Radiation and Diffraction of Water Waves by a Submerged Body with Ice Cover in Finite Depth

This paper presents the three-dimensional Green-function method to predict the radiation and diffraction of water waves by a submerged body in water of uniform finite depth with an ice cover. The fluid is assumed to be perfect and irrotational, the ice is modelled as an elastic plate. The zero-speed Green function of finite depth satisfying the linearized covered-surface condition is derived in three dimensions, the numerical results for the Green function and its derivatives are given. The integral equations are established by distributing the source strength on the body surface, the radiation and diffraction problems are solved. A submerged sphere is taken as an example, the effects of the water depth and the flexural rigidity of ice cover on hydrodynamics are analysed, and the good agreement with the analytical solutions reveals that the present method is correct and reliable.

     

Water wave interaction with a sphere in a two-layer fluid flowing through a channel of finite depth

Using linear water wave theory, we consider a three-dimensional problem involving the interaction of waves with a sphere in a fluid consisting of two layers with the upper layer and lower layer bounded above and below, respectively, by rigid horizontal walls, which are approximations of the free surface and the bottom surface; these walls can be assumed to constitute a channel. The effects of surface tension at the surface of separation is neglected. For such a situation time-harmonic waves propagate with one wave number only, unlike the case when one of the layers is of infinite depth with the waves propagating with two wave numbers. Method of multipole expansions is used to find the particular solutions for the problems of wave radiation and scattering by a submerged sphere placed in either of the upper or lower layer. The added-mass and damping coefficients for heave and sway motions are derived and plotted against various values of the wave number. Similarly the exciting forces due to heave and sway motions are evaluated and presented graphically. The features of the results find good agreement with previously available results from the point of view of physical interpretation.     

Scattering of water waves by thin vertical plate submerged below ice-cover surface

The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green's integral theorem in terms of difference of potential functions across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.     

Water waves generated due to initial axisymmetric disturbances in water with an ice-cover

This paper is concerned with the generation of water waves due to prescribed initial axisymmetric disturbances in a deep ocean with an ice-cover modelled as a thin elastic plate. The initial disturbances are either in the form of an impulsive pressure distributed over a certain region of the ice-cover or an initial displacement of the ice-cover. Assuming linear theory, the problem is formulated as an initial-value problem in the velocity potential describing the ensuing motion in the fluid. In the mathematical analysis, the Laplace and Hankel transform techniques have been utilised to obtain the deformation of the ice-covered surface as an infinite integral in each case. The method of stationary phase is used to evaluate the integral for large values of time and distance. Figures are drawn to show the effect of the presence of ice-cover on the wave motion.     

Generation of impulsive pressure wave by spark discharge in water and its propagation

An experimental investigation was performed to find a new method for diagnosing three-dimensional flows in which obstacle bodies or cavities are included by means of a pressure wave. In rectangular closed tanks 200 × 337 × 250 mm (acrylic resin) and 300 × 450 × 400 mm (brass) filled with water, an impulsive pressure wave was generated by an instantaneous small spark discharge. The pressure waveforms were measured at a point on the wall with a high-frequency pressure transducer, and the data were recorded with an A/D converter. The measured wave fluctuations differed depending on wall conditions of the tank and on whether there was a submerged body in the water. The size of the submerged body also affected the pressure fluctuation. When acrylic resin and brass were used as wall materials, both the phase and amplitude of the reflecting wave differed. When a stainless steel sphere of diameters of 50.8, 30.2, or 19.1 mm was submerged in the tank, two kinds of pressure waves were observed, one passing through the sphere and the other diffracted around it. These results suggest the possibility of identifying bodies of simple shape by interpreting the precisely measured output pressure wave signals.     

Nonlinear FE-based investigation of flexural damping of slacking wire cables

The flexural damping of wire cable due to the flexural hysteresis influences the dynamic behavior of slacking wire cables significantly. However, the details of the local model, accounting for the flexural hysteresis between the wire strands, are quite challenging to include in large-scale engineering applications. This paper addresses these difficulties by modeling the flexural damping of slacking wire cables using homogenized Rayleigh damping. By using the nonlinear finite element method and high-speed imaging technique, three aspects of the work were examined. First, the mechanical properties of the slacking cable were identified experimentally. Second, a sample cable was fixed at one end and allowed to vibrate freely at the other end. The shapes of the vibrating cable were captured by a high-speed digital camera and processed by photogrammetry. The cable demonstrated a high flexural damping at zero tension and its damping was measured to be as high as 37.7% of the critical damping. Third, the cable was modeled and analyzed using our newly developed nonlinear curved beam element with the Rayleigh damping. The finite element predictions of the cable motion agree well with the experimental measurement. These predictions demonstrate that the new element is capable of describing the dynamic response of the cable and that the Rayleigh damping is sufficient to model the flexural damping of slacking wire cables.     

