Nonlinear analysis of thin rectangular plates on Winkler–Pasternak elastic foundations by DSC–HDQ methods

This article introduces a coupled methodology for the numerical solution of geometrically nonlinear static and dynamic problem of thin rectangular plates resting on elastic foundation. Winkler–Pasternak two-parameter foundation model is considered. Dynamic analogues Von Karman equations are used. The governing nonlinear partial differential equations of the plate are discretized in space and time domains using the discrete singular convolution (DSC) and harmonic differential quadrature (HDQ) methods, respectively. Two different realizations of singular kernels such as the regularized Shannon’s kernel (RSK) and Lagrange delta (LD) kernel are selected as singular convolution to illustrate the present DSC algorithm. The analysis provides for both clamped and simply supported plates with immovable inplane boundary conditions at the edges. Various types of dynamic loading, namely a step function, a sinusoidal pulse, an N-wave pulse, and a triangular load are investigated and the results are presented graphically. The effects of Winkler and Pasternak foundation parameters, influence of mass of foundation on the response have been investigated. In addition, the influence of damping on the dynamic analysis has been studied. The accuracy of the proposed DSC–HDQ coupled methodology is demonstrated by the numerical examples.     

再议用最小偏向角测光波波长的实验原理

本文通过严谨的数学推导给出利用光栅衍射的最小偏向角测光波波长的实验原理。     

Damage detection of a rectangular plate by spatial wavelet based approach

This paper presents a technique for structure damage detection based on spatial wavelet analysis. Many damage detection methods require modal properties before and after damage. This method only needs the spatially distributed signals (e.g. the displacements or mode shapes) of the rectangular plate after damage. First, spatially distributed signals of the rectangular plate with damage are obtained by finite element method. The damaged region is represented as the elements with reduced stiffness. Then these spatially distributed signals are analyzed by wavelet transformation. It is observed that distributions of the wavelet coefficients can identify the damage position of rectangular plate by showing a peak at the position of the damage. It is also demonstrated that this method is very sensitivity to the damage size.     

Diffusioosmotic flow in rectangular microchannels

The diffusioosmosis of an electrolyte solution inside a uniformly charged rectangular channel at steady locally developed conditions is the subject of this study. Utilizing a finite element based numerical procedure, we try to estimate the errors incurred by modeling the actual rectangular geometry of typical microchannels as a slit. We demonstrate that the flow pattern and direction are generally dependent upon the width‐to‐height ratio of the channel. Such a finding, besides showing the ineffectiveness of the slit geometry in representing a rectangular channel of small aspect ratio, informs us of another mechanism of controlling the diffusioosmotic flow. Inspections of the mean velocity reveal that, although it drastically grows by increasing the aspect ratio at smaller values of this parameter, no significant change is observed when the aspect ratio is 5 or higher. The same trend is observed when EDL is shrunk and is considered as a basis for the introduction of a slip‐like velocity, similar to the concept of the Helmholtz–Smoluchowski electroosmotic velocity, which will be of high practical importance when dealing with a micronsized channel. Because of its significance, an expression is presented for this slip velocity utilizing the curve fitting of the results, assuming a typical Peclet number.     

On “Radiative transfer in three-dimensional rectangular enclosures containing inhomogeneous, anisotropically scattering media”

Our 1985 paper (JQSRT 1985; 33: 533-549) reported the result of the research we conducted back then to better understand heat transfer processes in large-scale combustion chambers, especially in pulverized coal-fired furnaces. It was one of the first works exploring radiative transfer in three-dimensional enclosures where absorption and scattering coefficients due to combustion particles and gases were allowed to vary within the medium. This flexibility of the mathematical model made it useful for applications to realistic furnaces and different types of high-temperature systems. This note briefly discusses the motivation behind the paper and the immediate extension of the idea to different systems.     

Polychromatic colorings of arbitrary rectangular partitions

A general (rectangular) partition is a partition of a rectangle into an arbitrary number of non-overlapping subrectangles. This paper examines vertex 4-colorings of general partitions where every subrectangle is required to have all four colors appear on its boundary. It is shown that there exist general partitions that do not admit such a coloring. This answers a question of Dimitrov et al. [D. Dimitrov, E. Horev, R. Krakovski, Polychromatic colorings of rectangular partitions, Discrete Mathematics 309 (2009) 2957-2960]. It is also shown that the problem to determine if a given general partition has such a 4-coloring is NP-Complete. Some generalizations and related questions are also treated.     

Natural frequencies of rectangular Mindlin plates coupled with stationary fluid

The present study is concerned with the free vibration analysis of a horizontal rectangular plate, either immersed in fluid or floating on its free surface. The governing equations for a moderately thick rectangular plate are analytically derived based on the Mindlin plate theory (MPT), whereas the velocity potential function and Bernoulli’s equation are employed to obtain the fluid pressure applied on the free surface of the plate. The simplifying hypothesis that the wet and dry mode shapes are the same, is not assumed in this paper. In this work, an exact-closed form characteristics equation is used for the plate subjected to a combination of six different boundary conditions. Two opposite sides are simply supported and any of the other two edges can be free, simply supported or clamped. To demonstrate the accuracy of the present analytical solution, a comparison is made with the published experimental and numerical results in the literature, showing an excellent agreement. Then, natural frequencies of the plate are presented in tabular and graphical forms for different fluid levels, fluid densities, aspect ratios, thickness to length ratios and boundary conditions. Finally, some 3-D mode shapes of the rectangular Mindlin plates in contact with fluid are illustrated.     

矩形截面直管中的振荡流动

通过解析求解纳维尔-斯托克斯方程,本文给出了矩形截面直管中的层流振荡流动解。该解适用于不同的截面高宽比r和不同的振荡流动雷诺数。对典型的r和λ(雷诺数的平方根),给出了振荡流动速度的振幅比和相位差的等值线分布以及振荡流动速度随时间的变化,可以看出流动的速度分布如何从低频高粘性类型向高频低粘性的边界层流型逐渐变化;也可以看出管的边壁和角部对振荡流动的影响。当振荡频率ω为零时,本文结果即成为通过矩形截面定常管流的Stokes解。     

拟正则双序集用矩形双序集的余扩张

称双序集E为双序集F用矩形双序集的余扩张,若存在满双序集态射θ：E→F,使对每个α∈F,αθ－1是E的矩形双序子集．本文讨论了拟正则双序集的这种余扩张的性质,给出了它们的结构．作为应用,证明了拟正则的硬双序集实为正则双序集．