弹性双柱在规则波作用下振动响应

通过速度势的特征展开方法,建立垂直圆柱对波浪绕射的解析解,得到作用在柱体上的波浪力计算表达式,通过谐波增量平衡法(IHB法),计算研究弹性双柱相对位置对双柱振动响应的影响。设计了弹性双柱体模型试验,数值结果与模型试验结果较吻合,为海洋工程结构振动设计提供一种解决方法。     

A comparison of complete and approximate solutions for second-order diffraction loads on arrays of vertical ci cular cylinders

This paper presents a comparison between two theoretical methods for computing the second-order diffraction loads on arrays of bottom-mounted, surface-piercing vertical circular cylinders in regular waves. One method presents a complete solution for the second-order hydrodynamic loads on the cylinder array via a numerical integration over the mean fluid free-surface. The other method is based on a large spacing approximation between the array members and involves the solution of a set of equivalent isolated body problems to obtain estimates for the second-order hydrodynamic loads. Numerical results for a pair of cylinders indicate very good agreement between the two methods at center-to-center spacing of both three and five radii, indicating that the approximate method may be sufficient to compute hydrodynamic interference effects to the second-order in many practical engineering situations.     

Interactions between fully nonlinear water waves and cylinder arrays in a wave tank

Fully nonlinear interactions between water waves and vertical cylinder arrays in a numerical tank are studied based on a finite element method (FEM). The three-dimensional (3D) mesh is constructed through an extension of a 2D Delaunay surface grid along the vertical line. The velocity potential is obtained by solving a linear matrix system of FEM, and a difference scheme is then used to calculate the velocity on the free surface to track its movement. Waves and hydrodynamic forces are obtained for both bottom mounted and truncated cylinders. The simulations have provided many results to show the nature of mutual interference between cylinders in arrays and its effects on waves and forces at the nearly trapped mode frequency. The effect of the tank wall on waves and forces has been investigated, and the nonlinear features of waves and forces have also been discussed.     

Interaction of cnoidal waves with an array of vertical concentric porous cylinders

An array of large concentric porous cylinder arrays is mounted in shallow water exposed to cnoidal waves. The interactions between waves and cylinders are studied theoretically using an eigenfunction expansion approach. Semi-analytical solutions of hydrodynamic loads and wave run-up on each cylinder are obtained using first approximation to cnoidal waves. The square array configuration of four-legged identical concentric porous cylinder is investigated in present study. Numerical results reveal the variation of dimensionless wave force and wave run-up on individual cylinder with angle of incidence, porosity parameter, spacing between outer and inner cylinders, spacing between concentric porous cylinders and wave parameter. Different mechanism of wave force is found under different range of scattering parameter.     

Interaction of regular waves with a group of dual porous circular cylinders

Diffraction of linear waves around a group of dual porous cylinders consisting of a thin and porous outer cylinder with an impermeable inner cylinder is investigated analytically based on the eigenfunction expansion method proposed by Spring and Monkmeyer [Spring BH, Monkmeyer PL. Interaction of plane waves with vertical cylinders. In: Proceedings 14th international coastal engineering conference. 1974. p. 1828–47] and further modified by Linton and Evans [Linton CM, Evans DV. The interaction of waves with arrays of vertical circular cylinders. Journal of Fluid Mechanics 1990;215:549–69]. The present formulation is an extension of the work of Wang and Ren [Wang KH, Ren X. Wave interaction with a concentric porous cylinder system. Ocean Engineering 1994;21(4):343–60], wherein; the interaction of linear waves with a single concentric porous cylinder system was studied. This paper aims at investigating the influence of multiple interactions between the cylinders in the group on the hydrodynamic wave forces, wave run-up and free-surface elevation in their vicinity. Further, the study focuses on the variation of the forces and run-up on the individual cylinders within the group compared to that on isolated cylinders.     

Wave interaction with cylindrical porous piles

The interaction of waves with arrays of porous circular cylinders is studied theoretically and, under the assumption of potential flow and linear wave theory, an analytical solution is derived. The solution is valid for either submerged or emerged structures. The extension to the cases of unidirectional and multidirectional waves is obtained by means of a transfer function. For specific conditions the model gives the same solution as those previously presented by other authors. Numerical results are presented which exemplify diverse wave and mechanical parameters on the wave transformation due to the presence of a system of circular cylinders.     