The slow rotation of a sphere submerged in a fluid with a surfactant surface layer

The effect of a layer of an adsorbed surfactant monomolecular film of fluid which covers the surface of a large volume of a different substrate fluid is considered with respect to the fluid motion caused by the slow rotation of a submerged sphere. For a semi-infinite substrate, the boundary value problem posed with the surfactant boundary condition of Scriven and Goodrich is solved exactly for any depth of the submerged sphere. Comprehensive numerical calculations are given for the torque and surface velocity for various values of the parameters defining the depth of the sphere and the surface shear viscosity. Asymptotic expressions for the solution are given for the cases of a deeply submerged sphere or when the substrate has a finite depth. The relevance of the work to providing an experimental technique for measuring surface shear viscosity is also considered.     

Hydroelastic analysis of very large floating structure over viscoelastic bed

Effect of viscoelastic bed on the hydroelastic response analysis of very large floating structures is studied using the linear water wave theory and small amplitude structural response in finite water depth. The floating structure is modeled using Euler–Bernoulli beam equation and the bottom bed is assumed to be viscoelastic in nature and is based on the Voigt’s model. The dispersion relation, phase speed and response amplitude of the floating structure as well as viscoelastic bed surface, pressure distribution along water depth are analyzed to study the effect of viscoelastic bed parameters, flexural rigidity of the floating structure, time period on flexural gravity wave motion. The study reveals that structural response of the floating structure can be mitigated for moderate thickness of the viscoelastic layer. Moreover, both shear modulus and viscosity of the viscoelastic layer play dominant role in reducing the structural response compared to the flexural rigidity of the structure. Further, pressure distribution within the viscoelastic bed decreases at a higher rate compared to the inviscid fluid layer irrespective of shear modulus and viscosity. The present study will be of immense help in the site selection of very large floating structures in the coastal water and installation of various marine facilities over muddy bed.     

基于三维接触有限元分析的管片等效抗弯刚度和错台研究

针对盾构隧道管片接头等效抗弯刚度预测研究中，对梁-弹簧与三维模型整体等效性考虑的不充分，以三维接触有限元计算结果作为测量信息，借助基于挠度等效的反问题求解，提出了一种确定管片接头等效抗弯刚度的新方法；并利用不同轴力-偏心距组合下的反演结果，建立了基于Kriging代理模型的轴力-弯矩-等效抗弯刚度的非线性关系，提出了由此关联的管片结构非线性问题的数值求解方法。与三维有限元结果相比，所提方法可较为准确地预测管片结构的内力和变形，表现出良好的整体等效性。此外，借助三维接触有限元分析，进一步深入探讨了螺栓孔间隙与衬垫本构关系对管片纵向错台量的影响。     

A new method for measuring damping in flexural vibration of thin fibers

In this paper we describe a new method for measuring damping in flexural vibration of filamentous matter, such as polymeric or metallic fibers. This method enables us to measure the damping characteristics of very thin fibers (down to lateral dimensions of a few micrometers). The fiber sample is clamped at one extremity and excited in the flexural vibration mode of a cantilever beam configuration, using a piezoelectric actuator. While the fiber sample vibrates around a flexural eigenfrequency, structural damping is determined from the measurement of the curve of phase difference between excitation and motion. This technique does not require the amplitude of the fiber motion to be determined. The phase curve is inferred from the periodic disturbance occurring when the fiber acts as a shutter for a light beam. This method can be applied to fibers of arbitrary shape and material. Examples are shown of measurements with polymer and metallic fibers. Flexural damping is evaluated at atmospheric pressure and in vacuum. The technique is validated by a comparison with polypropylene damping measurements from standard dynamic mechanical thermal analysis techniques.     

A forced-vibration technique for measurement of material damping

This article describes a technique for measuring material damping in specimens under forced flexural vibration. Although the method was developed for testing fiber-reinforced composite materials, it could be used for any structural material. The test specimen is a double-cantilever beam clamped at its midpoint and excited in resonant flexural vibration by an electromagnetic shaker. Under steady state conditions, material damping is defined in terms of the ratio of input energy to strain energy stored in the specimen. If external losses are negligible, the input energy must equal the energy dissipated in the specimen. Input energy and strain energy are found from measured specimen dimensions, resonant frequency, input acceleration and bending strain. Problems associated with minimization of external energy losses in the apparatus and verification of measurements are discussed in detail. Measured damping of aluminum-alloy calibration specimens shows good agreement with calculated thermoelastic damping. Examples of measured damping showing amplitude and frequency dependence in fiber-reinforced plastic materials are presented.     

