A time-varying parameter model of a body oscillating in pitch

Among the assumptions upon which linear time-invariant models of floating bodies are based is that the body motions are so small that any change in the body’s angular position can be disregarded. However, it is often a major design requirement of a wave energy conversion device that the response amplitude is large, thereby invalidating one of the assumptions of the linear model. In particular, the immersed geometry of a body undergoes considerable variation when it is moved in pitch. With regard to this we investigate the difference in performance between a quasi-linear model in which the change of immersed surface is modelled by time-varying parameters and a basic linear model in which the immersed surface is time-invariant. The time-varying parameter model is realized by interpolation between the appropriate parameter values of a set of linear time-invariant (LTI) models derived for the different immersed surfaces that occur at discrete body displacements. It is shown that the responses predicted using the time-varying parameter model are closer to those measured experimentally than those of a standard frequency-domain model. Particular improvement occurs when the responses are large, such as at or near the resonance frequency. A problem which may limit the general use of the model is also discussed.     

Wave energy conversion under constrained wave-by-wave impedance matching with amplitude and phase-match limits

This paper investigates an approach to limit the fullness of ‘tuning’ provided by wave-by-wave impedance matching control of wave energy devices in irregular waves. A single analytical formulation based on the Lagrange multiplier approach of Evans [1] is used to limit the velocity amplitude while also limiting the closeness of the phase match between velocity and exciting force. The paper studies the effect of the present technique in concurrently limiting the device velocity and the required control/actuation force. Time domain application requires wave-profile prediction, which here is based on a deterministic propagation model. Also examined in the time domain is the effect of possible violation of the displacement constraint, which for many designs implies impacts at hard stops within the power take-off mechanism. Time domain simulations are carried out for a 2-body axisymmetric converter (with physical end-stops) in sea states reported for a site off the US east coast. It is found that the approach leads to effective power conversion in the less energetic sea states, while as desired, considerable muting of the optimal response is found in the larger sea states. Under the assumptions of this work, the end-stop collisions are found to have a minor effect on the power conversion. The present approach could be used to guide the design of power take-off systems so that their displacement stroke, maximum force, and resistive and reactive power limits are well-matched to the achievable performance of a given controlled primary energy converter.     

Solution of the nonlinear roll model by a generalized asymptotic method

Mathematical modeling of the nonlinear roll motion of ships is one subject widely dealt with in nonlinear ship dynamics. This paper investigates setting up a form of nonlinear roll motion model and developing its periodic solution by the generalized Krylov–Bogoliubov asymptotic method in the time domain. In this model, nonlinearities are introduced through damping and restoring terms. The restoring term is approximated as a third-order odd polynomial whereas the quadratic term is favored to represent the nonlinear damping. The ship is assumed to be under the influence of a sinusoidal exciting force. Although the method is expressible to contain any order of the perturbing term, a single degree is chosen to avoid cumbersome mathematical complexity. In order to improve the solution a first-order correction term is also included. Moreover, a numerical example is carried out for a small vessel in order to validate the solution scheme.     

常Q滞弹性介质地震波动数值模拟——时域本构优化逼近

在地震波动模拟中计入常Q滞弹性阻尼,可有效降低模拟波形的误差.就时域有限差分和有限元模拟而言,常基于广义标准线性体建立阻尼介质的时域本构逼近.广义标准线性体由若干标准线性体并联得到,增加标准线性体个数能有效提高模拟精度,但计算量及计算存储将成倍增长.目前尚未有普适的标准线性体个数优化取值方案.本文基于广义标准线性体参数的非线性优化拟合方法,详细分析了时域本构逼近误差的影响因素,清楚揭示了逼近误差仅取决于频带宽度,与频带上下限取值无关这一特性,阐明了构建具有普适性标准线性体个数优化取值方案的可行性.论证了波形模拟精度主要取决于波传播距离与模拟波长的比值以及标准线性体的个数取值.综合考虑上述两个控制因素,结合在波动正反演问题中广为采纳的波形时频误差衡量准则,对不同Q值介质给出了标准线性体个数优化取值表.进一步,本文提出采用不同个数标准线性体以近似不同Q值的阻尼介质时域本构,解决了以往波动数值模拟中统一采用相同个数标准线性体而导致的计算量及计算存储浪费或模拟精度低下等问题,并基于数值实验验证了这一方法的精度.本文工作对推进滞弹性介质波动数值模拟及其在全波形反演问题中的应用具有理论价值和实践意义.     

