Nonlinear dynamics of offshore structures under sea wave and earthquake forces

A study of dynamic response of offshore structures in random seas to inputs of earthquake ground motions is presented. Emphasis is placed on the evaluation of nonlinear hydrodynamic damping effects due to sea waves for the earthquake response. The structure is discretized using the finite element method. Sea waves are represented by Bretschneider’s power spectrum and the Morison equation defines the wave forcing function. Tajimi-Kanai’s power spectrum is used for the horizontal ground acceleration due to earthquakes. The governing equations of motion are obtained by the substructure method. Response analysis is carried out using the frequency-domain random-vibration approach. It is found that the hydrodynamic damping forces are higher in random seas than in still water and sea waves generally reduce the seismic response of offshore structures. Studies on the first passage probabilities of response indicate that small sea waves enhance the reliability of offshore structures against earthquakes forces.     

60万桶FPSO船体在十年一遇海况下的大幅运动模拟

简述了船舶在规则波中纵向大幅运动的计算方法,并将该方法推广到不规则波的运动计算中.基于切片理论的扩展方法,考虑由于船体的湿表面变化而产生的非线性因素,采用频域计算方法和时域计算方法相结合,线性处理和非线性修正相补充的方法,对水面船舶在不规则波中的纵向大幅运动进行计算.文中采用的谱分析技术,理论上讲不适用于船舶的大幅运动,但由于大量计算结果表明船舶纵向运动响应非线性不强,这就为我们的计算提供了基本条件,并以FPSO船体为例,运用C++语言编程实现船体在十年一遇海况下的大幅运动模拟,得到船舶运动六自由度的运动响应曲线.     

地震作用下海冰与桥墩的间距对桥墩动力响应的影响研究

位于冰水海域的桥墩,在波浪力作用下,桥墩结构与周围海冰往往出现间隙,地震作用下海冰与结构的动力相互作用呈现复杂多样化。本文在弹性力学中的弹性波传播理论及结构动力学的基础上,考虑不同的海冰与桥墩间距,建立了地震作用下桥墩、冰与水体的流固耦合动力方程。并以一矩形桥墩为研究对象,研究了地震作用下,海冰与桥墩的间距对矩形桥墩结构的动力响应及动水压力的影响。研究表明:地震作用下,海冰与桥墩间距对桥墩顶部的最大位移和最大加速度响应的影响不显著,但是对桥墩侧面动水压力和墩底内力影响较大;当海冰与桥墩存在间距且小于1倍结构尺寸时,墩底的弯矩和剪力达到最大值。     

多向不规则波浪作用下群墩结构所受波浪力的实验研究

实际海域中波浪是多向不规则的,波浪的方向分布宽度对作用在结构物上的波浪力具有显著的影响。为了研究方向分布对大尺度群墩结构所受波浪力的影响规律,该文通过物理模型实验模拟了多向不规则波浪与群墩结构的相互作用。通过对波浪荷载的时间过程线进行统计分析得到了作用在墩柱上的正向力、横向力。实验结果表明波浪的方向分布对群墩结构中墩柱所受横向力具有明显的影响。多向波浪作用时,墩柱所受横向力随着方向分布宽度的增大有显著的增大趋势,且后排墩柱受方向分布宽度的影响较前排墩柱更明显。     

Wave forces on a submerged vertical plate

Summary A vertical plate of finite length and depth is attacked by gravity waves in water of finite depth. The forces and moments acting on the plate are computed by using the theory of linearized waves. The forces depend on three dimensionless parameters combining the draft, length, water depth and wave length and on the angle of attack. The problem is reduced to the solution of two infinite linear systems of equations. Numerical solutions are presented for different particular combinations of the parameter values. In most of the cases the standing wave approximation yields sufficiently accurate results.     

Aberrations of diffracted wave fields. I. Optical imaging

The concept of aberrations of diffracted waves is revisited by using the Rayleigh-Sommerfeld theory of diffraction, and it is pointed out that these aberrations are in a class by themselves; they are only deceptively similar to the aberrations of a rotationally symmetric imaging system. Although an exact Fourier-transform expression can be written for the diffracted wave field, its numerical calculation is cumbersome because of the dependence of the aberrations of the diffracted wave on the observation point. This is true regardless of whether the diffracted wave field is observed on a plane or a hemisphere. It is shown that the Fresnel and Fraunhofer approximations, which neglect these aberrations and thereby simplify the calculations, are valid in imaging applications.     

Forces and moments for electrodynamic levitation systems--Large-scale test results and theory

The dynamic circuit theory for the analysis of the suspension characteristics of electrodynamic magnetic levitation schemes for realistic magnet and guideway configurations is reviewed. Electrodynamic forces and moments have been measured on a large-scale stationary superconducting magnet interacting with an aluminum strip mounted on the rim of a 7.6-m diameter rotating test wheel. Good agreement is found between analytical and experimental results over the speed range to 100 km/h for the electrodynamic forces of test configurations which provide a rigorous test for theory. The speed dependence of moments is reported and used to estimate the force distribution on the superconducting coil. The dynamic circuit theory is then used to determine the suspension characteristics of the levitation system for the proposed Canadian Maglev vehicle.     

