粘弹性拉张型地震破裂过程的解析解

本文应用包括地壳破裂发震过程中具有激发及衰减的非线性Rayleigh阻尼,用Voigt粘弹性模型表示地壳,它能更全面地反映地壳介质分子之间的内摩擦造成的粘滞性阻尼,在数学方法上,用解非线性问题解析法的摄动理论结合动坐标的富氏级数,把问题的非线性控制方程组化为各阶线性化的控制方程组后,再简化为标准的Mathieu方程构成的耦连方程组,再用WKBJ方法,给出其在稳定区域的近似解,从而得出了问题的解析解。     

Observed advantage for negative binomial over Poisson distribution in partial duration series

The goodness of fit of the negative binomial and the Poisson distributions to partial duration series of runoff events is tested. The data have been recorded by eight hydrometric stations located on ephemeral rivers in Isreal. For each station, a number of threshold discharges are considered, by that series of nested subsamples are formed. Owing to size limitations, a Chi-square test is conducted on samples associated with low to moderate threshold discharges. Positive results, at a 5% significance level, are obtained in 30 out of the 53 tests of the Poisson distribution, and in 22 out of the 28 tests of the negative binomial distribution. The fit of the Poisson distribution to samples of conventionally recommended sizes (of 2 to 3 events per year) is found positive for five rivers and negative for the three other rivers The fit of the negative binomial distribution to these samples is found positive for six rivers, inconclusive for one river and short of data for the eighth river. Mixed results are obtained as the threshold level is raised. Therefore, no direct extrapolation is possible to samples associated with high thresholds.An indirect extrapolation is drawn through a comparison of the actual properties of the samples with those expected under a perfect fit of the distribution functions. Ranges of such properties are defined with respect to the properties of the tested samples and to the test results. The actual properties of nine of the eleven samples associated with high thresholds (i.e. mean number of events <-0.1year ^–1) are found within these ranges. This provides a hint for a probable good fit of either distribution, and particularly the negative binomial, to the occurrence frequency of high events.     

Hydrodynamic effects in a reservoir with semicircular cross-section and absorptive bottom

A three-dimensional dam-reservoir system under seismic load is analysed. The dam is assumed to be rigid. The reservoir is an infinite channel with semi-circular cross-section. The exact analytical solution, based on the assumption of potential fluid motion is presented, as well as numerical results for selected parameters.The most significant parameters are: the direction and frequency content of the seismic input; the radiation damping at the reservoir bottom; and the compressibility of the fluid. The response of the system depends strongly on the direction of the input ground motion. This is shown by the transfer functions as well as by the pressure time histories due to two earthquakes with different frequency content. The energy absorption at the reservoir bottom is important. A simple plane-wave model shows, that even for a rock foundation, the amount of transmitted energy can reach up to 80%. For comparison the case without bottom absorption is also shown. Compressbility has to be included to capture the resonance effects. The exact analytical solution is also used to verify numerical results obtained by a new method that combines a finite element model with a rigorous radiation boundary for the infinite channel in the time domain.     

CFD approach to roll damping of ship with bilge keel with experimental validation

The most common method of reducing roll motion of ship-shaped floating systems is the use of bilge keel which act as damping elements. The estimation of the damping introduced by bilge keel is still largely based on empirical methods. The present work adopts the CFD approach to the estimation of roll damping, both without and with bilge keel and validates the results with experiments conducted in a wave flume. Specifically, free oscillation tests are conducted at model scale to obtain roll damping, both by experiments and CFD simulation and reasonably good comparisons are obtained. The experiments also include PIV study of the flow field and attempt has been made to correlate the measured flow field with that obtained by CFD. The CFD methodology has the potential to determine rationally the size and orientation of bilge keels in design with reasonably accurate estimate of the additional roll damping that it provides to ship's roll motion.     

Study on Global Performances and Mooring-Induced Damping of A Semi-Submersible

The harsh environmental conditions bring strong nonlinearities to the hydrodynamic performances of the offshore floating platforms, which challenge the reliable prediction of the platform coupled with the mooring system. The present study investigates a typical semi-submersible under both the operational and the survival conditions through numerical and experimental methods. The motion responses, the mooring line tensions, and the wave loads on the longitudinal mid-section are investigated by both the fully non-linearly coupled numerical simulation and the physical experiment. Particularly, in the physical model test, the wave loads distributed on the semi-submersible’s mid-section were measured by dividing the model into two parts, namely the port and the starboard parts, which were rigidly connected by three six-component force transducers. It is concluded that both the numerical and physical model can have good prediction of the semi-submersible’s global responses. In addition, an improved numerical approach is proposed for the estimation of the mooring-induced damping, and is validated by both the experimental and the published results. The characteristics of the mooring-induced damping are further summarized in various sea states, including the operational and the survival environments. In order to obtain the better prediction of the system response in deep water, the mooring-induced damping of the truncated mooring lines applied in the physical experiment are compensated by comparing with those in full length. Furthermore, the upstream taut and the downstream slack mooring lines are classified and investigated to obtain the different mooring line damping performances in the comparative study.     

