Analysis of random nonlinear water waves: the Stokes–Woodward techniqueLa technique de Stokes–Woodward pour l'analyse de vagues aléatoires non linéaires

A generalization of the Woodward's theorem is applied to the case of random signals jointly modulated in amplitude and frequency. This yields the signal spectrum and a rather robust estimate of the bispectrum. Furthermore, higher order statistics that quantify the amount of energy in the signal due to nonlinearities, e.g., wave–wave interaction in the case of water waves, can be inferred. Considering laboratory wind generated water waves, comparisons between the presented generalization and more standard techniques allow to extract the spectral energy due to nonlinear wave–wave interactions. It is shown that our analysis extends the domain of standard spectral estimation techniques from narrow-band to broad-band processes. To cite this article: T. Elfouhaily et al., C. R. Mecanique 331 (2003).     

A coupled hydrodynamic–structural model of the M4 wave energy converter

A method is developed for modelling wave energy converters consisting of floats connected by slender structural elements. The hydrodynamic and structural dynamic analyses are separated in a two-stage process, though the model is fully coupled. The method of dynamic substructuring is used to achieve this separation. The linear diffraction/radiation problem is solved with a finite element idealisation for axisymmetric floats, and drag forces are incorporated by equivalent linearization. Results for a planar representation of the M4 device, and comparisons of theory and experiments undertaken for two scale models tested in regular and random waves, confirm the validity of the theoretical approach. A series of parametric studies is performed to clarify the important physical variables, including natural periods, the ratio of a characteristic length of the device to the wave length, and power take-off.     

Transition waves in bistable structures. II. Analytical solution: wave speed and energy dissipation

We consider dynamics of chains of rigid masses connected by links described by irreversible, piecewise linear constitutive relation: the force-elongation diagram consists of two stable branches with a jump discontinuity at the transition point. The transition from one stable state to the other propagates along the chain and excites a complex system of waves. In the first part of the paper (Cherkaev et al., 2004, Transition waves in bistable structures. I. Delocalization of damage), the branches could be separated by a gap where the tensile force is zero, the transition wave was treated as a wave of partial damage. Here we assume that there is no zero-force gap between the branches. This allows us to obtain steady-state analytical solutions for a general piecewise linear trimeric diagram with parallel and nonparallel branches and an arbitrary jump at the transition. We derive necessary conditions for the existence of the transition waves and compute the speed of the wave. We also determine the energy of dissipation which can be significantly increased in a structure characterized by a nonlinear discontinuous constitutive relation. The considered chain model reveals some phenomena typical for waves of failure or crushing in constructions and materials under collision, waves in a structure specially designed as a dynamic energy absorber and waves of phase transitions in artificial and natural passive and active systems.     

Experimental and numerical study of shock wave propagation in water generated by pulsed arc electrohydraulic discharges

The objective of this study is to simulate the propagation of the shock wave in water due to an explosion. The study is part of a global research program on the development of an alternative stimulation technique to conventional hydraulic fracturing in tight gas reservoirs aimed at inducing a distributed state of microcracking of rocks instead of localized fracture. We consider the possibility of increasing the permeability of rocks with dynamic blasts. The blast is a shock wave generated in water by pulsed arc electrohydraulic discharges. The amplitude of these shock waves is prescribed by the electrohydraulic discharges which generate high pressures of several kilobars within microseconds. A simplified method has been used to simulate the injected electrical energy as augmentation of enthalpy in water locally. The finite element code EUROPLEXUS is used to perform fluid fast dynamic computation. The predicted pressure is consistent with the experimental results. In addition, shock wave propagation characteristics predicted with simulation can be valuable reference for design of underwater structural elements and engineering of underwater explosion.     

M-lump,rogue waves,breather waves,and interaction solutions among four nonlinear waves to new (3+1)-dimensional Hirota bilinear equation

In this research article, we study a new (3+1)-dimensional Hirota bilinear equation which can describe the dynamics of ion-acoustic wave and Alvin wave of small but finite amplitude in plasma physics and describe the propagation process of nonlinear waves in shallow water. First, we apply two methods to study the equation, namely the Hirota bilinear method and long-wave limit method M-lump solution, and line rogue waves are reported. Furthermore, we investigate the velocity, propagation trajectory, and interaction phenomenon of M-lump solution(M=2,3). Then, based on the multi-solitons, two cases of high-order breather solution are constructed by selecting some special parameters. Finally, four types interaction solutions are successfully obtained by employing long-wave limit method and selecting some special parameters. More importantly, we explore physical collision phenomenon of the interaction between nonlinear waves. In order to better illustrate the characteristics of the interaction solutions, the results are shown in three-dimensional plots and numerical simulation. To our knowledge, all of the obtained solutions in this article are novel. The results of this article may be provide an important theoretical basis for explaining some nonlinear phenomena in the field of fluid mechanics and shallow water.

