Vibration analysis of a multi-span rotating ring with ray tracing method

A ray tracing method is applied to analyze both the free and forced responses in a rotating multi-span section ring. In this paper, element coordinates are established and coupled by dispersion and transmission matrices. Structure vibration displacements are expressed in a wave form with a combination of propagation, fast-attenuating and near-field waves. Meanwhile, an exciting force is considered as a point discontinues with different elements on both sides. The wave reflection and transmission matrices are introduced through coupling different elements by applying wave transmission coefficients and transfer matrices. For numeric computation, the reflection and transmission matrices are assembled, independent waveguide elements are integrated and the responses of rotating rings with non-uniform section area are derived. The structure modeling and a numeric computation with corresponding solutions illustrate the validity of the presented approach. The investigation result also shows that the presented approach can be extended to compute accurately on the dynamic characteristics of a rotating complex structure (high speed bearing cage).     

Nonlinear free surface action with an array of vertical cylinders

Nonlinear diffraction of regular waves by an array of bottom-seated circular cylinders is investigated in frequency domain, based on a Stokes expansion approach. A complete semi-analytical solution is developed which allows an efficient evaluation of the second-order potentials in the entire fluid domain, and the wave forces on the structure. Expressions are derived for the second-order potential in the vicinity of individual cylinders. These expressions have a simple form, thus providing an effective means for investigating the wave enhancement due to nonlinear interactions with multiple cylinders. Based on the present method, the wave run-up and free-surface elevations around an array of two, three and four cylinders are investigated numerically.     

Wave interaction with a new type perforated breakwater

In this study examined is the wave interaction with a new modified perforated breakwater, consisting of a perforated front wall, a solid back wall and a wave absorbing chamber between them with a two-layer rock-filled core. The fluid domain is divided into three sub-domains according to the components of the breakwater. Then by means of the matched eigenfunction expansion method, an analytical solution is obtained to assess the hydrodynamic performance of the new structure. An approach based on a step approach method is introduced to solve the complex dispersion equations for water wave motions within two-layer porous media. Numerical results of the present model are compared with previous limiting cases. The effects of rock fill on the reflection coefficient and the horizontal wave force are discussed. The project supported by the Program for Changjiang Scholars and Innovative Research Teams in Universities (IRT0420). The English text was polished by Keren Wang.     

Boundary element method for wave trapping by a multi-layered trapezoidal breakwater near a sloping rigid wall

This study examines the multiple layers in a rubble mound breakwater and their effect on reflection and dissipation of incoming ocean waves. The numerical model is developed using multi-domain boundary element method for oblique water wave trapping near a sloping wall by a multi-layered trapezoidal porous structure, which is utilized to model armour, filter and core layers while examining the hydrodynamics in different configurations. Both, the constant element and linear element approaches to boundary element method are discussed. The cases of bottom-standing porous structures as being submerged and fully extended are considered. The wave hydrodynamics over the structure is described by the reflection and dissipation coefficients along with the forces acting on the sloping wall, and is influenced by wave and structural parametrics of the system. The influence of armour layer in different configurations is highlighted for various structural and wave parameters.

     

Oscillations of elastically mounted cylinders in regular waves

Under the assumption of potential flow and linear wave theory, a semi-analytic method based on eigenfunciton expansion is proposed to predict the hydrody-namic forces on an array of three bottom-mounted, surface-piercing circular cylinders. The responses of the cylinders induced by wave excitation are determined by the equa-tions of motion coupled with the solutions of the wave radiation and diffraction problems. Experiments for three-cylinder cases are then designed and performed in a wave flume to determine the accuracy of this method for regular waves.     

