化后的瞬态油膜力,利用差分法求得动静压轴承油膜刚度和阻尼,并分析了不同转速下轴承刚度和阻尼的变化规律.     

An equivalent multiscale method for 2D static and dynamic analyses of lattice truss materials

A uniform multiscale computational method is developed for 2D static and dynamic analyses of lattice truss materials in elasticity based on the extended multiscale finite element method. A kind of multi-node coarse element is proposed to describe the more complex deformations compared with the original four-node coarse element and the mode base functions are added into the original multiscale base functions to consider the effects of inertial forces for the dynamic problems. The constructions of the displacement and mode base functions are introduced in detail. In addition, the orthogonality of the displacement and mode base functions are also proved, which indicates that the macroscopic displacement DOF and modal DOF are irrelevant and independent of each other. Finally, some numerical experiments are carried out to verify the validity and efficiency of the proposed method by comparison with the reference solution obtained by the standard finite element method on the fine mesh.     

Biomechanical analyses of static and dynamic fixation techniques of retrograde interlocking femoral nailing using nonlinear finite element methods

Femoral shaft fractures can be treated using retrograde interlocking nailing systems; however, fracture nonunion still occurs. Dynamic fixation techniques, which remove either the proximal or distal locking screws, have been used to solve the problem of nonunion. In addition, a surgical rule for dynamic fixation techniques has been defined based on past clinical reports. However, the biomechanical performance of the retrograde interlocking nailing systems with either the traditional static fixation technique or the dynamic fixation techniques has not been investigated by using nonlinear numerical modeling. Three-dimensional nonlinear finite element models were developed, and the implant strength, fixation stability, and contact area of the fracture surfaces were evaluated. Three types of femoral shaft fractures (a proximal femoral shaft fracture, a middle femoral shaft fracture, and a distal femoral shaft fracture) fixed by three fixation techniques (insertion of all the locking screws, removal of the proximal locking screws, or removal of the distal locking screws) were analyzed. The results showed that the static fixation technique resulted in sufficient fixation stability and that the dynamic fixation techniques decreased the failure risk of the implant and produced a larger contact area of the fracture surfaces. The outcomes of the current study could assist orthopedic surgeons in comprehending the biomechanical performances of both static and dynamic fixation techniques. In addition, the surgeons could also select a fixation technique based on the specific patient situation using the numerical outcomes of this study.