Wave Propagation in a Green–Naghdi Thermoelastic Solid with Diffusion

The Green and Naghdi theory of thermoelasticity is applied to study plane-wave propagation in an elastic solid with thermo-diffusion. The governing equations of an elastic solid with generalized thermo-diffusion are solved to show the existence of three coupled longitudinal waves and a shear vertical (SV) wave in a two-dimensional model of the solid with thermo-diffusion. The reflection of plane waves from a thermally insulated stress-free surface of an elastic solid with thermo-diffusion is also studied. A non-homogeneous system of four equations in reflection coefficients is obtained. The speeds of the plane waves are computed numerically and plotted against frequency for a particular range. The complex absolute values of the reflection coefficients of all reflected waves are computed numerically and plotted against the angle of incidence of the striking wave at the free surface. The effects of diffusion parameters are shown graphically for speeds and reflection coefficients of plane waves.     

近岸波浪破碎区污染物运动的数值模拟

波浪斜向近岸传播中由波浪破碎作用所引起的近岸波流体系是近岸非常重要的环境水动力因素,对该区域污染物的运动分布起着重要的影响作用。结合近岸波浪传播的抛物型缓坡方程、近岸波流场数学模型及污染物在近岸波流作用下运动的数学模型,对近岸斜向入射波浪破碎所产生的沿岸波流场中污染物的分布运动过程进行了数值模拟,并结合实验结果对数值模拟结果进行了分析验证。     

浮式鲆鲽类网箱在波流场中动态响应的数值模拟

根据浮式鲆鲽类养殖网箱的结构特点,基于有限元方法对波流共同作用下网箱的运动受力进行数值模拟,并将数值模拟结果与水槽模型实验结果进行比较分析。结果显示:在3种工况条件下,计算机模拟值与实验值吻合较好,验证了程序及数学模型的可靠性。借助于计算机3D可视化技术,可对波流场中网箱结构的运动过程进行虚拟呈现。其中,当流速为26cm/s时,网箱底框架最大倾角可达9°;波浪作用下底框架最大倾角为12°。当波流联合作用时,底框架最大倾角与最大锚绳受力值均高于波浪或水流单独作用时。当水流入射方向与波浪成角度时,底框架最大倾角与锚绳受力随着夹角的增加而减小。今后将通过海上实测进一步对模拟结果进行验证,使数值模拟能够更加精确。     

Iceberg drift modelling and validation of applied metocean hindcast data

An iceberg drift model covering the Barents and Kara Seas has been developed. The skills of the model relies both on the ability to describe physical actions from the environment on the icebergs and the accuracy of the applied metocean variables (wind, waves and currents). Experiences from the East Coast of Canada show that iceberg modelling may work reasonably well and indicate that iceberg drift models are able to fulfil both of the above mentioned requirements. By applying similar models in other regions, it may be assumed that wind, waves and currents affect the iceberg in a similar way as at the East Coast of Canada. However, the reliability of available metocean data sources will vary significantly from region to region. Due to this, a study with the objective to evaluate the quality of the underlying metocean models has been performed.A significant amount of recorded wind, wave and current data from various regions in the Barents Sea have been applied in comparisons with hindcast data from selected atmospheric and oceanographic models. Results show that the quality of wind and wave data applied by the iceberg drift model is very good. Regarding current velocity, there is a poor match between data from the applied oceanographic model and measurements. A method for improving the current magnitude has been introduced.The relative importance of winds, waves and currents on iceberg drift has also been investigated. In general, currents are most important for iceberg drift. However, in open waters, the wave drift may become the most important forcing. The presented iceberg drift model is considered to provide good results in situations with strong winds (and waves) and low currents while situations with low winds will give less reliable results. It is concluded that the quality of incorporated metocean data in any iceberg drift model need to be documented in order to fully understand possible limitations in iceberg drift simulations. Further work should focus on improvements in oceanographic modelling in order to establish a more reliable oceanographic hindcast for the Barents Sea.     

Reflection and refraction of plane waves at interface between two piezoelectric media

This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell’s law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles.     

Fully nonlinear wave-current interactions and kinematics by a BEM-based numerical wave tank

A numerical wave tank (NWT) with fully nonlinear free-surface boundary conditions is developed to investigate nonlinear wave–wave and wave–current interactions and the resulting kinematics. In the present paper, the variation of wave amplitude and wave length of a monochromatic wave under several different speeds of steady uniform currents is studied through direct numerical simulations in the time domain. The nonlinear wave–current interactions are solved using a boundary integral equation method (BIEM) and a Mixed Eulerian–Lagrangian (MEL) time marching scheme. Both a semi-Lagrangian approach and Lagrangian (material-node) approach are employed and their performance is compared. A regridding algorithm based on cubic spline fitting is devised for updating the free-surface moving boundary in a stable and accurate manner. The incident waves are generated by feeding prescribed analytical waves on the input boundary. An efficient artificial numerical beach is devised and applied to dissipate wave energy and minimize wave reflections from the downstream wall. Nonlinear wave kinematics as a result of nonlinear wave–current interactions is calculated and the results are compared with a multi-layer Boussinesq model. The spatial variation of nonlinear wave profiles and kinematics affected by currents are also addressed and discussed.     

