On the radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas

The radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas of finite depth is investigated. The analytical expressions for the radiated and diffracted potentials are derived as infinite series by use of the method of separation of variables. The unknown coefficients in the series are determined by the eigenfunction expansion matching method. The expressions for wave forces, hydrodynamic coefficients and reflection and transmission coefficients are given and verified by the boundary element method. Using the present analytical solution, the hydrodynamic influences of the angle of incidence, the submergence, the width and the thickness of the structure on the wave forces, hydrodynamic coefficients, and reflection and transmission coefficients are discussed in detail.

PREDICTION OF VORTEX-INDUCED VIBRATION OF FLEXIBLE RISER USING AN IMPROVED WAKE-OSCILLATOR MODEL

Based on improving the wake-oscillator model, an analytical model for vortex-induced vibration (VIV) of flexible riser under non-uniform current is presented, in which the variation of added mass at lock-in and the nonlinear relationship between amplitude of response and reduced velocity are considered. By means of empirical formula combining iteration computation, the improved analytical model can be conveniently programmed into computer code with simpler and faster computation process than CFD so as to be suitable to application of practical engineering. This model is validated by comparing with experimental result and numerical simulation. Our results show that the improved model can predict VIV response and lock-in region more accurately. At last, illustrative examples are given in which the amplitude of response of flexible riser experiencing VIV under action of non-uniform current is calculated and effects of riser tension and flow distribution along span of riser are explored. It is demonstrated that with the variation of tension and flow distribution, lock-in region of mode behaves in different way, and thus the final response is a synthesis of response of locked modes.

INVESTIGATING A NEAR-BED SUBMARINE PIPELINE IN A CURRENT

This paper considers the lift forces acting on a pipeline with a small gap between the pipeline and the plane bottom or scoring bottom. A more reasonable fluid force on the pipeline has been obtained by applying the knowledge of modified potential theory (MPT), which includes the influences of the downstream wake. By finite element method, an iteration procedure is used to solve problems of the nonlinear fluid-structure interaction. Comparing the deflection and the stress distributions with the difference sea bottoms, the failure patterns of a spanning pipeline have been discussed. The results are essential for engineers to assess pipeline stability.

Control Of Vortex Shedding From A Square Cylinder

Small circular, square, and thin-strip cross-sectional elements are used to suppress vortex shedding from a square cylinder at Reynolds numbers in the range of 1.12 x 10(4)-1.02 x 10(5). The axes of the element and cylinder are parallel. The element's size, position, and angle of attack are varied. Measurements of the fluctuating surface pressures and wake velocities, together with smoke flow visualization, show that vortex shedding from both sides of the cylinder is suppressed and the mean drag and fluctuating lift on the cylinder is reduced if the element is installed in an effective zone downstream of the cylinder. The effective zone of the circular element is shown to be much smaller than those of the other elements. The effects of Reynolds number and blockage ratio are investigated. A phenomenon of monoside vortex shedding is observed. The role of the element's bluffness is investigated and the suppression mechanism is discussed.

Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators

The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage.

Interaction of linear waves with an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth

The linear water wave scattering and radiation by an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth is investigated by use of the multipole expansion method. The diffracted and radiated potentials are expressed as a linear combination of infinite multipoles placed at the centre of each cylinder with unknown coefficients to be determined by the cylinder boundary conditions. Analytical expressions for wave forces, hydrodynamic coefficients, reflection and transmission coefficients and energies are derived. Comparisons are made between the present analytical results and those obtained by the boundary element method, and some examples are presented to illustrate the hydrodynamic behavior of multiple horizontal circular cylinders in a two-layer fluid. It is found that for two submerged circular cylinders the influence of the fluid density ratio on internal-mode wave forces is more appreciable than surface-mode wave forces, and the periodic oscillations of hydrodynamic results occur with the increase of the distance between two cylinders; for four submerged circular cylinders the influence of adding two cylinders on the wave forces of the former cylinders is small in low and high wave frequencies, but the influence is appreciable in intermediate wave frequencies.