     

随机杆系结构几何非线性分析的递推求解方法

建立了随机静力作用下考虑几何非线性的随机杆系结构的随机非线性平衡方程. 将和 位移耦合的随机割线弹性模量以及随机响应量表示为非正交多项式展开式，运用传统的摄动方法获 得了关于非正交多项式展式的待定系数的确定性的递推方程. 在求解了待定系数后，利用非 正交多项式展开式和正交多项式展开式的关系矩阵，可以很方便地得到未知响应量的二阶统计矩. 两杆结构和平面桁架拱的算例结果表明，当随机量涨落较大时，递推随机有限元方法比基于 二阶泰勒展开的摄动随机有限元方法更逼近蒙特卡洛模拟结果，显示了该方法对几何非线性 随机问题求解的有效性.     

动力吸振器复合非线性能量阱对线性镗杆系统的振动控制

研究了线性动力吸振器复合非线性能量阱对线性镗杆在外部简谐激励下的振动控制. 忽略镗杆系统中的非线性因素, 建立了附加线性动力吸振器和非线性能量阱的镗杆系统的三自由度运动方程, 研究了附加复合式动力吸振器的镗杆系统的受迫振动. 通过平均法得到了附加复合式动力吸振器的镗杆系统的近似解析解, 并利用数值解验证了近似解析解的准确性, 两者具有很好的一致性. 利用近似解析解详细分析了线性动力吸振器和非线性能量阱的参数对镗杆振动抑制性能的影响. 对给定质量的复合式动力吸振器进行了参数优化, 其中线性动力吸振器参数采用H_∞优化方法的近似解析解进行了优化, 非线性能量阱的阻尼利用系统的近似解析解进行了优化. 分析结果表明, 线性动力吸振器与非线性能量阱组合可以有效抑制线性镗杆系统的振动, 而且采用参数优化后的复合式动力吸振器可以获得更好的减振效果. 通过附加非线性能量阱, 不但可以提高线性动力吸振器的振动抑制效果, 而且还可以提高振动控制系统的鲁棒性.      

基于新建筑抗震设计规范考虑场地土特性的人工波生成及可靠性研究

基于新《建筑抗震设计规范》对场地土特性和人工波选择的要求,将地震动作为随机过程,利用修正胡聿贤-周锡元模型以及基于Hartley正交基的地震动随机过程经双调制生成不同场地土特性的人工地震波,以6层钢筋混凝土结构非线性随机地震反应分析为例,研究了不同场地土特性人工波对结构位移可靠度的影响。结果表明,场地土因素对人工波生成以及结构的动力响应影响较大,不同场地土人工波具有明显的统计学特性,均满足建筑抗震设计规范的选波要求,为最新《建筑抗震设计规范》要求考虑大量不同场地土效应的地震波生成提供了新的解决办法。     

面向微振信号的驻极体减振俘能装置设计与建模

随着航天工程的飞速发展以及先进制造业对加工精度要求的持续提高,对低频微振信号的控制与利用越发受到关注.本文采用驻极体材料,参考动力减振器理论,开发了一种面向低频微振环境的减振俘能一体化装置,建立了驻极体减振俘能装置的机电耦合模型.为兼顾减振和俘能的双重要求,本文分析和等效了静电力对系统动力学特性的影响,并进行了参数的评估,提出了适用于驻极体减振俘能的优化方法.建立了AMEsim和Simulink的联合仿真环境,对模型和结果进行了仿真验真.建模和仿真的结果表明,本文建立的驻极体减振俘能装置的机电耦合模型可以准确描述装置的运动过程,建模与仿真的误差在5%以内.驻极体减振俘能装置对参数变化十分敏感,且副结构刚度、初始间距等对减振俘能性能的影响都明显强于副结构阻尼.经过优化,本文设计的驻极体减振俘能装置,能够兼顾减振和俘能需求,可以实现接近于理想动力减振器的减振效果,也可以在牺牲15%减振效果前提下,获得1700 V输出电压和3.1 m W俘能功率.本文建立的机电耦合模型和动态静电力解析模型,有助于理解驻极体减振俘能机构的工作原理,揭示了非线性静电力的变化过程和作用机理.     

