Draft effect on wave action with a semi-infinite elastic plate

1Introduction Wave action on coastal and offshore structuresis investigated by many researches. In the recent pa-pers we can seen that Li et al. (2006) developed athree-dimesional(3D) numerical model for obliquewave action on vertical walls, Li et al. (20…     

斜向波对台阶地形上有限吃水半无限长弹性板的散射作用

基于线性势流理论和欧拉-伯努利梁理论,采用匹配特征函数展开法建立斜向波对台阶地形上有限吃水半无限长弹性板散射的解析解。与以往研究不同,本文同时考虑波浪入射角度、弹性板吃水、三种不同板端条件（自由板端、简支板端、固定板端）以及海底地形的影响。本文还直接将板端条件引入匹配边界条件,建立线性方程组求解速度势中的展开系数,计算过程简单、高效。计算结果表明：本文方法收敛性好,并满足能量守恒方程。将本文计算结果与文献中的特例结果进行对比,吻合良好。分析了波浪入射角度、弹性板吃水、不同板端条件以及海底地形对弹性板水动力参数的影响,研究结果可以为工程设计提供参考。     

Numerical experiments on the Rayleigh-Ritz method when applied to doubly connected plates in the case of free edge holes

Numerical experiments are performed on the determination of the fundamental frequency of transverse vibration of simply supported rectangular plates having rectangular holes with free edges. This constitutes a rather common technological situation since holes are present in plates or slabs due to operational conditions, namely passage of conduits or ducts, electric conductors, etc., Satisfying exactly the governing natural boundary conditions at the hole edges is practically an impossible task. This study reviews numerical experiments where the displacement function is expanded into a double Fourier series which constitutes the exact solution when the plate is simply connected. Satisfactory convergence is achieved when the plate is doubly connected.     

Bending of orthotropic super-elliptical plates on intermediate point supports

Bending analysis of orthotropic super-elliptical plates of uniform thickness was investigated. Optimum location of the point supports was searched by minimizing the maximum absolute deflection. The support location which minimizes the bending moments at the supports was reported. The Ritz method was used and the total potential energy functional was modified by introducing the Lagrange multipliers to improve the accuracy of the stress resultants. The deflection and the bending moments computed at various points for a large variety of plate shapes ranging from an ellipse to a rectangle were checked with those of rectangular and elliptical plates. Good agreement was obtained for both cases. The structural response was found to be sensitive to support position.     

Wave loading on axisymmetric bodies using axisymmetric hybrid integral equation method

The wave diffraction problem on axisymmetric structures are solved by treating the fluid field as two separate domains. The velocity potential in the inner domain is represented by a 1/r type Green's function whilst that of the outer domain is represented by an eigenfunction expansion. The simple form of the Green's function in the inner domain reduces significantly the computational effort whilst the eigenfunction expansion in the outer domain is able to satisfy the radiation boundary condition completely. The method requires to have elements cover the entire containing boundary. Results for a number of typical structural geometries are presented and discussions are made on the effect of various parameters.     

A Simple Empirical Formula for Predicting the Ultimate Strength of Ship Plates with Elastically Restrained Edges in Axial Compression

An investigation is conducted on the static ultimate limit state assessment of ship hull plates with elastically restrained edges subjected to axial compression. Both material and geometric non-linearities were considered in finite element(FE) analysis. The initial geometric imperfection of the plate was considered, while the residual stress introduced by welding was not considered. The ultimate strength of simply supported ship hull plates compared well with the existing empirical formula to validate the correctness of the applied boundary conditions, initial imperfection and mesh size. The extensive FE calculations on the ultimate strength of ship hull plates with elastically restrained edges are presented. Then a new simple empirical formula for plate ultimate strength is developed, which includes the effect of the rotational restraint stiffness, rotational restraint stiffness, and aspect ratios. By applying the new formula and FE method to ship hull plates in real ships, a good coincidence of the results between these two methods is obtained, which indicates that the new formula can accurately predict the ultimate strength of ship hull plates with elastically restrained edges.     