An exact solution for the three-phase piezoelectric cylinder model under antiplane shear and its applications to piezoelectric composites

A three-phase piezoelectric cylinder model is proposed and an exact solution is obtained for the model under a farfield antiplane mechanical load and a far-field inplane electrical load. The three-phase model can serve as a fiber/interphase layer/matrix model, in terms of which a lot of interesting mechanical and electrical coupling phenomena induced by the interphase layer are revealed. It is found that much more serious stress and electrical field concentrations occur in the model with the interphase layer than those without any interphase layer. The three-phase model can also serve as a fiber/matrix/composite model, in terms of which a generalized self-consistent approach is developed for predicting the effective electroelastic moduli of piezoelectric composites. Numerical examples are given and discussed in detail.

Capillary Effect on Vertically Excited Surface Wave in Circular Cylindrical Vessel

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension.

Multiple Axial Cracks in A Coated Hollow Cylinder due to Thermal Shock

The transient thermal stress problem of an inner-surface-coated hollow cylinder with multiple pre-existing surface cracks contained in the coating is considered. The transient temperature, induced thermal stress, and the crack tip stress intensity factor (SIF) are calculated for the cylinder via finite element method (FEM), which is exposed to convective cooling from the inner surface. As an example, the material pair of a chromium coating and an underlying steel substrate 30CrNi2MoVA is particularly evaluated. Numerical results are obtained for the stress intensity factors as a function of normalized quantities such as time, crack length, convection severity, material constants and crack spacing. (c) 2005 Elsevier Ltd. All rights reserved.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

A thermal-elastic analysis on laser-induced reverse bulging and plugging in circular brass foil

A new failure mode is observed in circular brass foils induced by laser beam. The new failure is based on the following experimental facts : (1) the peripheries of the circular brass foils are fixed and the surfaces of the foils are radiated by laser beam ; (2) the laser beam used is considered to be non-Gaussian spatially, actually an approximately uniform distribution limited in a certain size spot ; (3) the pulse on time of laser beam should be 250 μs, i.e. so called long duration pulse laser. The failure process consists of three stages ; i.e. thermal bulging, localized shear deformation and perforation by plugging. The word reverse in reverse bulging and plugging mode means that bulging and plugging occur in the direction of incident laser beam. To study the newly-discovered type of failure quantitatively, analytical solutions for the axisymmetric temperature field and deflection curve are derived. The calculated results show that the newly discovered failure mode is attributed to the spatial structure effect of laser beam indeed.

A generalized self-consistent method accounting for fiber section shape

A three-phase confocal elliptical cylinder model is proposed for fiber-reinforced composites, in terms of which a generalized self-consistent method is developed for fiber-reinforced composites accounting for variations in fiber section shapes and randomness in fiber section orientation. The reasonableness of the fiber distribution function in the present model is shown. The dilute, self-consistent, differential and Mori-Tanaka methods are also extended to consider randomness in fiber section orientation in a statistical sense. A full comparison is made between various micromechanics methods and with the Hashin and Shtrikman's bounds. The present method provides convergent and reasonable results for a full range of variations in fiber section shapes (from circular fibers to ribbons), for a complete spectrum of the fiber volume fraction (from 0 to 1, and the latter limit shows the correct asymptotic behavior in the fully packed case) and for extreme types of the inclusion phases (from voids to rigid inclusions). A very different dependence of the five effective moduli on fiber section shapes is theoretically predicted, and it provides a reasonable explanation on the poor correlation between previous theory and experiment in the case of longitudinal shear modulus.

Generalized Maugis-Dugdale Model of an Elastic Cylinder in Non-Slipping Adhesive Contact with a Stretched Substrate

We have recently developed a generalized JKR model for non-slipping adhesive contact between an elastic cylinder and a stretched substrate where both tangential and normal tractions are transmitted across the contact interface. Here we extend this model to a generalized Maugis-Dugdale model by adopting a Dugdale-type adhesive interaction law to eliminate the stress singularity near the edge of the contact zone. The non-slipping Maugis-Dugdale model is expected to have a broader range of validity in comparison with the non-slipping JKR model. The solution shares a number of common features with experimentally observed behaviors of cell reorientation on a cyclically stretched substrate.

A Lagrangian for von Karman Equations of Large Deflection Problem of Thin Circular Plate

By the semi-inverse method proposed by He, a Lagrangian is established for the large deflection problem of thin circular plate. Ritz method is used to obtain an approximate analytical solution of the problem. First order approximate solution is obtained, which is similar to those in open literature. By Mathematica a more accurate solution can be deduced.