DAMPING OF VERTICALLY EXCITED SURFACE WAVE IN WEAKLY VISCOUS FLUID

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.     

Modeling of a magnetorheological damper by recursive lazy learning

Nowadays dampers based on magnetorheological (MR) fluids are receiving significant attention specially for control of structural vibration and automotive suspensions systems. In most cases, it is necessary to develop an appropriate control strategy which is practically implementable when a suitable model for MR dampers is available. It is not a trivial task to model the dynamic of MR dampers because of their inherent non-linear and hysteretic dynamics. In this paper, a recursive lazy learning method based on neural networks is considered to model the MR damper behavior. The proposed method is validated by comparison with experimental obtained responses. Results show the estimated model correlates very well with the data obtained experimentally. The method proposed learns quickly that it is only necessarily a learning cycle, it can learn on-line and it is easy to select the network structure and calculate the model parameters.     

Weak Solutions to the Cahn-Hilliard Equation with Degenerate Diffusion Mobility in ℝN

This paper is concerned with a popular form of Cahn-Hilliard equation which plays an important role in understanding the evolution of phase separation. We get the existence and regularity of a weak solution to nonlinear parabolic, fourth order Cahn-Hilliard equation with degenerate mobility M(u)=u^m(1-u)^m which is allowed to vanish at 0 and 1. The existence and regularity of weak solutions to the degenerate Cahn-Hilliard equation are obtained by getting the limits of Cahn-Hilliard equation with non-degenerate mobility. We explore the initial value problem with compact support and obtain the local non-negative result. Further, the above derivation process is also suitable for the viscous Cahn-Hilliard equation with degenerate mobility.     

有限液体负载下压电平板声板波理论分析

主要推导平板声板波受有限液体负载后能量衰减与波速改变情形, 以部分波传理论分析该受液体负载的压电平板波传行为, 并以一128$^{\circ}Y$向切角的铌酸锂芯片为例,分析前20个声板波受水与甘油负载下 的能量衰减,并固定某一平板板波, 针对不同甘油厚度负载下, 计算其相速度与衰减变化,该理论分析对于液体负载下的平板板波传感器应用具有极大的参 考价值.     

具有黏滞阻力时的最速降线

针对实际应用中存在黏滞阻力的最速降线的问题, 首先推导出适于此类问题的解除约束的广义变分原理, 它适用于具有摩擦阻尼和多自由度系统优化的问题. 得到描述有黏滞阻力情况下最速降线相关函数的微分方程, 它在黏滞阻力为零时即退化为滚轮线. 利用MATLAB数值计算给出了最速降线受黏滞阻力的影响: 在黏滞阻力系数较小时最速降线趋于变凹, 当阻力系数增大到一定值之后最速降线趋于平缓, 当阻力系数很大时最速降线趋于直线.     

Convergent Flows of Molten Polymers Modeled by Generalized Second-Grade Fluids of Power-Law Type

The molding processes of polymer melts involve geometrically complex dies. Such dies are usually tapered or streamlined to achieve a maximum output rate under conditions of laminar flow. The model of a generalized second-grade fluid of power-law type is used and the results obtained are illustrated by examples of convergent flows in conical and wedge-shaped dies.     

自然对流边界层中湍流的发生

自然对流边界层中从层流到湍流的转捩经历了浮力振型、无摩擦振型和黏性振型的三重流动不稳定性相继产生的前转捩过程,以及近壁迅速出现强湍流源,随之平缓地向自模拟的湍流边界层过渡的热转捩过程.浮力振型在修正Grashof数G>40时开始失稳并成为主要振型,在振幅分布中3种振型的临界层位置处出现3个峰值;在G>100时浮力振型消失,无摩擦振型失稳并成为主要振型,振幅分布中在近壁区还出现黏性振型的峰值;在G>170时无摩擦振型经非线性演化在外层形成较弱的湍流,但内层黏性应力仍远高于湍流应力,振幅分布中仅有与黏性振型相应的峰值,在频谱中黏性振型的基频、第一、第二、第三阶亚谐频随G的增加相继出现,此时黏性不稳定波的高频成分已转化为湍流,但低频成分仍按线性规律增长,直至湍流惯性子区开始形成;至G>800时黏性振型消失,并在G=850附近时近壁区出现强湍流源,湍流应力、湍能产生项和近壁湍流热流率剧增.在热转捩后期,湍流应力和湍能产生项明显下降,流动在内外层趋于平衡.     

化学反应对流过半无限垂直多孔板的粘性耗散非定常磁流体流动的影响

分析了化学反应,对流过半无限竖直多孔板的、粘性耗散的、非定常的磁流体流动的影响．利用随时间变化的相似参数,将运动、能量、溶质的控制方程变换为常微分方程,并用有限单元法数值地求解所得到的常微分方程．用图形给出了不同参数对速度、温度和浓度分布的影响,用表格给出了不同物理参数值时,表面摩擦力、Nusselt数和Sherwood数的数值．     

一类非凸粘性平衡律方程的粘性激波解的存在性与稳定性

本文首先利用几何奇异摄动方法，证明了粘性系数充分小时一类非凸粘性平衡律方程的粘性冲击波的存在性，推广了原来在非线性项严格凸的条件下得到的结果．进而，利用谱分析和上下解方法，证明了对固定的小的粘性系数此类波是全局渐近指数稳定的，推广了反应扩散方程中经典的全局稳定性结果．