A simple mathematical model for free vibration analysis of combined system consisting of framed tube,shear core,belt truss and outrigger system with geometrical discontinuities

Dynamic analysis of beam-like structure is significantly important in modeling real cases such as tall buildings, aircraft wings, spacecraft antennas and many other applications. This paper tries to determine the first natural frequency of tall buildings including framed tube, shear core, belt truss and outrigger system with multiple jumped discontinuities in the cross section of framed tube and shear core. In this regard, the entire length of the tall building is partitioned into uniform segments between each two successive discontinuity points. The effect of belt truss and outrigger system is modeled as a concentrated rotational spring applied at the belt truss and outrigger system location. Many cantilevered tall structures can be treated as cantilever bars with multiple jumped discontinuities in the cross section for the analysis of their free vibration. In this paper, the continuous approach was accepted and by using the Hamilton’s variational principle, the general form of governing equation for free vibration of tall building can be obtained. By applying the separation of variable method on time and space, the governing Partial Differential Equation (PDE) of motion is reduced to an Ordinary Differential Equation (ODE) with one variable coefficient while the other coefficients are constant based on the assumption that the transverse displacement is a harmonic vibration. To find exact solution of ODE, we must have exact distribution of EI(x), AG(x), N(x) and m(x) in the height of the structure. Some of these parameters such as EI(x), AG(x) and m(x), are constant throughout the height of each segment. These parameters can be expressed exactly by using of multi criteria function, while N(x) is variable in the height of each segment. Therefore, the ODE by using the method of variable separation and partitioned method can be expressed for each segment. We must apply the continuity conditions in conjunction with different segments for obtaining unique mode shape for mentioned system. Tall building characteristics matrix can be derived based on the boundary conditions and the continuity conditions applied at the partitioned points. This matrix is particularly used to find combined system first natural frequency and mode shape. Three numerical examples with different stepped discontinuities in their cross sections are studied to demonstrate the reliability of this method. The results of the proposed mathematical model give a good understanding of the structure’s dynamic characteristics; it is easy to use, yet reasonably accurate and suitable for quick evaluations during the preliminary design stages which require less time.     

Non-linear Viscoelastic Rheological Properties of PCC/PEG Suspensions

The shear thinning and shear thickening rheological properties of PCC/PEG suspension were investigated with the increase of oscillatory amplitude stress at different constant frequencies. The results show that the complex viscosity was initially independent of stress amplitude and obvious shear thinning occurred, then dramatic shear thickening took place after reaching the minimum viscosity. Typically, in a constant frequency of 5 rad/s, the elastic modulus, viscous modulus, and tanδ （δ is the out-of-phase angle） vs. the stress amplitude was investigated. It is found that the elastic modulus initially appeared to be independent of stress amplitude and then exhibited a rapid decrease, but the viscous modulus was independent of amplitude stress at lower amplitude stress. After reaching the minimum value the viscous modulus showed a rapid increase. On the other hand, tanδ increased from 0.6 to 92, which indicates that the transition from elastic to viscous had taken place and tanδ showed a steep increase when shear thickening occurred. Lissajous plots are shown for the dissipated energy vs. different maximum stress amplitude in the shear thinning and shear thickening regions. The relationship of dissipated energy vs. maximum stress amplitude was determined, which follows a power law. In the shear thinning region the exponent was 1.91, but it steeply increases to 3.97 in the shear thickening region.     

广西靖西红粘土的变形和强度特性研究

对广西靖西取得的3种红粘土原状土样以及室内制备的重塑土样进行单轴压缩试验和三轴剪切试验（包括浸水饱和后的试验）,其目的是研究静力荷载作用下红粘土的固结变形和强度特征。研究表明,在较大的压缩应力作用下,土样仍有较大的孔隙比;红粘土的破坏面为一个曲面变化形态,试样首先沿较为软弱的不规则面发生,然后才形成贯通的滑动面;尽管土样在破坏时出现明显的剪切破坏面（表现为一定的脆性破坏特征）,但其应力应变关系呈现应变硬化的特点,表明红粘土有很强的粘滞特性。     

Mechanics and mechanism of cut resistance of protective materials

A sliding sharp edge penetrating material is one of the most dangerous cases of cutting because it requires the smallest applied load. A better understanding of the cutting mechanism is a fundamental step to develop new and more performing protective materials. This study aims at analyzing cutting mechanics and mechanism in the presence of friction. The International Standard ISO 13997 cut test method consists in measuring the distance that a straight blade slides horizontally to cut through a material under a constant applied normal force and was used to investigate cutting phenomena.In practice, cut resistance of a material is contributed by the intrinsic strength of material and the frictional distribution. Two types of friction distributions are involved in cutting: a macroscopic friction induced by the gripping of the material and by the applied normal load on the two sides of the blade; and the other the sliding friction associated with cut through of the material that occurs along the face of the blade tip. For most materials, frictional forces due to lateral gripping could be several times greater than the friction due to the applied normal force. Thus, the cutting energy required for breaking molecular chains is much smaller than the energy dissipated for friction. The elastic modulus, the structure of the material as well as the sliding velocity have significant influence on the friction. Therefore all these properties can affect the cutting resistance results.     

