An efficient 3-D infinite element for water wave diffraction problems

An efficient and simple infinite element for modelling the far field potential of water wave diffraction problems is presented. The shape functions in the radial direction comprise the first two terms of the asymptotic expansions of Hankel functions. The integrals with infinite limit for calculating the coefficient matrix have been worked out. Numerical tests on the diffraction by a surface-piercing circular cylinder give surprisingly accurate resultant forces even if the infinite elements are placed very near to the cylinder. Other typical three dimensional examples also show that satisfactory results can be obtained by the use of this simple infinite element. A computer program, WALOAD, has been developed for computing the wave forces on fixed two and three dimensional bodies.     

On periodic and solitary pure gravity waves in water of infinite depth

Non-linear two-dimensional waves propagating at a constant velocity at the surface of a fluid of infinite depth are considered. The fluid is assumed to be inviscid and incompressible and the flow irrotational. Gravity is taken into account, but surface tension is neglected. Accurate solutions are computed by boundary integral equation methods. Previous results on irregular waves are confirmed and extended. The computations strongly suggest the existence of non-periodic waves. These waves resemble generalised solitary waves in the sense that they are characterised by a train of oscillations in the far field.     

An analytical solution for the diffraction problem of a submerged vertical cylinder considering bottom-mounted barrier effect

Using the methods of variable separation and eigenfunction expansion for velocity potentials, an analytical expression for the composite structure of a submerged cylinder over a coaxial, bottom-mounted cylinder in finite depth is developed. This model is also applicable for the isolated submerged truncated cylinder by careful choice of bottom cylinder height. The exciting forces on the submerged cylinder obtained by the proposed analytical solution and the boundary element method (BEM) agree well with each other, which shows good reliability of the analytical expression. Based on the proposed model, the effects of wave force on submerged cylinder owing to the existence of topographical obstacles of different sizes are investigated. The results show that various geometrical parameters of the bottom cylinder alter wave force on the upper cylinder significantly. Considering the impact of barrier, horizontal wave force and vertical wave force on submerged cylinder arrive there are several peaks at different frequencies, while the isolated cylinder always reaches the peak at a certain frequency. The peak value of wave forces may increase or decrease, but that of overturning moment has a maximum value of two to four times amplitude.     

The optimum optical penetration depth for high diffraction efficiency in guided acousto-optic devices

In guided acousto-optic interaction, diffraction efficiency is a strong function of the overlap integral. Overlap integral with different optical penetration depth is analyzed theoretically. The optimum penetration depth is obtained for high diffraction efficiency.     

Semi‐analytic solution for multiple interacting three‐dimensional inhomogeneous inclusions of arbitrary shape in an infinite space

This paper develops a semi‐analytic solution for multiple arbitrarily shaped three‐dimensional inhomogeneous inclusions embedded in an infinite isotropic matrix under external load. All interactions between the inhomogeneous inclusions are taken into account in this solution. The inhomogeneous inclusions are discretized into small cuboidal elements, each of which is treated as a cuboidal inclusion with initial eigenstrain plus unknown equivalent eigenstrain according to the Equivalent Inclusion Method. All the unknown equivalent eigenstrains are determined by solving a set of simultaneous constitutive equations established for each equivalent cuboidal inclusion. The final solution is obtained by summing up the closed‐form solutions for each individual equivalent cuboidal inclusion in an infinite space. The solution evaluation is performed by application of the fast Fourier transform algorithm, which greatly increases the computational efficiency. Finally, the solution is validated by taking Eshelby's analytic solution of an ellipsoidal inhomogeneous inclusion as a benchmark and by the finite element analysis. A few sample results are also given to demonstrate the generality of the solution. The solution may have potentially significant applications in solving a wide range of inhomogeneity‐related problems. Copyright © 2011 John Wiley & Sons, Ltd.     

An integral equation method for the diffraction of oblique waves by an infinite cylinder

A hybrid integral equation method is formulated to study the diffraction of oblique waves by an infinite cylinder. The water depth and the geometry of the floating cylinder are assumed to be uniform in the y-direction (one of the horizontal axes). Numerical discretization and integrations are performed in the vertical plane. Analytical solutions are used in far fields such that radiation boundary conditions are satisfied. Numerical results are obtained for the case of wave scattering by a floating rectangular cylinder in a constant water depth. The accuracy and efficiency of present method are compared with those obtained by other numerical techniques.     