Analytical solutions of the diffraction problem of a group of truncated vertical cylinders

An exact analytical method is described to solve the diffraction problem of a group of truncated vertical cylinders. In order to account for the interaction between the cylinders, Kagemoto and Yue's exact algebraic method is utilised. The isolated cylinder diffraction potential due to incident waves is obtained using Garret's solution and evanescent mode solutions are derived in a similar manner.Numerical results are presented for arrays of two and four cylinders. Comparisons between the results obtained from the method presented here and those obtained from numerical methods show excellent agreement.     

In-line response of vertical cylinders in regular and random waves

The in-line response of a vertical flexibly mounted cylinder in regular and random waves is reported.Both theoretical analyses and experimental measurements have been performed.The theoretical predictions are based on the Morison equation which is solved by the incremental harmonic balance method.Experiments are then performed in a wave flume to determine the accuracy of the Morison equation in predicting the in-line response of the cylinder in regular and random waves.The interaction between waves and vibrating cylinders are investigated.     

Interference effects between flexible cylinders in waves

An approximate method is presented to estimate the hydrodynamic loading and associated structural response of each of a pair of free-standing, bottom-nounted, flexible circular cylinders subjected to a regular train of linear surface waves. The cylinders are aligned parallel to the incident wave direction and the response of each is assumed to be one-dimensional and governed by a beam equation. The solution technique for the fluid velocity potential involves replacing scattered waves by equivalent plane waves together with non-planar, first-correction terms, and can be shown to be a large-spacing approximation. Numerical results are presented which show the influence of the various wave and structural parameters on the hydrodynamic loading and dynamic response of the individual cylinders.     

Interactions of cnoidal waves with cylinder arrays

The three-dimensional scattering of cnoidal waves by cylinder arrays are studied numerically by using the generalized Boussinesq equations. The boundary-fitted coordinate transformation and a dual-grid technique are used to simplify the finite-difference computation. Also, a set of open boundary conditions and an incident cnoidal wave are incorporated for time-domain simulation. The free-surface elevation and hydrodynamic forces on each cylinder are calculated to illustrate the evolution of nonlinear waves and their interactions with large cylinder arrays. Comparisons are made between the present nonlinear wave loads and those obtained from linear diffraction theory. The sheltering role played by the neighboring cylinders and the feature of wave interference are discussed.     

Clear water scour around a finite array of cylinders

This experimental study presents clear-water scour and deposition patterns around hexagonal arrays of circular cylinders in steady flow conditions. Understanding the scour processes around such configurations could facilitate the design of several hydraulic and marine engineering structures, such as bridge piers and piles. The flow alteration caused by the examined porous obstacles depends on the solid volume fraction of the obstacles and on the angle of attack of the incoming flow, due to the limited number of cylinders constituting the array. Flume experiments with erodible bed were carried out for four array densities (solid volume fractions: 0.14, 0.20, 0.32 and 0.56) under three different orientations (regular, angled and staggered configurations). The scour/deposition characteristics were obtained by means of laser scanner and the results were compared to solid cylinders of equal circumambient diameter. Different angles of attack of the incoming flow lead to different blockage ratios, which have direct impact on the scour characteristics and deposition patterns. The arrays with the higher solid volume fraction generated scour/deposition patterns similar to solid cylinder, while in the arrays with the lower solid volume fractions, local scour around the individual small cylinders became evident. Finally, considering that the load bearing capacity of a pier basically depends on the area of its cross-section, a comparison of the maximum induced scour depth and volume by the cylinder arrays and the solid cylinder with equal solid cross-sectional area is presented, in order to introduce an alternative pier configuration that induces less scour. The results showed that the array of cylinders could generate 27% less scour volume and 22% less scour depth compared to its single solid cylinder counterpart.     

关于小直径垂直桩柱结构的波浪力研究

本文归纳了应用Morison方程中涉及的研究成果。分别从阻力系数和惯性力系数。规则波与不规则波，二阶力和线性化，桩群受力等方面进行了论述。对目前该领域的研究给出了系统的介绍。     

Solitary wave interactions with an array of two vertical cylinders

This paper addresses a numerical investigation of nonlinear waves interactions with an array of two surface-piercing vertical cylinders and the corresponding nonlinear hydrodynamic loads on each individual cylinder. The primary interest of this study is concentrated on the problem of three-dimensional scattering of solitary waves by cylinder arrays and the nonlinear interactions between scattered waves. The theoretical model adopted for simulation is the generalized Boussinesq two-equation model. The boundary-fitted coordinate transformation and multiple-grid technique are utilized here to simplify the computation domain and to facilitate the applications of the boundary conditions on the cylinder surfaces. The velocity potential, free-surface elevation and subsequent evolution of the scattered wave field are numerically evaluated. The hydrodynamic forces on each cylinder during wave impact are also determined. A study of the sheltering effect by the neighboring structures on wave loads is conducted. It is found that the presence of the neighboring cylinder has shown significant influence on the wave loads and the scattering of the primary incident waves. For two transversely arranged cylinders, the transverse force coefficient increases as the separation distance decreases.     