On the stability of a deep beam subjected to nonconservative and dissipative forces

Summary For the case of a simply supported deep beam subjected to a transverse follower load applied at its center, the dependence of the critical flutter load upon the effects of internal and external damping and warping rigidity is considered. A Kelvin-Voigt solid is assumed, the external damping is assumed to be proportional to the velocity of the beam at a point, and, due to the nature of the nonconservative applied load, the flexural and torsional deformations of the beam are coupled. The resulting boundary value problem is nonself-adjoint in character, and the stability problem is solved in an approximate manner by means of an adjoint variational principle. Several graphs are presented to demonstrate the effect of the various damping and rigidity parameters on the value of the critical flutter load. The numerical results obtained here reveal that in the absence of external damping, the value of the critical flutter load becomes arbitrarily small as the internal damping parameter associated with flexure tends to zero.

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Sommario Per una trave alta, incernierata agli estremi e sollecitata da un carico rotante con la sezione cui sia applicato e distribuito simmetricamente rispetto alla mezzeria della trave, si considera la dipendenza del carico critico di flutter dagli effetti di smorzamento interno ed esterno e della rigidezza biflessionale. Si assnmono (i) un solido di tipo Kelvin-Voigt e (ii) uno smorzamento esterno che sia proporzionale alla velocità. Dovuta al genere del carico non conservativo, la deformazione consiste di spostamenti di flessione e torsione. Poichè il problema ai limiti che descrive il moto del sistema possiede coefficienti variabili e non è antoaggiunto, si risolve il problema di constatare il valore del carico critico per un procedimento approssimativo mediante un principio variazionale. Si mostrano grafici che rivelano gli effetti dei diversi parametri di smorzamento e rigidezza sul valore del carico critico. I risultati numerici ottenuti qui mostrano che nell'assenza di smorzamento esterno il valore del carico critico diviene arbitrariamente minnto qualora il parametro di smorzamento interim associate con flessione lenda a zero.

     

On the limits of added-mass theory in separated flows and with varying initial conditions

It remains unclear to what extent inviscid added-mass theory accounts for the forces exerted on an accelerating body subjected to separated flow. In this study, reactant forces and velocity-field data are systematically acquired using experimental measurements and simulations of an accelerating circular flat plate. Cases accelerated from rest are compared to cases accelerated from a steady flow state. When the added-mass forces predicted by potential theory and the resistance forces associated with the instantaneous plate velocity are accounted for, the remaining (residual) forces comprise approximately 20% of the peak force, even at high accelerations. In addition, the computed residual forces during accelerations both from rest and steady-state cases yield good collapse with respect to one another, indicating that the total forces are not a strong function of the initial state of the wake. These results suggests that inviscid added-mass theory is inadequate to predict the full reactant force even in the ‘ideal’ condition of impulsive motion from rest.     

Experimental investigation of added mass effects on a Francis turbine runner in still water

The mechanical design of hydraulic turbines is conditioned by the dynamic response of the runner that is usually estimated by a computational model. Nevertheless, the runner has complex boundary conditions that are difficult to include in the computational model. One of these boundary conditions is the water in which the runner is submerged. The effect of the added mass and damping of water can modify considerably the natural frequencies of the runner. An experimental investigation in a reduced scale model of a turbine runner, using modal analysis, was carried out. Several impact tests with the runner freely suspended in air and in water were done. The response was measured with accelerometers located in different positions of the runner. From the modal analysis, the natural frequencies, damping ratios, and mode-shapes were determined. The same mode-shapes obtained in air were obtained in water but with lower natural frequencies and higher damping ratios in water. The difference in the natural frequencies is shown to be dependant basically on the added mass effect of the water and not on its added damping. This difference also depends on the geometry of the mode, presenting different values for different mode-shapes. Using nondimensional values, the reduction in the natural frequencies can be extrapolated to other Francis runners presenting similar geometrical characteristics.     