柔性构件多次撞击力的计算方法

研究目的是精确计算多次撞击过程中的撞击力。通过研究柔性构件中的瞬态波传播理论,提出了计算多次撞击力的瞬态波效应法,避免了求解具有未知奇异载荷项的非线性方程问题。通过双柔性杆轴向多次撞击的实例分析,研究了初始撞击速度,杆长比对撞击力和撞击发生时间的影响,表明瞬态波效应法可以计算多次撞击力,并可以研究"次撞击"现象。     

Dispersion relations and modes of wave propagation in inclusion-reinforced composite plates

This paper is intended to examine the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness on the dispersion relations and modes of wave propagation in inclusion-reinforced composite plates. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Mori–Tanaka mean-field theory is used to predict the effective elastic moduli of the composite plate explicitly. The effective elastic moduli are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior. The resulting moduli are then used to determine the dispersion relations and the modal patterns of Lamb waves using the dynamic stiffness matrix method. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions are symmetrical or antisymmetric about the midplane of the plate. Classifying the wave type in an anisotropic plate is not as simple as that in an isotropic plate, and has not received proper attention in the literature. The wave types and orders are identified by analyzing the dispersion curves and inspecting the calculated modal patterns, and the results indicate that the Lamb waves in an orthotropic composite plate can also be classified as either symmetric or antisymmetric waves. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns. Propagation speed is generally increased with the aspect ratio, e.g., using longer fibers generally results in a higher propagation speed.     

Statistical analysis of nonlinear, second-order forces and motions of offshore structures short-crested random seas

A general theory for statistical analysis of nonlinear, second-order forces and motions of compliant offshore structures in short-crested random seas is described. It is shown that the theory is a natural extension of existing theory for the special case of long-crested waves. Similarly as for this special case, the core of the method is the solution of an eigenvalue problem, which is well suited for numerical analysis. All the information needed for the statistical analysis is contained in the obtained eigenvalues and eigenvectors. It is demonstrated that in the case of slowly-varying, second-order forces and motions, the PDF can be given explicitly and is determined completely by the eigenvalues. An analysis of the extreme values is also presented. In contrast to existing theories, in the present paper no restriction is imposed on the bandwidth of either wave energy or directional spread.     

Stochastic response of guyed tower under second-order wave force

Guyed towers have low natural frequencies compared with generally encountered wave frequencies. They are therefore highly susceptible to low frequency second-order wave forces resulting from the nonlinear phenomenon in the integrated fluid pressure on the submerged structure. A simplified approach is presented here to obtain the second-order wave forces encountered in random sea state for offshore guyed towers using a simulation procedure. Nonlinear response of a guyed tower to second-order and first-order wave forces, and a combination of the two are obtained in time domain. The time histories of responses and the wave forces are analysed to investigate their stochastic characteristics.     

Aerodynamic properties of a wing performing unsteady rotational motions at low Reynolds number

Summary The aerodynamic forces and flow structures of a wing of relatively small aspect ratio in some unsteady rotational motions at low Reynolds number (Re=100) are studied by numerically solving the Navier-Stokes equations. These motions include a wing in constant-speed rotation after a fast start, wing accelerating and decelerating from one rotational speed to another, and wing rapidly pitching-up in constant speed rotation. When a wing performs a constant-speed rotation at small Reynolds number after started from rest at large angle of attack (=35°), a large lift coefficient can be maintained. The mechanism for the large lift coefficient is that for a rotating wing: the variation of the relative velocity along the wing-span causes a pressure gradient and hence a spanwise flow which can prevent the dynamic stall vortex from shedding. When a wing is rapidly accelerating or decelerating from one rotational speed to another, or rapidly pitching-up during constant speed rotation, even if the aspect ratio of the wing is small and the flow Reynolds number is low, a large aerodynamic force can be obtained. During these rapid unsteady motions, new layers of strong vorticity are formed near the wing surfaces in very short time, resulting in a large time rate of change of the fluid impulse which is responsible for the generation of the large aerodynamic force.     

Wave forces on steeply-sloping sea walls

Summary The forces exerted by non-breaking, normally-incident water waves on a sloping sea wall are investigated within the framework of linearised potential theory. The slope of the sea wall is assumed to be large. The solution is in the form of an eigenfunction expansion, the coefficients of which are found by two methods. The first is a perturbation scheme based on the smallness of the reciprocal of the slope and is carried out to second order in this quantity. The second is a Galerkin technique. Results are presented for the case of a planar, outward-sloping sea wall. In shallow water it is found that the normal wave force decreases as the slope of the wall increases. In deep water, the reverse is true whilst in water of intermediate depth the normal wave force is only weakly dependent upon the slope of the sea wall.     

