New explicit approximate solution of MHD viscoelastic boundary layer flow over stretching sheet

In this paper, the study the momentum and heat transfer characteristics in an incompressible electrically conducting non‐Newtonian boundary layer flow of a viscoelastic fluid over a stretching sheet. The partial differential equations governing the flow and heat transfer characteristics are converted into highly nonlinear coupled ordinary differential equations by similarity transformations. The resultant coupled highly nonlinear ordinary differential equations are solved by means of, homotopy analysis method (HAM) for constructing an approximate solution of heat transfer in magnetohydrodynamic (MHD) viscoelastic boundary layer flow over a stretching sheet with non‐uniform heat source. The proposed method is a strong and easy to use analytic tool for nonlinear problems and does not need small parameters in the equations. The HAM solutions contain an auxiry parameter, which provides a convenient way of controlling the convergence region of series solutions. The results obtained here reveal that the proposed method is very effective and simple for solving nonlinear evolution equations. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic Contact Behavior of a Golf Ball during an Oblique Impact

The oblique impact between a golf ball and a rigid steel target was studied using a high-speed video camera. Video images recorded before and after the impact were used to determine the inbound velocity v _i, rebound velocity v _r, inbound angle θ_i, rebound angle θ_r, and the coefficient of restitution e. The results showed that θ_r and e decreased as v _i increased. The maximum compression ratio η_c, contact time t _c, average angular velocity , and tangential velocity , along the target were determined from images obtained during the impact. The images demonstrated that η_c increased with v _i while t _c decreased. In addition, and increased almost linearly as v _i increased. A rigid body model was used to estimate the final angular velocity ω* and tangential velocity ν_t* at the end of the impact; these results were then compared with experimental data.     

用跃变旋转矢量研究滑动摩擦空气阻尼弹簧振子

运用跃变旋转矢量法,即通过旋转矢量的起点、长度和相位的变化规律对受到空气弱阻尼作用和滑动摩擦力作用的弹簧振子的振动进行了研究.讨论了在滑动摩擦力作用下空气阻尼为临界阻尼和欠阻尼情况下的弹簧振子的运动,根据阻尼和初值情况得出不同的振动曲线.并对弹簧振子4种相图和相图旋转矢量进行了比较.     

竖板表面温度的变化对磁流体动力学流动的影响

在横向磁场作用下,不可压缩的粘性导电流体,流经一个半无限的竖板,完成了壁面温度变化对磁流体动力学流动的分析.假定由粘性耗散和感应磁场产生的热量可以忽略不计.无量纲的控制方程为二维非稳态耦合的非线性方程.结果显示,磁场参数对空气和水的速度有着抑制作用.     

On an elasto-dynamic evolution equation with non dead load and friction

In this paper, we are interested in the dynamic evolution of an elastic body, acted by resistance forces depending also on the displacements. We put the mechanical problem into an abstract functional framework, involving a second order nonlinear evolution equation with initial conditions. After specifying convenient hypotheses on the data, we prove an existence and uniqueness result. The proof is based on Faedo-Galerkin method.     

Effects of composition drift on the effectiveness of random copolymer reinforcement at polymer–polymer interfaces

Random copolymer layers are surprisingly effective at reinforcing polymer–polymer interfaces. One hypothesis is that composition drift during synthesis can account for the higher than expected toughening. To test this hypothesis, we polymerized a series of poly(d‐styrene‐r‐2‐vinylpyridine) (dPS_f‐r‐PVP_1?f) copolymers with various fractions (f) of deuterated styrene to only 10% completion to avoid composition drift. The fracture energies (G_c) of polystyrene/dPS‐r‐PVP/poly(2‐vinylpyridine) interfaces with relatively thick layers of dPS‐r‐PVP were measured. G_c decreased relative to interfaces reinforced with composition‐drifted dPS‐r‐PVP. Conversely, G_c increased when two or more copolymers were blended together. In such samples, the copolymers form distinct layers with multiple interfaces characterized by the difference in f (Δf) between adjacent layers. We find that G_c is governed by Δf_max, the largest difference in adjacent compositions, and, therefore, by the width of the narrowest interface (w_min). G_c increases strongly as w_min increases from 3 to 5 nm. Remarkably, these w_min values are about half the entanglement spacing in bulk polystyrene. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2363–2377, 2001     