Degradation of alachlor in aqueous solution by using hydrodynamic cavitation

Samples of zirconium(IV)iodotungstate have been synthesized under varying mixing order and ratios of aqueous solution of potassium iodate, sodium tungstate and zirconium oxychloride at pH 1. A tentative formula was proposed on the basis of chemical composition, FTIR and thermogravimetric studies. The material shows a capacity of 0.68 meq g⁻¹ (for K⁺) which can be retained up to 200 °C. pH titration data reveal its monofunctional behavior. The distribution coefficient values of metal ions have been determined in various solvent systems. A number of important and analytically difficult quantitative separations of metal ions have been achieved using columns packed with this exchanger. In order to demonstrate practical utility of this material, Hg²⁺ and Pb²⁺ have been selectively separated and determined in the synthetic mixtures. Assay of Al³⁺ and Mg²⁺ in commercial tablets and analysis of lead in the standard reference material have also been attempted.     

Degradation of alachlor in aqueous solution by using hydrodynamic cavitation

The degradation of alachlor aqueous solution by using hydrodynamic cavitation was systematically investigated. It was found that alachlor in aqueous solution can be deomposed with swirling jet-induced cavitation. The degradation can be described by a pseudo-first-order kinetics and the degradation rate was found to be 4.90 × 10⁻² min⁻¹. The effects of operating parameters such as fluid pressure, solution temperature, initial concentration of alachlor and medium pH on the degradation rates of alachlor were also discussed. The results showed that the degradation rates of alachlor increased with increasing pressure and decreased with increasing initial concentration. An optimum temperature of 40 °C existed for the degradation rate of alachlor and the degradation rate was also found to be slightly depend on medium pH. Many degradation products formed during the process, and some of them were qualitatively identified by GC–MS.     

An analytical solution for long-wave scattering by a submerged circular truncated shoal

An analytical solution of the long-wave (or shallow-water) equation in closed-form is obtained for simple harmonic waves scattered by a submerged circular truncated shoal. This analytical solution is firstly validated against Longuet-Higgins’s classical analytical solution for a submerged cylinder, and then validated against numerical solutions obtained by using the DRBEM (dual reciprocity boundary-element method) model for a submerged circular truncated cone. Finally, the analytical solution is used to investigate the changing trend of maximum wave amplification, the trace pattern of focal position of wave-energy versus the wave period and the influence of shoal submergence on wave-energy trapping.     

The Dugdale solution for two unequal straight cracks weakening in an infinite plate

A crack arrest model is proposed for an infinite elastic perfectlyplastic plate weakened by two unequal, quasi-static, collinear straight cracks. The Dugdale model solution is obtained for the above problem when the developed plastic zones are subjected to normal cohesive quadratically varying yield point stress. Employing complex variable technique and the superposition principle the desired solution is obtained. A qualitative study of load required to arrest the plastic zones opening with respect to affecting parameters viz. inter-crack distance, plastic zone and crack length is carried out. The results obtained are presented graphically.     

Singular solution of a water wave problem in an ocean of finite depth

The Green's Function of a Water Wave Problem for an Ocean of Finite Depth, bounded internally by a circular cylinder, has been obtained by the use of an appropriate Fourier Series. The technique employed in this investigation may be used when the liquid is internally bounded by cylindrical regions of the form D × I where D is any two dimensional region in the undisturbed free surface and I is the linear interval [0, h].     

Magnetostatic field of a conductor of semicircular cross section in a highly permeable half-space: exact analytic solution for infinite permeability with perturbative correction

Poisson's equation for the magnetic vector potential is solved using complex Fourier (Laplace) transforms in bipolar coordinates, the natural system for the subject two-dimensional geometry. The source is a dc current uniformly distributed over the semicircular cross section of a long conductor that is buried in, and flush with, the otherwise planar boundary of an infinitely permeable material. Exact closed-form potentials are obtained in the conformal mapping of the Neumann boundary value problem that characterizes the case of an infinitely permeable magnetic medium. One term of a perturbative correction that accounts for finite permeability is constructed for both the uniform source distribution and for the associated Green's function.     

A MoM solution for TM scattering by dielectric cylinders above an infinite flat surface

A simple solution method is presented for transverse magnetic plane wave scattering by a dielectric cylinder of arbitrary cross-section in front of an infinite flat dielectric surface. The interface between two semi-infinite, dissimilar half-spaces is considered by a perturbed equivalent magnetic current. Coupled integral equations are obtained from a special form of surface equivalence principles and are solved numerically by the Method of Moments. The scattered tangential electric field at interface is displayed and far-zone fields are compared to the results available in the literature.     