The region of nonlinear effects for intensive sound pulses in the ocean

The formation of a stationary shock wave is studied in media with an arbitrary power dependence of the damping coefficient on the frequency. The conditions for existence of a stationary shock wave are defined and it is shown that when acoustic signals propagate in the ocean the region of nonlinear effects is limited. For acoustic waves generated by explosive sources a calculation is given of the location of the transition point of the nonlinear wave into a linear one, and the dependence of this point on the charge weight is defined.     

结构中微裂纹与超声波的混频非线性作用数值仿真研究

针对结构中微裂纹检测难题,本文对结构中微裂纹与超声波的混频非线性作用进行了数值仿真研究。基于经典非线性理论,得到了两列超声纵波相互作用产生混频效应的理论条件。通过有限元仿真,研究了两列纵波与微裂纹相互作用产生混频的条件,并分析了界面处静应力、摩擦系数和裂纹方向对混频效应的影响。研究发现,超声波与微裂纹相互作用产生混频非线性效应的发生条件仍符合经典非线性理论下的混频产生条件。裂纹界面处施加的静应力对差频横波幅值有明显影响;当施加静应力与无裂纹模型得到的最大应力值接近时,混频非线性效应最强;裂纹界面的摩擦系数对超声波的混频非线性效应影响较小;透射差频横波传播方向与经典非线性理论预测的理论差频分量方向基本一致,且几乎不受裂纹方向变化的影响,而反射差频横波的传播方向随裂纹方向的改变而有所不同。本文研究工作为微裂纹检出及方向识别做了有益探索。     

A non-hydrostatic numerical scheme for dispersive waves generated by bottom motion

A numerical scheme based on the staggered finite volume method is presented at the aim of studying surface waves generated by a bottom motion. We address the 2D Euler equations in which the vertical domain is resolved only by one layer. The resulting non-hydrostatic scheme is used to simulate surface waves generated by bottom motion in a water tank. Here we mimic Hammack experiments numerically, in which a bed section is moved upwards or downwards, resulting in transient dispersive waves. For an impulsive downward bottom thrust, free surface responds in terms of a negative leading wave, followed with dispersive train of waves. For an upward bottom thrust, amplitude of the leading wave decays as the wave propagates, and no wave of permanent form evolves— instead, there appears a train of solitons. In this article, we show that our numerical scheme can produce the correct wave profiles, comparable with the analytical and experimental results of Hammack. Simulations using intermediate and slow bottom motions are also presented. In addition, we perform a simulation of a wave generated by submerged landslide, that compares well against previous numerical simulations. Via this simulation, we demonstrate that our scheme can incorporate a moving wet–dry boundary algorithm in the run-up simulation.     

骑行波的非线性演化方程

从能量的角度出发,采用Ｈａｍｉｌｔｏｎ描述交结合变分原理和摄动分析,并借助于符号运算导出了骑行在大波上的小波的Ｈａｍｉｔｏｎ密度函数和非线性动力学方程。这里的大流和小波是对波高而言的。在Ｈａｍｉｌｔｏｎ描述中,正则变量取为波高和速度势。本文导出了描述小波演化的二阶方程,在一阶近下的方程与Ｈｅｎｙｅｙ等人（１９８８）的结果一致。     

接地惯容式减振器对悬臂输流管稳定性和动态响应的影响研究

输流管道广泛应用于机械、航空、核电和石油等重要工程领域.为防止管道结构因流致振动破坏造成的损失, 很有必要对其稳定性、动力学响应及其调控进行深入研究.本文提出一种由惯容器、弹簧和阻尼器并联组成的减振器模型, 研究了这种接地惯容减振器对悬臂输流管稳定性和非线性振动的影响. 首先, 基于哈密顿原理给出了带有接地惯容减振器非保守系统的非线性动力学模型; 然后, 利用高阶伽辽金方法对非线性方程进行离散化; 最后, 分别从线性和非线性角度分析了不同减振器参数下输流管道的被动控制效果, 着重讨论了惯容系数和减振器安装位置对悬臂管稳定性和动态响应的影响机制.线性理论模型的研究结果显示, 接地惯容减振器可显著影响悬臂管的失稳临界流速, 故通过调节减振器参数能有效提高输流管道的稳定性;惯容系数和弹簧刚度对系统稳定性的控制效果还与减振器的安装位置密切相关.非线性理论模型的分析结果显示, 惯容系数和减振器位置对输流管的非线性动态响应也有显著影响, 且这种影响还依赖于管道的流速取值; 在某些参数条件下, 减振器还可使输流管道由周期运动演化为复杂的混沌行为. 本文研究结果表明, 通过设计合理的惯容式减振器参数, 可提升悬臂输流管道的稳定性并有效抑制其颤振幅值.      

