Analytical and experimental investigation on transverse vibrations of solid, circular and annular plates carrying a concentrated mass at an arbitrary position with marine applications

This investigation arose from the practical necessity of placing a centrifugal pump rigidly attached to a thin, circular cover plate of a water tank in a medium size ocean vessel. Due to lack of space, it was necessary to locate the system off—center of the circular configuration. It was considered necessary to calculate the fundamental frequency of the coupled system.The first part of the present study is concerned with the determination of the fundamental frequency of vibration of a circular plate carrying a concentrated mass at an arbitrary position, using a variational approach.Numerical results are obtained for the stated problem for several combinations of the intervening geometric and mechanical parameters.An experimental investigation is also performed in the case of clamped plates.Based on the results for solid circular plates, the fundamental frequency of annular plates with a free inner edge and a concentrated mass is also obtained.Circular plates are fundamental structural elements in ocean engineering applications: from off-shore platforms to underwater acoustic transducers. In a great variety of circumstances, they must carry operational systems in an eccentric fashion. Since the dynamic performance is always of interest, one must know at least some of the basic dynamic parameters.     

Influence of wave approach angle on TLP's response

The current study focuses on the response analysis of triangular tension leg platform (TLP) for different wave approach angles varying from 0° through 90° and its influence on the coupled dynamic response of triangular TLPs. Hydrodynamic loading is modeled using Stokes fifth-order nonlinear wave theory along with various other nonlinearities arising caused by change in tether tension and change in buoyancy caused by set down effect. Low frequency surge oscillations and high frequency tension oscillations of tethers are ignored in the analysis. Results show that wave approach angle influences the coupled dynamic response of triangular TLP in all degrees of freedom except heave. Response in roll and sway degrees of freedom are activated which otherwise are not present in TLP's response to unidirectional waves. Pitch and roll responses are highly stochastic in nature indicating high degree of randomness. Variation in surge, sway and heave responses are nonlinear and are not proportional to change in wave height for the same period.     

黄河入海水沙通量变化规律

根据利津站1950-2003年的水、沙实测资料,采用水文学和数理统计学相结合方法,对黄河入海水沙通量进行分析,分别得出了水、沙通量的年代变化、年际变化、季节变化规律以及水、沙通量之间关系.结果表明：黄河入海水、沙通量递减趋势明显,尤其在近20a来这种趋势更加显著;年际、年内沙量变化幅度都大于水量;黄河入海水沙主要集中在汛期,汛期与非汛期的水沙量差异将会持续减小;年输沙量和年径流量、多年平均月输沙量和径流量分别以乘幂、多项式回归,各月多年输沙量和径流量以多项式、指数回归,相关性都很高.     

Truncation errors of selected finite difference methods for two-dimensional advection-diffusion equation with mixed derivatives

The spread of a passive contaminant in an open-channel reach is considered with use of a two-dimensional advection-diffusion equation with the included off-diagonal dispersion coefficients. This paper presents the calculation of truncation errors, namely numerical diffusion and numerical dispersion for various finite difference schemes. The accuracy of the considered finite-difference approximations is analysed by deriving and studying the relevant modified partial differential equation.     

Dynamic non-planar crack rupture by a finite volume method

Modelling dynamic rupture for complex geometrical fault structures is performed through a finite volume method. After transformations for building up the partial differential system following explicit conservative law, we design an unstructured bi-dimensional time-domain numerical formulation of the crack problem. As a result, arbitrary non-planar faults can be explicitly represented without extra computational cost. On these complex surfaces, boundary conditions are set on stress fluxes and not on stress values. Prescribed rupture velocity gives accurate solutions with respect to analytical ones depending on the mesh refinement, while solutions for spontaneous propagation are analysed through numerical means. An example of non-planar spontaneous fault growth in heterogeneous media demonstrates the good behaviour of the proposed algorithm as well as specific difficulties of such numerical modelling.     

New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions

The hydraulic head distribution in a wedge-shaped aquifer depends on the wedge angle and the topographic and hydrogeological boundary conditions. In addition, an equation in terms of the radial distance with trigonometric functions along the boundary may be suitable to describe the water level configuration for a valley flank with a gentle sloping and rolling topography. This paper develops a general mathematical model including the governing equation and a variety of boundary conditions for the groundwater flow within a wedge-shaped aquifer. Based on the model, a new closed-form solution for transient flow in the wedge-shaped aquifer is derived via the finite sine transform and Hankel transform. In addition, a numerical approach, including the roots search scheme, the Gaussian quadrature, and Shanks’ method, is proposed for efficiently evaluating the infinite series and the infinite integral presented in the solution. This solution may be used to describe the head distribution for wedges that image theory is inapplicable, and to explore the effects of the recharge from various topographic boundaries on the groundwater flow system within a wedge-shaped aquifer.     

QTM地址码与经纬度坐标的快速转换算法

球面四元三角网(QTM——Quarternary Triangular Mesh)结构是目前研究全球海量数据管理的有效方法之一。但是，在现有的QTM地址码与经纬度的转换算法中，“ZOT投影法”的转换速度快，但生成的编码缺乏方向性；“ETP投影法”生成的编码具有固定的方向性，但转换速度慢。为解决这个矛盾，提出一个新的转换算法——“行列逼近法”(CAM——Cavalcade Approach Method)，其算法的基本原理是根据QTM的行和列，按一定的方向递归逼近地址码。文章给出了算法的详细步骤，并在实验中应用不同点数在不同层次对几种典型的转换算法进行了对比分析，结果表明：“行列逼近法”在保证所生成的地址码具有固定方向性的同时，时间消耗仅为“等三角投影法”的7％～20％左右。     

The SIA method for spatial analysis of precipitation in the upper-middle reaches of the Yangtze River

Using geographic information system (GIS) techniques and the newest seasonal and annual average precipitation data of 679 meteorological stations from 1971 to 2000, the multiple regressions equations of the precipitation and topographical variables are established to extract the effect of topography on the annual and seasonal precipitation in the upper-middle reaches of the Yangtze River. Then, this paper uses a successive interpolation approach (SIA), which combines GIS techniques with the multiple regressions, to improve the accuracy of the spatial interpolation of annual and seasonal rainfall. The results are very satisfactory in the case of seasonal rainfall, with the relative error of 6.86%, the absolute error of 13.07 mm, the average coefficient of variation of 0.070, and the correlation coefficient of 0.9675; in the case of annual precipitation, with the relative error of 7.34%, the absolute error of 72.1 mm, the average coefficient of variation of 0.092, and the correlation coefficient of 0.9605. The analyses of annual mean precipitation show that the SIA calculation of 3-5 steps considerably improves the interpolation accuracy, decreasing the absolute error from 211.0 mm to 62.4 mm, the relative error from 20.74% to 5.97%, the coefficient of variation from 0.2312 to 0.0761, and increasing the correlation coefficient from 0.5467 to 0.9619. The SIA iterative results after 50 steps identically converge to the observed precipitation.