Dynamic optical visualization on the interaction between propagating crack and stationary crack

Dynamic interactions between the propagating crack and the static crack in PMMA material are studied by combining high-speed Schardin camera with optical caustic method. A series of dynamic optical bifocal patterns (the specimen-focused image and the off-focused image) around the propagating crack tip and the static crack tip are recorded for PMMA thin strip which contains two collinear-edge-cracks subjected to tensile loading, the variations of the caustic diameter and the distortion of the caustic shape are revealed due to the influence of local stress singularity at the crack tip. Interactions between the moving crack and the static crack are analyzed by means of the evolution of dynamic fracture parameters. The influence of crack interaction on fracture parameters is discussed based on both a K-dominance assumption and a higher order transient crack-tip expansion. These results will be useful to the evaluation of dynamic properties and the design of structures in the cracked polymer material.     

Interaction of faults under slip‐dependent friction. Non‐linear eigenvalue analysis

We analyse the evolution of a system of finite faults by considering the non‐linear eigenvalue problems associated to static and dynamic solutions on unbounded domains. We restrict our investigation to the first eigenvalue (Rayleigh quotient). We point out its physical significance through a stability analysis and we give an efficient numerical algorithm able to compute it together with the corresponding eigenfunction. We consider the anti‐plane shearing on a system of finite faults under a slip‐dependent friction in a linear elastic domain, not necessarily bounded. The static problem is formulated in terms of local minima of the energy functional. We introduce the non‐linear (static) eigenvalue problem and we prove the existence of a first eigenvalue/eigenfunction characterizing the isolated local minima. For the dynamic problem, we discuss the existence of solutions with an exponential growth, to deduce a (dynamic) non‐linear eigenvalue problem. We prove the existence of a first dynamic eigenvalue and we analyse its behaviour with respect to the friction parameter. We deduce a mixed finite element discretization of the non‐linear spectral problem and we give a numerical algorithm to approach the first eigenvalue/eigenfunction. Finally we give some numerical results which include convergence tests, on a single fault and a two‐faults system, and a comparison between the non‐linear spectral results and the time evolution results. Copyright © 2004 John Wiley & Sons, Ltd.     

Cu-Al-Be合金逆马氏体相变过程中内耗的等温变化研究

本文研究了Cu-Al—Be合金等温逆马氏体相变过程中内耗的变化规律。研究发现，在相变温区，样品内耗值随等温时间的延长而有规律地下降。我们认为，这一现象是由于晶体内部缺陷运动引起的。在等温过程中，点缺陷向界面偏聚,逐渐限制界面移动，引起内耗的下降。     

Visualization and Quantification of the Medial Surface Dynamics of an Excised Human Vocal Fold During Phonation

SUMMARY: The purpose of this investigation was to investigate physical mechanisms of vocal fold vibration during normal phonation through quantification of the medial surface dynamics of the fold. An excised hemilarynx setup was used. The dynamics of 30 microsutures mounted on the medial surface of a human vocal fold were analyzed across 18 phonatory conditions. The vibrations were recorded with a digital high-speed camera at a frequency of 4,000 Hz. The positions of the sutures were extracted and converted to three-dimensional coordinates using a linear approximation technique. The data were reduced to principal eigenfuctions, which captured over 90% of the variance of the data, and suggested mechanisms of sustained vocal fold oscillation. The vibrations were imaged as the following phonatory conditions were manipulated: glottal airflow, an adductory force applied to the muscular process, and an elongation force applied to the thyroid cartilage. Over the range of variables studied, only the variation in glottal airflow yielded significant changes in subglottal pressure and fundamental frequency. All recordings showed high correlation for the distribution of the dynamics across the medial surface of the vocal fold. The distribution of the different displacement directions and velocities showed the highest variations around the superior region of the medial surface. Although the computed vibration patterns of the two largest empirical eigenfunctions were consistent with previous experimental observations, the relative prominence of the two eigenfunctions changed as a function of glottal airflow, impacting theories of vocal efficiency and vocal economy.