基于高度计数据的南极冰水边界识别算法研究

海冰边缘线是南极海冰监测的重要内容之一。本文基于ENVI RA-2(ENVISAT Radar Altimeter 2)高度计数据开展了南极海冰边缘线提取方法研究。首先根据海冰和海水后向散射系数的不同,利用其各自方差对两者进行区分,获得了冰水分界线;其次通过ENVISAT-ASAR(ENVISAT-Advanced Synthetic Aperture Radar)数据和冰况图对提取的海冰边缘线的正确性进行了验证;最后简要分析了误差存在的原因。研究结果表明,高度计数据在提取大范围海冰边缘线方面具有优势。     

A unified, polynomial approach for the approximate solution of thermoelastic problems in rectangular plates

The present paper, of a tutorial nature, solves two different thermoelastic problems using a unified approach: (a) thermoelastic stresses and deflections in thin, rectangular plates with edges elastically restrained against rotation when small-deflection theory is used and stress resultants in the middle plane of the plates are neglected; and (b) thermoelastic plane stress situations in rectangular plates with stress-free edges subjected to a two-dimensional temperature distribution.The first problem is attacked using polynomial coordinate functions which identically satisfy the governing boundary conditions, and the Ritz method is used to determine the plate response. When the flexibility coefficients approach zero (clamped edge conditions) the calculated results practically coincide with the exact solution for the test case treated in this paper. On the other hand this degenerate solution turns out to be a very convenient approximation for obtaining a solution to Airy's problem described in the second place and which is also solved in a straightforward manner using a variational approach.     

Some additional results on vibrating, simply supported rectangular plates with free, rectangular cut-outs

The present study deals with numerical experiments performed using the doublesine Fourier expansion and the Ritz method to determine natural frequencies of vibration of simply supported rectangular plates with free rectangular holes parallel to the plate sides.The problem is of basic structural interest in naval and ocean engineering systems since holes are frequently practiced in plate-type structural elements to allow for the passage of ducts, elevators, etc…     

生长在不同基底材料上的网纹藤壶底板形貌结构比较

通过观察在不同材质表面上黏附的网纹藤壶底板的微观结构,发现不同的基底材料对网纹藤壶底板结构有明显影响。在底板不同区域,其微观结构呈现多样化,这可能与底板处于不同形成期或与底板承担的侧壁链接、藤壶胶运输等功能有关。网纹藤壶底板结构复杂性高、可塑性强,这为藤壶适应严酷多变的海洋环境提供了必要的结构基础。     

Research on the hydrodynamic characteristics of heave plate structure with different form edges of a spar platform

The hydrodynamic characteristics of heave plates with different form edges of Truss Spar Platform are studied in this paper.Numerical simulations are carried out for the plate forced oscillation by the dynamic mesh method and user defined functions of FLUENT.The added mass coefficient and the damping coefficient of heave plate with tapering condition and the chamfer condition are calculated.The results show that,in a certain range,the hydrodynamic performance of heave plate after being tapered is better.     

Hydrodynamic performance of a dual cylindrical caisson breakwater

The hydrodynamic performance of a dual cylindrical caisson breakwater (DCBW) formed by a row of caissons each of which consisting of a porous outer cylinder circumscribing an impermeable inner cylinder has been theoretically investigated. The theoretical formulation is based on the eigenfunction expansion method proposed by Spring and Monkmeyer (1974) which was further modified by Linton and Evans [Linton, C.M., Evans, D.V., 1990. The interaction of waves with arrays of vertical circular cylinders. Journal of Fluid Mechanics 215, 549–569] for an array of impermeable cylinders. The present formulation is an extension of the work of Wang and Ren [Wang, K.H., Ren, X., 1994. Wave interaction with a concentric porous cylinder system. Ocean Engineering 21(4), 343–360], wherein; the interaction of linear waves with a single concentric porous cylinder system was studied. In the present study, the formulation has been extended to the case of a group of porous dual cylinder system. Parametric studies are carried out to study the influence of porosity (G₀) on the outer caisson, width of the doughnut chamber (a/b) and the angle of wave incidence on the variation in the hydrodynamic loading, wave run-up, free-surface elevation in its vicinity as well as the transmission on its lee-side. The importance of the presence of the inner cylinder in achieving the required hydrodynamic performance in terms of either protection or providing tranquility on its lee side keeping higher stability for the breakwater system is highlighted.     