P1波在非饱和土地基表面的反射特性

非饱和土是地表天然土体中最常见的一种形式。与饱和土不同,非饱和土内可传播四种体波:一种剪切波(S波)和三种压缩波(P1波、P2波、P3波)。其中P1传播特性与饱和土中的快压缩波相似:传播速度最快,且衰减系数最低。因此,该文运用非饱和孔隙介质理论阐述了弹性波在非饱和土中的传播特性,分析了平面P1波在非饱和土介质自由边界上的反射问题。根据边界条件,分别导出了在非饱和土自由边界上的四种反射波:反射P1波、反射P2波、反射P3波及反射S波的振幅反射系数及能量反射系数的理论表达式,并且在此基础上进行了数值计算。算例中讨论了四种反射波的振幅反射系数及能量反射系数受P1波入射角及地基土体饱和度变化的影响情况。结果表明:各反射波的振幅反射系数及能量反射系数不仅与入射角有关,也受到饱和度变化的影响。这些结论对土动力学的理论研究以及工程地震勘探具有一定指导意义。     

三维波流耦合水槽模拟模型

水中结构物通常会受到波浪和水流的联合作用,为了得到作用在结构上的波流荷载,该文基于Flow-3D软件建立了三维波流水槽的模拟模型。为了准确模拟波浪和水流的相互作用,避免将造波边界和水流边界同时叠加在入口边界处,采用质量源造波法来实现内造波。利用Flow-3D的二次开发功能在水槽两端设置海绵层消波区,并结合Sommerfeld辐射边界条件来实现水槽的通流消波。对波浪的传播、波流相互作用试验的流场以及波流和柱体结构相互作用试验的流场进行数值模拟,结果表明:所建立的三维波流水槽模型可以准确地模拟波浪和水流的相互作用以及波流对结构的联合作用,并有效地进行消波,避免了二次反射,可用于波浪和水流联合作用下水中结构物波流荷载的研究。     

Acoustic and elastic scattering by continuously stratified media

Acoustic and elastic wave propagation is considered in continuously stratified layers. Upon Fourier transformation, the analysis is developed for time-harmonic waves. Acoustic waves are eventually taken to be described by a one-dimensional Helmholtz equation which is shown to be equivalent to a Volterra integral equation. This allows a natural application of the method of successive approximations to initial-value problems. A fundamental system of solutions so obtained is then applied to the investigation of the reflection–transmission process produced by an obliquely incident plane wave impinging on a layer which suffers from jump discontinuities of the material parameters. The reflection and transmission coefficients are determined. For definiteness, the low-frequency limits and the particular case of homogeneous layers are examined in detail. The whole procedure, with an appropriate setting, is then applied to the equation for elastic waves.     

Longitudinal elastic waves in columns due to earthquake motion

An analysis is presented of longitudinal waves in a thin elastic column. Velocity is specified at one end, and the boundary condition at the other end is expressed in terms of a range of effective impedances of an attached structure. Propagation, reflection and interference of the waves are followed by the method of characteristics. Integration of differential equations along characteristics yields the wave-induced stress, which is then applied to problems of earthquake excitation. Numerical examples are given for recorded updown ground motion of the Kobe Earthquake.     

椭球面镜声波反射聚焦数值模拟研究

据Hamilton线性理论解,给出沿椭球面镜轴线的电弧放电等离子声源(AD-PSS)反射波计算结果,分析由镜面引起的相位变化对中心波、边缘波及尾波传播影响。在聚焦前区中心波压力为正,边缘波、尾波压力为负;聚焦后区则相反。在线性条件下,反射波压力峰值出现于椭球面镜几何焦点,越过焦点后反射波压力幅值迅速衰减。利用有限元软件COMSOL对椭球面镜声反射过程进行数值模拟,揭示反射波传播演化过程及声场分布规律。据KZK方程及等效声源法,分析非线性效应对声传播过程影响。研究表明,非线性效应将使椭球面镜实际焦点位置偏离几何焦点,即正压实际焦点出现在几何焦点后,负压实际焦点出现在几何焦点前;随非线性系数增加正压实际焦点后移,负压实际焦点前移。     