Experimental characterization of the instability of the vortex ring. Part I: Linear phase

The results of experiments performed to study the linear phase of the instability of vortex rings are presented. The experiments were performed in water. The vortex rings are generated by pushing water through the cylindrical nozzle of a pipe submerged in an aquarium. The experiments were made with the help of planar laser induced fluorescence as well as 2D2C and 2D3C particle image velocimetry. They show the straining field causing the instability, and for the first time experimentally the growth of a band of linear unstable modes. They also confirm previous studies concerning the shape of the instability and theories predicting the number of waves and the bandwidth of unstable modes. However, the measurement of the growth rate shows the influence of viscous damping, and consequently, the limit of the theories based on the hypothesis of an ideal fluid.     

基于刚度分解法的输电铁塔结构杆件力分析

提出了输电铁塔应用刚度分解法的分析过程,利用刚度分解法分别建立了铁塔各段等效抗弯刚度矩阵和等效抗剪刚度矩阵代替空间桁架分析法中的总刚度矩阵,求得各段铁塔杆件受力。采用迭代方法求得全塔结构受力,使计算过程简化,实例计算结果与计算机计算结果吻合很好,可为输电铁塔结构设计提供参考。     

New analytical solutions to water wave radiation by vertical truncated cylinders through multi-term Galerkin method

New analytical solutions to water wave radiation by vertical truncated circular cylinders are developed based on linear potential flow theory. Two typical cylinder configurations of a surface-piercing cylinder and a submerged floating cylinder are considered. The multi-term Galerkin method is employed in the solution procedure, in which the fluid velocity on the interface between different regions is expanded into a set of basis function involving the Gegenbauer polynomials, and the cube-root singularity of fluid velocity at the side edges of the truncated cylinders is correctly modeled. The present solutions have the merits of very rapid convergence. The results with six-figure accuracy for added mass and radiation damping can be obtained using a few truncated numbers in the basis function for three motions (surge, heave and roll). The calculated results of the present solutions agree well with that by a higher-order boundary element method solution. Calculation examples are presented to investigate the influence of the motion frequency on the added mass and the radiation damping of the truncated cylinders with different geometric parameters. The present solutions can be used as a reliable benchmark for numerical solutions to water wave radiation by complicated structures.

     

Flutter of a rectangular plate

We address theoretically the linear stability of a variable aspect ratio, rectangular plate in a uniform and incompressible axial flow. The flutter modes are assumed to be two-dimensional but the potential flow is calculated in three dimensions. For different values of aspect ratio, two boundary conditions are studied: a clamped-free plate and a pinned-free plate. We assume that the fluid viscosity and the plate viscoelastic damping are negligible. In this limit, the flutter instability arises from a competition between the destabilising fluid pressure and the stabilising flexural rigidity of the plate. Using a Galerkin method and Fourier transforms, we are able to predict the flutter modes, their frequencies and growth rates. The critical flow velocity is calculated as a function of the mass ratio and the aspect ratio of the plate. A new result is demonstrated: a plate of finite span is more stable than a plate of infinite span.     

On shear lag effects in orthotropic composite beams

Based upon the linearised theories of the bending and stretching of thin plates, an analysis is presented for the interaction between non-prismatic beams and an orthotropic concrete plate. It is shown that an exponential representation for the steel beam profiles provides a suitable basis for studying interaction in continuous non-prismatic beams, and for deducing suitable effective widths of slab for design purposes. The influence of “elastic” shear connection modulus is studied, as well as the effect of the varying flexural rigidity of the steel beams. The dependence of interaction on shear connection modulus in continuous beams is demonstrated through deflexion and slip characteristics, and so also is the dependence of interaction on the severity of the variation of flexural rigidity. The solution can be specialised to the limiting case of prismatic steel beams and a concrete slab and also to the solutions of rectangular plates with certain edge conditions.     

Virtual testing for modal and damping ratio identification of submerged structures using the PolyMAX algorithm with two-way fluid–structure Interactions

Based on the powerful Computational Structural Dynamics method coupled to a Computational Fluid Dynamics approach, the PolyMAX algorithm is used along with the simulation of two-way fluid–structure interactions, as a new virtual testing method for estimating the structural modal parameters and damping ratios of a vibrating structure in either air or some other fluid. The viscosity and motion of fluid are accounted for, as are the shape of the flow passage and a variety of boundary conditions. The method is shown to be able to simulate the vibration of a structure within a real operating environment in which the structure experiences a specified excitation load while the vibration responses of the structure are obtained through a two-way FSI model. Based on the PolyMAX method for estimating the modal parameters, these vibration responses are processed and analyzed. Finally, the dynamic parameters (i.e., the natural frequencies and the damping ratios) of the vibrating structure are identified. For validation, the natural frequencies and damping ratios of two simple submerged cantilever plates were simulated both in air and water and the simulated results were found to agree closely with experimental data.