波浪与新型双排开孔圆筒防波堤相互作用三维数值模拟

双排开孔圆筒防波堤是基于圆筒、板式结构的一种复合式新型结构型式;基于不可压缩两相流模型建立三维数值波浪水槽,通过RNG k-ε湍流模型进行湍流封闭,并采用TruVOF方法捕捉自由液面,开展波浪与双排开孔圆筒防波堤相互作用数值模拟,探究相对排间距、开孔率对新型双排开孔圆筒防波堤消浪性能的影响,分析了后排开孔圆筒防波堤附近的复杂水动力现象和流动特性.结果表明,在本文研究工况范围内,沿程平均波高随相对排间距的增大先增大后减小,随开孔率的增大而增大,周期对沿程平均波高的影响没有明显规律;当B/D=9, e=23.11%时,新型双排开孔圆筒防波堤消浪效果最优,反射系数在0.4～0.46之间,透射系数在0.3～0.35之间,耗散系数在0.8～0.85之间;自由液面破碎、水气掺混、环状涡运动演化是新型双排开孔圆筒防波堤紊动耗能消波的主要原因;相对排间距会引起后排防波堤附近涡量分布以及剪切层形态的变化,从而导致不同的紊动特性,影响双排开孔圆筒防波堤消浪特性.研究结果可以为新型双排开孔圆筒防波堤工程设计与消浪机理研究提供理论支撑.     

Propagation of Thermo-Elastic Waves at Several Typical Interfaces Based on the Theory of Dipolar Gradient Elasticity

The reflection and transmission properties of thermo-elastic waves at five possible interfaces between two different strain gradient thermo-elastic solids are investigated based on the generalized thermo-elastic theory without energy dissipation(the GN theory). First, the function of free energy density is postulated and the constitutive relations are defined. Then,the temperature field and the displacement field are obtained from the motion equation in the form of displacement and the thermal transport equation without energy dissipation in the strain gradient thermo-elastic solid. Finally, the five types of thermo-elastic interfacial conditions are used to calculate the amplitude ratios of the reflection and transmission waves with respect to the incident wave. Further, the reflection and transmission coefficients in terms of energy flux ratio are calculated and the numerical results are validated by the energy conservation along the normal direction. It is found that there are five types of dispersive waves, namely the coupled longitudinal wave(the CP wave), the coupled thermal wave(the CT wave), the shear wave, and two evanescent waves(the coupled SP wave and SS wave), that become the surface waves at an interface. The mechanical interfacial conditions mainly influence the coupled CP waves, SV waves, and surface waves, while the thermal interfacial conditions mainly influence the coupled CT waves.     

RESONANCES IN WAVE DIFFRACTION/RADIATION FOR ARRAYS OF ELASTICALLY CONNECTED CYLINDERS

As shown by Maniar & Newman in 1997, for a long array of bottom-mounted cylinders in the open sea, resonant modes occur as “near-trapping” and large diffraction forces are excited on the cylinders. The mechanism of such a resonant phenomenon was subsequently explained by the present authors in connection with the Dirichlet trapped modes for an array of cylinders aligned perpendicular to the walls in a wave channel. This paper examines similar resonant phenomena for radiation problems. Considered is an array of elastically connected cylinders in a wave channel. The cylinders are surface-piercing and extend to the sea-bottom. They constitute an array in a line, and each cylinder is allowed to oscillate only in the direction parallel to the line. Nonradiating wave modes, which cause only added mass force and no hydrodynamic damping are demonstrated to exist for an array of cylinders across the wave channel. Each mode corresponds to a “dry-mode” for the periodic array of elastically connected cylinders. This result leads to the existence of pure-resonant modes for a periodic array of elastically connected cylinders across the channel. Trapped modes for the corresponding diffraction problem are obtained as the limiting case when the stiffness of the springs has an infinite value.     