基于广义模型约束的时间域航空电磁反演研究

由于航空电磁具有海量数据,因此快速有效的成像和反演手段至关重要.本文针对层状介质模型推导与实现了广义模型约束条件下时间域航空电磁一维反演.从正则化反演的目标函数出发,通过改变模型约束项构造Lp范数反演和聚焦反演,进而通过改变模型求解域构造出基于小波变换的稀疏约束反演.针对不同反演方法目标函数的构建方式,本文进一步从数学原理上分析不同反演方法的预期效果,并通过理论模型和实测数据进行验证.结果表明L0.8范数反演、聚焦反演和基于小波变换的稀疏约束反演可以得到更符合地下层状介质陡变界面的反演结果.     

SH波水平入射穿越垂直断层隧道动力响应分析

结合黏弹性人工边界的时域波动输入方法和显式有限元法,设计了含垂直断层三维场地的SH波输入方法。基于建立的输入方法,研究了垂直断层对隧道地震响应的影响,并通过自由场算例验证了该方法具有较好精度。数值模拟结果表明:对于断层迎波侧的隧道结构,断层会对其地震动响应产生显著的放大作用,对于断层逆波侧的隧道结构,断层会对其产生隔离地震动的作用;相对周围围岩,断层介质的剪切波速越小,其产生的放大效应和隔震效果也会越显著;断层宽度越小,其对隧道地震动响应的影响范围也就越小,但是断层宽度的变化对于断层两侧隧道的地震动响应的影响并不明显。     

航空瞬变电磁法对地下典型目标体的探测能力研究

航空电磁法的探测能力受飞行高度、发射波形、发射磁矩和发射基频等因素的影响,致使不同分量间的勘探能力存在差异.航空电磁如对所有磁场和磁感应分量、on-和off-time数据进行观测和解释,不仅数据量大、耗时长,而且出现大量冗余数据.目前国内针对此问题尚无系统解决方法.本文针对吊舱式直升机航空电磁系统,采用积分方程法求解频率域响应,经汉克尔变换转换到时间域,计算了地下三维目标体的B和dB/dt时间域响应.利用异常体响应与背景场响应作比值,并通过设定响应阀值定义最大勘探深度,进而分析不同发射波形、不同分量以及on-和off-time期间的航空电磁系统的探测能力.基于本文分析手段,可根据实际勘探目标,确定一套探测能力较强的航空电磁最佳参数组合,为野外测量和数据处理提供技术指导,高效完成勘探任务.     

横观各向同性饱和两相介质动力反应计算分析

针对横观各向同性饱和两相介质的弹性波动方程组,应用基于显式逐步积分计算格式的时域显式有限元方法对其在输入地震波作用下的动力反应进行计算和分析,并将计算结果与完全各向同性饱和两相介质的计算结果进行对比研究。结果显示横观各向同性饱和两相介质与完全各向同性饱和两相介质的动力反应具有较为显著的差异。同时表明时域显式有限元方法是进行横观各向同性饱和两相介质动力反应计算分析的一种有效方法。     

Numerical analysis and validation of weakly nonlinear ship motions and structural loads on a modern containership

This paper aims to validate a numerical seakeeping code based on a 3D Rankine panel method by comparing its results with experimental data. Particularly, the motion response and hull-girder loads on a real modern ship, a 6500 TEU containership, are considered in this validation study. The method of solution is a 3D Rankine panel method which adopts B-spline basis function in the time domain. The numerical code is based on the weakly nonlinear scheme which considers nonlinear Froude-Krylov and restoring forces. The main focus of this study is given to investigate the nonlinear characteristics of wave-induced loads, and to validate this present scheme for industrial use in the range of low Froude number. The comparisons show that the nonlinear motions and hull-girder loads, computed by the present numerical code, have good overall agreements with experimental results. It is found that, for the better accuracy of computational results, particularly at extreme waves in oblique seas, the careful treatment of soft-spring (or compatible) system is recommended to the control of non-restoring motions such as surge, sway, and yaw.     

A time-domain viscous damping model based on frequency-dependent damping ratios

This paper introduces the mathematics and procedures used in developing a time-dependent damping model for integration analyses of structural response. To establish the time-dependent viscous damping model, frequency-dependent damping ratios of the structure under a series of steady-state unit impulses corresponding to actual loads are first calculated. For simplicity, the ratios can be incorporated with the static stiffness of the structure to model approximately the impulse induced damping spectrum. According to the nature of the problem, these ratios can be calculated from the theoretical impedance functions and experimental observations. With the computed damping spectrum, the damping coefficient in the time domain can be obtained with the Fourier transform technique. Adopting the impulse–response method, the damping can be modeled rationally through integration with changing loads. Numerical examples are presented to show the feasibility of this model while the transform criterion is satisfied.