Self-pumped phase-conjugate interferometer with a photorefractive iron-doped lithium-niobate crystal

A single object wave is amplitude divided by a beam splitter into two waves of equal intensity that are made to interfere at the back surface of an iron-doped lithium-niobate crystal so that the normal to the back surface is the angular bisector of the input waves. The interference results in the formation of a phase grating (Bragg grating) in the volume of the crystal. These waves are diffracted at the Bragg grating on both the front focal plane and the back focal plane of the crystal. The wave diffracted in the back focal plane from the Bragg grating and counterpropagating to the incident wave is observed to be the phase conjugate of the input object wave. The wave diffracted in the front focal plane of the Bragg grating is incorporated into the design of an interferometer to measure a specific in-plane displacement of the object wave. It is theoretically evaluated and experimentally demonstrated that interferometers such as those that incorporate conjugate-wave pairs are highly sensitive.     

Interaction of time-harmonic SH waves with a crack-like inclusion: edge region analysis

Elastodynamic stress concentration near the tips of a crack-like inclusion of finite length generated by the diffraction of high-freqency time-harmonic SH waves is analyzed. It is shown that the stress intensity factors at the tips of inclusion are provided by the fields describing the solution of the static boundary value problem for a semi-infinite strip and edge waves travelling between the two inclusion tips. The solution to the problem is expressed in a closed form that is computationally effective and yields accurate results in the resonance region of dimensionless wave numbers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Diffraction of shear waves by a rigid strip in a medium of monoclinic type

Summary The paper discusses the two dimensional problem of diffraction of shear waves by a rigid strip in an infinite medium of monoclinic type. This problem is reduced to a system of dual integral equations of which the solution provides the diffracted field. The method of steepest descent has been used in the determination of the diffracted fields at a large distance from the strip. Diffraction pattern for displacement and stress field have been computed and the effect of anisotropy is distinctly marked.With 6 Figures     

Interaction of shear waves with a griffith crack situated in an infinitely long elastic strip

This paper deals with the propagation of shear waves in a wave guide which is in the form of an infinite elastic strip with free lateral surfaces. This strip contains a Griffith crack. An integral transform method is used to find the solution of the equation of motion from the linear theory for a homogeneous, isotropic elastic material. This method reduces the problem into an integral equation. It has been observed that only shear waves with frequencies less than a parameter-value, depending on the width of the wave guide, can propagate. The integral equation is solved numerically for a range of values of wave frequency and the width of the strip. These solutions are used to calculate the dynamic stress intensity factor, displacement on the surface of the crack and crack energy. The results are shown graphically.     

Boundary element analysis of wave-current interaction around a large structure

A numerical approach for wave-current interaction around a large structure is investigated, based on potential flow theory, linear waves and small current velocity approximation. The velocity potential in a wave-current coexisting field is separated into a steady current potential and an unsteady wave potential. The boundary element method was then employed to compute the unsteady wave potential with effects of both a uniform current and a large body taken into consideration. It is demonstrated that the steady current potential can be expressed as the sum of a uniform current and a steady disturbance due to the presence of the object. The variation of current velocity in the vicinity of the object is then calculated by using a surface vorticity boundary integral meethod. Boundary element analysis is also used for the numerical solutions of the surface vorticity method. Substituting both unsteady wave potential and current velocity into the first-order dynamic surface boundary condition, the water surface elevation around a large structure in a wave-current coexisting field can then be obtained. Comparisons of numerical predictions with experimental results ar also made; qualitative good agreements are obtained.     

柱形地形上单浮体的辐射和散射问题

在有限水深、同轴但半径大于或等于浮体半径的圆柱体障碍物地形条件下，基于特征函数展开法，推导了垂直放置的圆柱形浮体由于波的辐射和散射作用所表现的动力学和运动学特征表达式，涉及浮体做垂荡、横荡和横摇运动所产生的辐射势，以及在入射波的作用下，由于浮体固定不动而产生的散射势，并推导了激励力、附加质量和阻尼系数表达式。采用与同轴、同半径圆柱体障碍物地形上单浮体水动力学特性相比的方式和激励力计算两种方法验证了推导的表达式，最后分析了障碍物几何尺寸对浮体水动力学特性的特有影响。     

Dynamic strain response of lake and sea ice to moving loads

The results from two experiments to measure the strains due to a vehicle moving over ice are discussed in the context of theoretical work derived from existing solutions in the literature. The experiments took place on two very different types of ice; the lake ice of Femund in Norway, and sea ice near Scott Base in the Antarctic. In both cases, strain was measured directly by means of strainmeters developed specifically for use on ice. The existence of a critical velocity at which the strain is resonant is discussed, and using values derived from the data, a dispersion equation for free waves is solved in the super-critical domain to provide wavelength estimates. At subcritical speeds a moving static load calculation provides the equivalent theory. The experimental results for lake ice and sea ice are similar, although some differences do exist. The magnification factor of the critical strain over static strain is, for example, larger for lake ice (2.25) than for sea ice (1.45). A critical velocity of 15.2 ms^?1 was observed for lake ice, for sea ice the value was 19.6 ms^?1; both are associated with the minimum phase velocity of free wave propagation.