Stochastic optimal control of flexible aircraft taxiing at constant or variable velocity

Active control landing gears are used to alleviate vibration during aircraft taxiing. A nonlinear stochastic dynamics model is established, considering the aircraft body pitch movement and elastic vibration excited by the random runway. The equivalent linearization method is adopted to ensure the model linearity near the balance point, and the Gaussian random process of the runway is generated from the Gaussian white noise using a shape filter. Based on the stochastic optimal control theory, the LQG controller is designed along with weighted quadratic performance index for a better ride comfort, shock absorption, road holding and least energy expenditure. The algebraic Riccati and Lyapunov equations are solved to obtain stationary response while taxiing aircraft at a constant velocity and the differential Riccati and Lyapunov equations are solved to obtain the nonstationary response while taxiing aircraft at a variable velocity. The aircraft dynamic responses are obtained through the runway random process modeled by Monte Carlo method. Simulation results show that active control landing gear can give a better ride comfort, shock absorption and road holding performance no matter whether taxiing is at constant or variable velocity.     

风浪联合发电系统水动力学研究进展

随着化石能源枯竭和全球变暖等环境问题的日益严重,海洋可再生能源(海上风能、波浪能和潮流能)成为研究热点. 为了有效开发海洋可再生能源,降低成本,多种能源综合开发成为现阶段的趋势. 海上风能与波浪能结合具有广阔的应用前景,联合发电系统不断创新. 水动力性能是联合发电系统与波浪相互作用的重要基础. 本文简要介绍多种应用在联合发电系统上的水动力学数值模拟方法,包括线性频域、线性时域、势流非线性方法标识码基于 Navier-Stokes 方程的黏性方法,对现有文献的水动力学数值模拟方法进行综述,从计算效率和精度标识码析其优缺点,且进一步阐述水动力控制优化的技术原理与实验技术主要科研难点,为联合发电系统的水动力设计提供依据. 得到以下主要结论:从计算效率上看,线性频域方法最优,其次为线性时域、势流非线性、黏性方法,从计算精标识码,与前者恰好相反;综合考虑计算效率和精度,采用考虑黏性修正的势流方法来研究是一个切实可行的方案;模标识码方法和优化控制技术目前还不够成熟,尚处于探索阶段.      

Extreme waves,modulational instability and second order theory: wave flume experiments on irregular waves

Here we discuss the statistical properties of the surface elevation for long crested waves characterized by Jonswap spectra with random phases. Experiments are performed in deep water conditions in one of the largest wave tank facilities in the world. We show that for long-crested waves and for large values of the Benjamin–Feir index, the second order theory is not adequate to describe the tails of the probability density function of wave crests and wave heights. We show that the probability of finding an extreme wave can be underestimated by more than one order of magnitude if second order theory is considered. We explain these observed deviations in terms of the modulational instability mechanism that for large BFI can take place in random wave spectra.     

Numerical simulation of fully nonlinear irregular wave tank in three dimension

A fully nonlinear irregular wave tank has been developed using a three‐dimensional higher‐order boundary element method (HOBEM) in the time domain. The Laplace equation is solved at each time step by an integral equation method. Based on image theory, a new Green function is applied in the whole fluid domain so that only the incident surface and free surface are discretized for the integral equation. The fully nonlinear free surface boundary conditions are integrated with time to update the wave profile and boundary values on it by a semi‐mixed Eulerian–Lagrangian time marching scheme. The incident waves are generated by feeding analytic forms on the input boundary and a ramp function is introduced at the start of simulation to avoid the initial transient disturbance. The outgoing waves are sufficiently dissipated by using a spatially varying artificial damping on the free surface before they reach the downstream boundary. Numerous numerical simulations of linear and nonlinear waves are performed and the simulated results are compared with the theoretical input waves. Copyright © 2006 John Wiley & Sons, Ltd.     

具有精确色散性的非线性波浪数学模型

以完全非线性的自由表面边界条件为基础,以波面升高\eta和自由表面速度势\phi _\eta为待求变量,建立了新的波浪方程．方程在色散性上是完全精确的,非线性近似至三阶．与缓坡方程相比较,两者都具有精确的色散性,但该方程属于非线性模型,可模拟波浪的非线性效应,且适用于不规则波．方程的特点是属于微分-积分方程,对如何处理方程中积分项进行了讨论,并数值模拟了不同周期的线性波和二阶Stokes波,也模拟了波群的非线性演化,以对模型进行验证．