ADCP测量水深的过滤与插值方法

声学多普勒流速剖面仪(Acoustic Doppler Current Profiler, ADCP)对河道流量进行测量有赖于准确的深度测量,在遇到错误的深度测量时应采用合理的数值对错误帧进行深度插值,以增加计算准确度。文章分析了ADCP在斜坡河底环境下进行深度测量的理论标准差,在此基础上提出了使用四波束深度标准差与平均值的比值来进行深度过滤的新方法,并采用对历史保存的深度测量值进行拟合预测计算,为无效帧进行更为准确的深度插值。该方法相对于以往的水深过滤方法,进一步的增加了对水深异常值的过滤能力,提高了流量的计算精度。     

Numerical solution for multiple crack problem in an infinite plate under compression

This paper investigates a numerical solution for multiple crack problem in an infinite plate under remote compression. The influence of friction is taken into account. In the first step of the solution, we make a full contact assumption on the crack faces. The full contact assumption means that one component of the dislocation distribution vanishes, and the first mode stress intensity factors (K ₁) at the crack tips become zero. On the above-mentioned assumption, the problem can be solved by using integral equation method, and the second mode stress intensity factors (K ₂) at the crack tips can be evaluated. Meantime, after solving the integral equation the normal contact stress on the crack faces can be evaluated. The next step is to examine the full contact assumption. If the contact stresses on the crack faces are definitely negative, the solution is true. Otherwise, the obtained solution is not true. It is found from present study that in most cases the full contact condition is satisfied, and only in a few cases the full contact condition is violated. Numerical examples are given. It is found that the friction can lower the stress intensity factors at crack tips in general.     

A hybrid element method for diffraction of water waves by three-dimensional bodies

A hybrid element method developed recently for two-dimensional problems of water waves in an infinite fluid is extended to three dimensions. In this method only a limited fluid domain close to irregular bodies is discretized into conventional finite elements, while the remaining infinite domain is treated as one element with analytical representations of high accuracy. Continuity at the junction surface is treated as natural boundary conditions in a variational principle. Computation experience and numerical results for several ocean structures are presented.     

X-ray diffraction of permalloy nanoparticles fabricated by laser ablation in water

Permalloy (NiFeMo) nanoparticles were fabricated by laser ablation of bulk material in water with a UV pulsed laser. Transmission electron microscope images showed that approximately spherical particles about 50 nm in diameter were formed in the ablation process. All diffraction peaks corresponding to the bulk material were present in the nanoparticles. In addition to these peaks several new peaks were observed in the nanoparticles, which were attributed to nickel oxide.     

Coupled FE–BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain

For thin elastic structures submerged in heavy fluid, e.g., water, a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies. Therefore, the eigenanalysis of the fluid–structure interaction system is necessary. In this paper, a coupled finite element and boundary element (FE–BE) method is developed for the numerical eigenanalysis of the fluid–structure interaction problems. The structure is modeled by the finite element method. The compressibility of the fluid is taken into consideration, and hence the Helmholtz equation is employed as the governing equation and solved by the boundary element method (BEM). The resulting nonlinear eigenvalue problem is converted into a small linear one by applying a contour integral method. Adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenvalues of interest. The Burton–Miller formulation is applied to tackle the fictitious eigenfrequency problem of the BEM, and the optimal choice of its coupling parameter is investigated for the coupled FE–BE method. Numerical examples are given and discussed to demonstrate the effectiveness and accuracy of the developed FE–BE method. Copyright © 2016 John Wiley & Sons, Ltd.     

Strip theory for underwater vehicles in water of finite depth

This paper addresses the need to know the unsteady forces and moments on an underwater vehicle in finite-depth water, at small enough submergences for it to be influenced by sea waves. The forces are those due to the waves themselves, as well as the radiation forces due to unsteady vehicle motions. Knowledge of these forces and the mass distribution of the vehicle allow solution of the equations of motion at a single-frequency. Since the theory is linear, any incident wave field can be decomposed into the sum of many individual single-frequency sinusoidal waves. The motions due to each frequency component can then be added together to obtain the total predicted vehicle motions. The wave forces are due to the undisturbed sea wave plus those due to the diffracted wave necessary to satisfy boundary conditions on the vehicle. The long-used strip theory for ships, with the inviscid-flow approximation, is modified for finite depth and inclusion of lift forces on the vehicle fins. The two-dimensional solutions for the forces on each strip are found by a different method than is commonly used for strip theory. This form of the theory is easier to deal with and requires much less computing time than a fully three-dimensional approach. Experiments are conducted and their results are compared with the theory. Excellent agreement is found between the theoretical and experimental wave forces, including the diffracted wave. It is shown that inclusion of the forces on the fins not only improves the theoretical wave forces, but also brings the results of theory for the radiation forces and moments due to vehicle motions much closer to the experimental values that the theory without inclusion of fin lift forces.     

The solution of a mixed boundary value problem in the theory of diffraction

Summary An exact solution is obtained for the problem of the diffraction of a cylindrical sound wave by an absorbent semi-infinite plane. The two faces of the half-plane have different impedance boundary conditions. The problem which is solved is a mathematical model for a noise barrier whose surface is treated with two different acoustically absorbent materials.The usual Wiener-Hopf method (which is the standard technique for solving half-plane problems) has to be modified to give a solution to the present mixed boundary value problem.