Perspectives on shear banding in complex fluids

In this review, I present an idiosyncratic view of the current state of shear banding in complex fluids. Particular attention is paid to some of the outstanding issues and questions facing the field, including the applicability of models that have “traditionally” been used to model experiments; future directions and challenges for experimentalists; and some of the issues surrounding vorticity banding, which has been discussed theoretically and whose experiments are fewer in number yet, in many ways, more varied in character.     

Rheo NMR and shear banding

The phenomenon of shear banding in complex fluids has been investigated using NMR velocimetry and NMR spectroscopy, mostly in wormlike micelle systems, but more recently in colloidal systems and multilayer vesicles. A particular advantage of NMR is the ability to simultaneously investigate structural ordering and to compare such ordering with local strain rates. In this paper, we describe the basics of Rheo-NMR and summarise its recent application to the study of shear banding.     

Processing the Couette viscometry data using a Bingham approximation in shear rate calculation

This paper presents an approach to computing the shear flow curve from torque–rotational velocity data in a Couette rheometer. The approximation techniques in shear rate calculation are generally dictated by the radius ratio between coaxial cylinders and the rheological behaviour of fluid tested. Here, the approach consists in analysing the sheared material as a Bingham fluid and computing an average shear rate when the fluid in the cylindrical gap is partially and fully sheared. We focus in particular on the applicability of the Bingham approximation in shear rate calculation. First, the approach is assessed by examining synthetic data generated with Newtonian, non-Newtonian and yield stress materials with known properties, varying the gap radius ratio. The results, which are compared with commonly used techniques in shear rate calculation, prove the relevance of the proposed approach. Finally, its efficiency is examined by applying it to process Couette data of yield stress fluids taken from published works.     

A physical decomposition of the stress tensor for complex flows

Traditionally, the components of the stress with respect to a relevant coordinate system are used for the purpose of stress visualisation and interpretation. A case for using a flow dependent measure to interpret and visualise stress is made for two dimensional flow, together with a suggestion for extending the idea to three dimensions. The method is illustrated for Newtonian and Oldroyd B fluids in both the eccentrically rotating cylinder and flow past a cylinder benchmark problems. In the context of a generalised Newtonian fluid, the relation between the flow-dependent stress measure to other field variables under certain flow conditions, is examined and is indicative of its importance in complex flow.

Crystallization of alkanes under quiescent and shearing conditions

We report molecular dynamics simulation of crystallization of model alkane systems conducted under constant pressure conditions. We have studied crystallization of n-eicosane (C₂₀H₄₂) and n-hexacontane (C₆₀ H₁₂₂) under quiescent and shearing conditions. We find preshearing before subjecting the melt to quiescent crystallization enhances the crystallization of higher molecular weight hexacontane, whereas, for low molecular weight eicosane, no significant change can be detected. For both alkanes applying steady planar shear significantly speeds up the crystallization. The crystal growth rate increases with the shear rate. However, we find that the critical shear rate above which the crystallization is enhanced, is inversely proportional to the size of the chains. In all cases the Weissenberg numbers of the sheared systems are moderate. We estimate them to be in the range of 0.01–10. Our quiescent simulations for eicosane predict crystallization temperature and lattice parameters of the crystalline phase in good agreement with experimental measurements. We have compared an order parameter used in the simulations against one analogous to that used in dilatometry experiments. Using this order parameter as a measure of crystallinity we predict the crystal growth rate of n-eicosane to be a maximum at ∼300 K in good agreement with experiments. Fitting crystallization growth data to Avrami's model we have calculated Avrami growth functions and exponents for many cases. For quiescent crystallization of n-eicosane we found the Avrami exponent calculated using our order parameter for defining degree of crystallinity, agrees well with that obtained in the experiments. For C60 the crystallization process is very slow at quiescent conditions; however preshearing enhances the crystal growth.     

西南大渡河某水电站溢洪道陡槽段雾化边坡稳定性分析

泄洪雨雾入渗导致边坡变形进而影响边坡稳定性的问题已成水电建设的重要工程问题之一。针对西南某水电站溢洪道陡槽段边坡挤压错动带发育、节理裂隙和控制性结构面发育等结构特点,分析该边坡开挖支护后泄洪雾化条件下潜在失稳的边界条件及变形破坏模式。根据边坡所处的地质环境条件,从泄洪雾化对边坡岩体的作用机制入手,得到了雨雾对该边坡稳定性的影响主要为雨雾沿着顺倾坡外拉裂面入渗,影响结构面力学特性,从而影响边坡稳定性。并按结构面类型取不同软化系数,采用数值模拟方法分析了泄洪雨雾入渗后边坡的变形破坏趋势。分析结果表明：在考虑不同的软化系数时,溢0+555.00下游侧边坡岩体稳定性有较大的差别,若以中间值075考虑,溢洪道陡槽段边坡的稳定性稍差,可能产生一定规模的剪切蠕动变形或块体失稳,必须加强一定的支护措施保证该处边坡在施工期安全和运营期间的长期稳定性。