Water wave interaction with an array of bottom-mounted surface-piercing porous cylinders

The interaction of water waves with arrays of bottom-mounted, surface-piercing circular cylinders is investigated theoretically. The sidewall of each cylinder is porous and thin. Under the assumptions of potential flow and linear wave theory, a semi-analytical solution is obtained by an eigenfunction expansion approach first proposed for impermeable cylinders by Spring and Monkmeyer (1974), and later simplified by Linton and Evans (1990). Analytical expressions are developed for the wave motion in the exterior and all interior fluid regions. Numerical results are presented which illustrate the effects of various wave and structural parameters on the hydrodynamic loads and the diffracted wave field. It is found that the porosity of the structures may result in a significant reduction in both the hydrodynamic loads experienced by the cylinders and the associated wave runup.     

波浪作用下沙质海床上大直径圆筒结构动态响应的实验研究

通过物理模型实验,对沙质海床上沉入式大直径圆筒结构对波浪的动态响应进行了较系统的实验研究。实验中考虑了大直径圆筒、波浪和海床三者之间的耦合作用,并实时记录了大直径圆筒结构的动态响应。实验数据分析表明,大直径圆筒在波浪作用下的动态响应以大圆筒随波浪的前后摆动为主,其摆动轴心并不是固定不变的。最后通过回归分析给出了估算大直径圆筒摆动转角幅值的经验公式。     

Wave interaction with one or two rows of closely spaced rectangular cylinders

Experimental results are reported on the wave reflection from and transmission through one row or two rows of closely spaced rectangular cylinders. An empirical expression is proposed for the friction factor which models the head loss due to closely spaced rectangular cylinders. Algebraic expressions are presented to calculate the reflection and transmission coefficients of regular waves for a single slotted wall or double slotted walls. The model is validated by the published and present experimental results. The proposed method can be used for the preliminary design of slotted-wall breakwaters.     

Burial and scour of short cylinders under combined random waves and currents including effects of second order wave asymmetry

This paper provides an approach by which the burial and scour of short cylinders under combined second order random waves and currents can be derived. Here the formulas for burial and scour for regular waves plus currents presented by Catano-Lopera and Garcia [Catano-Lopera, Y.A. and Garcia, M.H. (2006). Burial of short cylinders induced by scour under combined waves and currents. ASCE J. Waterway, Port, Coastal and Ocean Eng. 132(6), 439–449., Catano-Lopera, Y.A. and Garcia, M.H. (2007). Geometry of scour hole around, and the influence of the angle of attack on the burial of finite cylinders under combined flows. Ocean Eng. 34(5, 6), 856–869.] are used together with Stokes second order wave theory by assuming the basic harmonic wave motion to be a stationary Gaussian narrow-band random process. An example of calculation is also presented.     

Modelling linear wave transformation induced by dissipative structures—Random waves

The relevant theory is presented and numerical results are compared with the analytical solution for the interaction of non-breaking waves with an array of vertical porous circular cylinders on a horizontal bed. The extension to the cases of unidirectional and multidirectional waves is obtained by means of a transfer function. The influence of the mechanical properties of porous structures and wave irregularity on wave transformation is analysed. Results for unidirectional and multidirectional wave spectra are compared to those obtained for regular waves. The model presented reproduces well the analytical results and provides a tool for analysing several engineering problems.     

Influence of structural flexibility and wave interference on dynamic behavior of idealized offshore platform

An approximate method is presented to estimate the hydrodynamic loading and structural response of an idealized offshore platform subjected to a regular train of linear surface waves. The platform is taken to consist of four bottom-mounted, flexible, circular cylinders supporting a rigid deck and is assumed to be aligned parallel to the incident wave direction. The response of each column is assumed to be one-dimensional and to be governed by linear beam theory. The solution technique for the fluid velocity potential involves replacing scattered waves by equivalent plane waves together with non-planar, first-correction terms, and can be shown to be a large spacing approximation.Numerical results are presented which show the effect of hydrodynamic interference and structural flexibility on the platform response.     

Wave-Current Forces on Small Square Cylinders (Part I)

-Based on the extended Morison Equation and model tests, the in-line forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in detail in this paper. The hydrodynamic coefficient CD and Cu related to KC number and the effect of direction of wave incidence are also given, which can be used in engineering practice.