Application of an accurate advection algorithm to sea-ice modelling

Modern numerical sea-ice models contain detailed parameterizations of dynamic and thermodynamic processes affecting ice distribution and thickness. However, nearly all such models advect sea ice in response to wind and ocean forcing using either upstream or centered-difference methods, whose deficiencies are well known. We describe application of the second-order moment advection scheme of Prather [J. Geophys. Res. 91 (1986) 6671]. In idealized tests this method produces relatively distinct ice edges while maintaining positive ice thicknesses and concentrations. Sensitivity of an Arctic circulation model forced by climatological data is described.     

Wave motion over a submerged breakwater with an upper horizontal porous plate and a lower horizontal solid plate

This study examines the hydrodynamic performance of a modified two-layer horizontal-plate breakwater. The breakwater consists of an upper submerged horizontal porous plate and a lower submerged horizontal solid plate. By means of the matched eigenfunction expansion method, a linear analytical solution is developed for the interaction of water waves with the structure. Then the reflection coefficient, the transmission coefficient, the energy-loss coefficient and the wave forces acting on the plates are calculated. The numerical results obtained for limiting cases are exactly the same as previous predictions for a single submerged horizontal solid plate and a single submerged horizontal porous plate. Numerical results show that with a suitable geometrical porosity of the upper plate, the uplift wave forces on both plates can be controlled at a low level. Numerical results also show that the transmission coefficient will be always small if the dimensionless plate length (plate length versus incident wavelength) exceeds a certain moderate value. This is rather significant for practical engineering, as the incident wavelength varies over a wide range in practice. Moreover, it is found that the hydrodynamic performance of the present structure may be further enhanced if the lower plate is also perforated.     

Free vibration analysis of antisymmetric laminated rectangular plates with distributed patch mass using third-order shear deformation theory

A free vibration analysis of laminated composite plates carrying a distributed patch mass is analyzed and presented in this paper. The Hamilton's Principle, using third-order shear deformation theory, is applied to simply supported rectangular plates. The displacement of the plate is postulated by a double Fourier series. The effects of size and location of the distributed patch mass on the response of the plate are also presented. A thorough comparison with well known published results is presented for the case of free vibration of unloaded plates and good agreement is observed.     

Analysis of Ac in seawater by delayed coincidence counting

The activity of ²²⁷Ac in seawater was determined using a delayed coincidence counting technique based on the measurement of the short-lived daughter ²²³Ra (half-life of 11 days). Two 180-l aliquots of Ac free seawater from surface waters of the California borderlands were spiked with Harwell Uraninite standard and the added Ac and Ra were extracted on Mn-fibers. The measured activities on the fibers agreed to within 5% of the equilibrium Ac activity of the spike addition, well within the 2σ counting error of 7% for the measurements. Thus, any recovery error was indistinguishable from counting error. Large volume samples were collected from the water column of the Eastern North Pacific in December of 1998 and processed through Mn-fiber columns. The ²²³Ra activities on the fibers were measured four or more times over a period of 2 months by the technique of [J. Geophys. Res. 101 (1996) 1321] to determine if the activity of ²²³Ra was wholly supported by ²²⁷Ac. In most cases, no significant differences in ²²³Ra activity were observed during repeated counting of the same sample, again implying that ²²³Ra was supported wholly by ²²⁷Ac. In samples where unsupported ²²³Ra were present, samples were counted beyond five half live of the ²²³Ra (>60 days). Two depth profiles of ²²⁷Ac in the Eastern North Pacific showed similar shape and activity to profiles in the Western and Central Pacific measured with alpha-spectrometry by [Nature 310 (1984) 486). Surface waters of the Southern Ocean were relatively enriched in ²²⁷Ac compared to Eastern North Pacific waters, possibly indicating export of the parent ²³¹Pa from Atlantic surface waters or upwelling.     