Sensitivity Analysis of Air Gap Motion with Respect to Wind Load and Mooring System for Semi-Submersible Platform Design

A design of semi-submersible platform is mainly based on the extreme response analysis due to the forces experienced by the components during lifetime. The external loads can induce the extreme air gap response and potential deck impact to the semi-submersible platform. It is important to predict air gap response of platforms accurately in order to check the strength of local structures which withstand the wave slamming due to negative air gap. The wind load cannot be simulated easily by model test in towing tank whereas it can be simulated accurately in wind tunnel test. Furthermore, full scale simulation of the mooring system in model test is still a tuff work especially the stiffness of the mooring system. Owing to the above mentioned problem, the model test results are not accurate enough for air gap evaluation. The aim of this paper is to present sensitivity analysis results of air gap motion with respect to the mooring system and wind load for the design of semi-submersible platform. Though the model test results are not suitable for the direct evaluation of air gap, they can be used as a good basis for tuning the radiation damping and viscous drag in numerical simulation. In the presented design example, a numerical model is tuned and validated by ANSYS AQWA based on the model test results with a simple 4 line symmetrical horizontal soft mooring system. According to the tuned numerical model, sensitivity analysis studies of air gap motion with respect to the mooring system and wind load are performed in time domain. Three mooring systems and five simulation cases about the presented platform are simulated based on the results of wind tunnel tests and sea-keeping tests. The sensitivity analysis results are valuable for the floating platform design.     

Added mass and damping of a sphere section in heave

The Norwegian wave-power buoy¹ consists of a half-immersed floating sphere which is open to the sea at the bottom end. It is a two degree-of-freedom device involving the independent motion of the outer rigid sphere and the pressure across the internal free surface. A simpler model of the device is to represent the oscillatory flow through the bottom opening as another rigid body motion being that of the curved surface which would complete the sphere.The wave-induced forces on this surface and also the outer spherical surface due to independent oscillations of either are determined semi-analytically using a simple extension of the method of Havelock,² recently simplified and generalised by Hulme,³ for the complete half-immersed sphere. In particular the 2 × 2 added mass and damping matrices are determined as a function of frequency and relative size of bottom opening to sphere radius. These quantities are essential in any theoretical analysis of a multi-degree of freedom wave-energy device.     

两层流体中矩形箱浮体的附加质量和阻尼系数

研究了两层流体中矩形箱浮体的辐射问题。基于特征函数匹配理论,针对矩形箱浮体的三种振荡运动模式(横荡、垂荡和横摇),建立两层流体中矩形箱浮体辐射势的求解方法,导出矩形箱浮体附加质量和阻尼系数的计算公式。对所建立的求解模型进行了数值计算分析,结果表明在矩形箱浮体的某个振荡频率范围内,流体的分层效应对其附加质量和阻尼系数有显著影响的。     

Hull/mooring/riser coupled dynamic analysis and sensitivity study of a tanker-based FPSO

A computer program is developed for hull/mooring/riser coupled dynamic analysis of a tanker-based turret-moored FPSO (Floating Production Storage and Offloading) in waves, winds, and currents. In this computer program, the floating body is modeled as a rigid body with six degrees of freedom. The first- and second-order wave forces, added mass, and radiation damping at various yaw angles are calculated from the second-order diffraction/radiation panel program WAMIT. The wind and current forces for various yaw angles of FPSO are modeled following the empirical method suggested by OCIMF (Oil Company International Marine Forum).

The mooring/riser dynamics are modeled using a rod theory and finite element method (FEM), with the governing equations described in a generalized coordinate system. The dynamics of hull, mooring lines, and risers are solved simultaneously at each time step in a combined matrix for the specified connection condition. For illustration, semi-taut chain-steel wire-chain mooring lines and steel catenary risers are employed and their effects on global FPSO hull motions are investigated. To better understand the physics related to the motion characteristics of a turret-moored FPSO, the role of various hydrodynamic contributions is analyzed and assessed including the effects of hull and mooring/riser viscous damping, second-order difference-frequency wave-force quadratic transfer functions, and yaw-angle dependent wave forces and hydrodynamic coefficients. To see the effects of hull and mooring/riser coupling and mooring/riser damping more clearly, the case with no drag forces on those slender members is also investigated. The numerical results are compared with MARIN's wave basin experiments.     

Design analysis of a truss pontoon semi-submersible concept in deep water

Truss pontoon semi-submersible (TPS) is a new offshore structure concept in industry, where a truss spar is used to create the added mass by the heave plates. In the present paper, the effect of the heave plates on the vertical motion of the floating structure is demonstrated. A TPS is analyzed by utilizing the linear diffraction theory as well as the linear part of the Morison equation. The close agreement of the analysis results with the experimental results suggests that the simplified Morison equation can be used for the present analysis without sacrificing the quality of the results. However, good engineering judgment is required for estimating the values of the hydrodynamic coefficients as well as the amount of damping introduced in the structure. It is also found that the heave plates indeed introduce large added mass and considerable damping in the system motion in the vertical direction such that the resonant oscillation becomes less of a problem. This suggests that the TSP concept may have merits as a heave-controlled floating production structure in the deepwater development.