含单排周期微裂纹平板结构中的弹性波传播

受损伤固体中含有的微裂纹或微孔洞往往具有周期性，对含周期性缺陷结构中的弹性波分析是力学研究中的重要课题，它直接关系到结构的强度和使用寿命。目前对损伤固体中弹性波散射与透射研究结果主要是弹性动力学平面问题。1995年。Scarpetta和Sumbatyan采用解析法研究了平面波在双周期裂纹弹性介质中的传播问题。并推出显式分析结果。本文基于弹性动力学理论，分析研究了含有单排横向周期裂纹的平板中弯曲波的反射与透射问题。给出了含单排裂纹时反射波与透射波系数的数值结果。对于多排裂纹情况，可采用具有退化核第一类Fredholm积分方程方法分析求解，在求解中给出相应的无量纲数，例如无量纲波数、裂纹尺寸比等。本文分析结果可望能在工程振动控制中应用。     

Interfacial imperfection on reflection and transmission of plane waves in anisotropic micropolar media

This study is concerned with the reflection and transmission of plane waves at an imperfectly bonded interface between two orthotropic micropolar elastic half-spaces with different elastic and micropolar properties. There exist three types of coupled waves in xy-plane. The reflection and transmission coefficients of quasi-longitudinal (QLD) wave, quasi-coupled transverse microrotational (QCTM) wave and quasi-coupled transverse displacement (QCTD) wave have been derived for different incidence waves and deduced for normal force stiffness, transverse force stiffness, transverse couple stiffness and perfect bonding. The numerical values of modules of the reflection and transmission coefficients are presented graphically with the angle of incidence for orthotropic micropolar medium (MOS) and isotropic micrpolar medium (MIS). Some particular cases of interest have been deduced from the present investigation.     

Hydroelastic analysis of gravity wave interaction with submerged horizontal flexible porous plate

The present study deals with the surface gravity wave interaction with submerged horizontal flexible porous plate under the assumption of small amplitude water wave theory and structural response. The flexible porous plate is modeled using the thin plate theory and wave past porous structure is based on the generalized porous wavemaker theory. The wave characteristics due to the interaction of gravity waves with submerged flexible porous structure are studied by analyzing the complex dispersion relation using contour plots. Three different problems such as (i) wave scattering by a submerged flexible porous plate, (ii) wave trapping by submerged flexible porous plate placed at a finite distance from a rigid wall and (iii) wave reflection by a rigid wall in the presence of a submerged flexible porous plate are analyzed. The role of flexible porous plate in attenuating wave height and creating a tranquility zone is studied by analyzing the reflection, transmission and dissipation coefficients for various wave and structural parameters such as angle of incidence, depth of submergence, plate length, compression force and structural flexibility. In the case of wave trapping, the optimum distance between the porous plate and rigid wall for wave reflection is analyzed in different cases. In addition, effects of various physical parameters on free surface elevation, plate deflection, wave load on the plate and rigid wall are studied. The present approach can be extended to deal with acoustic wave interaction with flexible porous plates.     

基于卷积神经网络的涵洞式直立堤波浪透射预测

涵洞式直立堤是一种具有特殊用途的海岸工程结构物,对其透浪特性的研究具有重要工程意义.然而,目前众多学者对于涵洞式直立堤波浪透射问题的研究主要以理论分析、实验模拟及数值计算为主.随着机器学习技术的发展,传统水动力学问题迎来了新的求解理念.机器学习算法可根据训练数据集自主学习相应的规律,以数据映射的方式建立水动力学特征预测...     

Resonant reflection of a surface acoustic wave from strip waveguides

A numerical study is performed of the oblique reflection of a surface acoustic wave from a strip of finite width deposited on the surface of a half-infinite substrate. The finite element method is used. If the strip–substrate contact supports waveguide modes with the velocity exceeding the surface wave velocity on the free surface of the substrate, then an interval of angles of incidence exists where the surface wave efficiently excites a waveguide mode. The excitation of the waveguide mode is accompanied by a singular behavior of the reflection and the transmission coefficients. The dependence of the magnitude and the phase of the coefficients on the angle of incidence, the frequency, the width and the thickness of the strip is examined. In particular, it is found that the magnitude of the reflection coefficient abruptly almost vanishes and abruptly increases almost to unity within the resonance interval of angles of incidence.     