Scattering of Oblique Water Waves by Two Unequal Surface-Piercing Vertical Thin Plates with Stepped Bottom Topography

Based on linear water-wave theory, this study investigated the scattering of oblique incident water waves by two unequal surface-piercing thin vertical rigid plates with stepped bottom topography. By using the matched eigenfunction expansion method and a least square approach, the analytical solutions are sought for the established boundary value problem. The effects of the incidence angle, location of step, depth ratio of deep to shallow waters, and column width between two plates, on the reflection coefficients, the horizontal wave forces acting on the two plates, and the mean surface elevation between the two plates, are numerically examined under a variety of wave conditions. The results show that the existence of the stepped bottom between two plates considerably impacts the hydrodynamic performances of the present system. It is found that the effect of stepped bottom on the reflection coefficient of the present two-plate structure is evident only with waves of the low dimensionless frequency. Moreover, the influence of the step location on the hydrodynamic performance of the present two-plate structure is slight if the step is placed in between the two plates.     

Buckling of circular, annular plates of continuously variable thickness used as internal bulkheads in submersibles

This paper deals with the determination of the critical load in the buckling of isotropic, circular annular thin plates whose thickness varies slightly according to an exponential law.The outer edge of the plate is elastically restrained against rotation while the inner boundary is free. Classical small-deflection theory is used. An hidrostatic pressure acting in the middle plane is considered.The eigenvalues of the problem are obtained by means of an analytical approach based on the optimized Rayleigh-Ritz method. It is shοwnι that the results are in good agreement from an engineering viewpoint, with those available in the literature.     

Hydroelastic analysis of pontoon-type circular VLFS with an attached submerged plate

This paper is concerned with the hydroelastic analysis of a pontoon-type, circular, very large floating structure (VLFS) with a horizontal submerged annular plate attached around its perimeter. The coupled fluid–structure interaction problem may be solved by using the modal expansion method in the frequency domain. It involves, firstly, the decomposition of the deflection of a circular Mindlin plate with free edges into vibration modes that are obtained analytically. Then the hydrodynamic diffraction and radiation forces are evaluated by using the eigenfunction expansion matching method which can also be done in an exact manner. The hydroelastic equation of motion is solved by the Rayleigh–Ritz method for the modal amplitudes, and then the modal responses are summed up to obtain the total response. The effectiveness of the attached submerged annular plate in reducing the motion of VLFS has been confirmed by the analysis.     

The rise of Laminaria ochroleuca in the Western English Channel (UK) and comparisons with its competitor and assemblage dominant Laminaria hyperborea

The distribution of species is shifting in response to recent climate change. Changes in the abundance and distributions of habitat‐forming species can have knock‐on effects on community structure, biodiversity patterns and ecological processes. We empirically examined temporal changes in the abundance of the warm‐water kelp Laminaria ochroleuca at its poleward range edge in the Western English Channel. Resurveys of historical sites indicated that the abundance of L. ochroleuca has increased significantly in recent decades. Moreover, examination of historical records suggested that L. ochroleuca has extended its distribution from sheltered coasts on to moderately wave‐exposed open coasts, where it now co‐exists and competes with the assemblage dominant Laminaria hyperborea. Proliferation of L. ochroleuca at its poleward range edge corresponds with a period of rapid warming in the Western English Channel. Preliminary comparisons between L. ochroleuca and L. hyperborea highlighted some subtle but ecologically significant differences in structure and function. In summer, the average biomass of epiphytic stipe assemblages on L. hyperborea was 86 times greater than on L. ochroleuca whereas, on average, L. ochroleuca had a greater stipe length and its blade supported 18 times as many gastropod grazers (Gibbula cineraria). Differences in summer growth rates were also recorded, with L. ochroleuca being more productive than L. hyperborea throughout July. Comprehensive seasonally replicated comparisons are needed to examine the wider implications of proliferation of L. ochroleuca at its poleward range edge, but our study suggests that local biodiversity patterns and ecological processes (e.g. timing of productivity and trophic pathways) on shallow subtidal reefs may be altered by shifts in the relative abundances of habitat‐forming kelp species.