Mathematical study on wave interaction with a composite poroelastic submerged breakwater

In this paper the problem of wave propagation over an adjoining-type of composite submerged poroelastic breakwater with different materials is investigated theoretically. A new analytical solution for describing the dynamic response of wave interaction with poroelastic structures is presented. A set of simultaneous equations is developed and numerically solved in order to produce a general solution for each region subject to matching boundary conditions. The present paper focuses on the changes of influence parameters such as different component widths of the composite breakwater, permeability coefficients, composite materials and configurations of breakwater on wave variations.     

波浪与外壁开孔双筒柱群的相互作用

应用速度势的特征函数展开和透空壁内两壁间压力差和流体速度成正比的线性模型,建立 了波浪与外壁开孔同轴双筒桩柱群相互作用的线性解析解. 应用这一模型进行了数值计算, 用以检验孔隙系数对双筒柱上的波浪力和波面高度的影响. 结果表明,外壁孔隙系数的增加 对减小波浪力和柱外波面高度有很大影响.     

Transmission and reflection of acoustic waves by an obstacle in a waveguide

By an extension of the null field approach introduced by Waterman the transmission and reflection of acoustic waves by an obstacle in a waveguide are considered. The waveguide is assumed to have a constant cross section but otherwise the geometry is left arbitrary. The scattered field is obtained as a complicated mode sum containing the transition matrix of the obstacle, the reflection matrix of the waveguide wall and the transformation relations between the cylindrical and spherical basis functions. For a circular cross section of the waveguide relatively explicit expressions are given for the transmission and reflection coefficients, and numerical results are shown for spherical and spheroidal obstacles in rotationally symmetric configurations. Several natural extensions of the present results are finally recognized.     

Low-frequency wave propagation in an elastic plate floating on a two-layered fluid

For some technical applications related to the ice–sea interaction, it is necessary to predict waveguide properties of elastic plates floating on a relatively thin layer of water, which has a non-uniform density distribution across its depth. The issue of particular concern is propagation of low-frequency waves in such a coupled waveguide. In the present paper, a stratified fluid is modelled as two homogeneous, inviscid and incompressible layers with slightly different densities. The lighter layer of fresh water lies on top of the heavier layer of salty water. The former one produces fluid loading at the pre-stressed plate, whereas the latter one is bounded by the sea bottom. The classical asymptotic methods are employed to identify significant regimes of wave motion in such a three-component waveguide. Dispersion diagrams obtained from approximate dispersion relations are compared with their exact counterparts. The phenomena of veering and generation of waves with zero group velocity induced by pre-stress are identified and quantified.     

孤立波与多个潜水障碍物相互作用的数值研究

本文以完整二维Navier-Stokes方程为控制方程,采用VOF界面跟踪技术和差分方法,数值计算孤立波与多个淹没水下物体相互作用的问题。本文对潜水物体的高度接近水深时,孤立波通过水下孤立直立方柱、两个间距较大的水下直立方柱和两个间距较小的水下直立方柱等三种情况分别进行了计算,给出了波形随时间的演化图,可以看到反射波、前传波和跟随振荡型小波列的生成。对孤立波通过水下孤立直立方柱情形的计算结果,与实验结果和势流理论结果进行了比较。     

Wave reflection by a submerged cycloidal breakwater in presence of a beach with different depth profiles

In this work, formulas for the reflection and transmission coefficients of one-dimensional linear water waves propagating over a submerged structure with a cycloidal cross section in presence of a sloping beach are determined. In the specialized literature, the previous coefficients are obtained mainly for the limit of linear water waves, considering that the water depth upstream and downstream of the structure is flat. For the analysis, we have obtained an approximate analytical solution to the dimensionless Modified Mild-Slope Equation, which models the interactions of a wide range of water waves, from short waves to long waves. The results shown that the presence of small breakwaters not always generate increments on the reflection coefficients, but on the contrary case they contribute to the reflection of the waves decreasing, which is due to the interference of energy that exists between the inclined beach and the structure. To validate the approximate analytical solution, we present a comparison against analytical solutions reported in the specialized literature, obtained with the aid of linear long wave theory, and a numerical solution, all the solutions adjust properly. Results of this study are expected to be used by coastal engineers for preliminary feasibility and desk design of submerged cycloidal breakwaters.