Reflection of ultrasonic Lamb waves produced by thin conducting strips

The reflection of ultrasonic Lamb waves produced by a periodic array of thin conducting strips deposited on a piezoelectric plate was investigated both theoretically and experimentally. A repetitively mismatched transmission line model was used to analyze the performance of the reflector. The reflection coefficient of a single strip is given by R approximately Deltav/v, where Deltav/v is the fractional change in velocity produced by electrical shorting of the propagation surface. An attractive property of Lamb waves is that they can provide a much higher value of Deltav/v than is possible with surface acoustic waves. Therefore, efficient Lamb wave reflectors can be realized with relatively few strips in the reflector. For example, reflection coefficient very close to unity, R approximately 0.98, has been obtained in a Lamb wave reflector consisting of just 12 strips on a Y-X lithium niobate plate. The reflector has been used to realize a unidirectional transducer (UDT). A Lamb wave delay line consisting of two UDTs shows insertion loss of less than 3 dB with fractional bandwidth greater than 7%     

S波由饱和土入射于弹性土时在界面上的反射与透射

从地震工程实际出发，借助Biot多孔介质中的波动方程，根据各种界面条件导出了S波从饱和土入射于弹性土时在交界面上反射与透射的一般计算公式。作为算例，数值计算分析了S波从饱和土入射于饱和土与弹性土交界面时，饱和土中P1、P2和S波的反射系数以及弹性土中P波、SV射系数与界面排水条件、入射角以及频率之间的关系。结果表明：各种波的反射、透射系数与入射角、入射频率以及界面排水条件有关系。     

识别薄板中兰姆波和体波的阶梯板方法

斜探头在某些频率下激励出的兰姆波,其群速度与体波的传播速度相近,所以通过判断传播速度不易区分出兰姆波和体波。通过数值模拟和实验,分别研究了激励频率为2 MHz的纵波和S0模态兰姆波在阶梯板上的反射特性,发现:在阶梯板上入射S0模态兰姆波时,有反射回波;而入射纵波时,无反射回波。基于这种反射特性的差别,提出了一种利用阶梯板区别薄板中兰姆波和体波的方法,该方法可用于确认探头的激励特性。     

平面S波在非饱和土自由边界上的反射问题研究

运用非饱和孔隙介质理论阐述了弹性波在非饱和土中的传播特性,分析了平面S波在非饱和土层自由边界上的反射问题。根据边界条件,分别导出了在非饱和土自由边界上的四种反射波：反射P1波、反射P2波、反射P3波及反射S波的振幅反射率及能量反射率的理论表达式,并在此基础上进行了数值计算。算例中讨论了四种反射波的振幅反射率及能量反射率受平面S波入射角度及土层饱和度变化的影响情况。计算结果表明：各反射波的振幅反射率及能量反射率不仅与入射角有关,也受到饱和度变化的影响,这些结论对土动力学的理论研究以及相关工程地震勘探具有一定指导意义。     

光纤布拉格传感器兰姆波检测的反射谱分析

传统的兰姆波多采用压电陶瓷换能器激发和接收。建立了新的超声兰姆波无损检测系统,其基本思想是采用布拉格光纤传感器作为兰姆波的接收器。光纤光栅传感的基本原理是通过检测光栅反射的中心波长移动实现对外界参量如超声的测量。超声作用下光纤光栅的反射谱发生变化,对超声作用下光纤光栅的反射谱变化进行了数值分析,结果表明,超声对光栅反射谱的影响与超声波长与光栅长度的比值是高度相关的。只有当这个比值相当大时,反射谱的形状才不会变化而中心波长发生偏移,此时光纤传感器可用来探测兰姆波。这个结论为利用新的兰姆波无损检测系统在布拉格光栅长度的设计和兰姆波波长的选择方面提供了有用的工具。     

Reflection of plane waves in thermo-diffusion elasticity without dissipation under the effect of rotation

The governing equations of rotating thermoelastic solids with diffusion are solved in context of the Green–Naghdi theory (Type II) to show the numerical existence of four coupled plane waves. The required boundary conditions at the stress free and thermally insulated surface of the model are satisfied to obtain the reflection coefficients of various reflected waves for an incident plane wave. These coefficients are found to depend on rotation parameter, the angle of incidence of striking waves, thermo-diffusion parameters, and other material constants. Complex absolute values of speeds and reflection coefficients are computed for a particular material representing the model. Graphical representation of numerical results show the effects of rotation and diffusion on speed and reflection coefficients of plane waves.     

Wave reflection in a rotating pyroelectric half-plane

This paper describes the rotation effects on the wave reflection in a pyroelectric half-plane using an inhomogeneous wave approach. The rotation in the governing pyroelectric equation is characterized by considering the Coriolis and centrifugal accelerations. A scenario is modeled where a quasi-transverse wave is incident on the free boundary surface, resulting in reflected waves like temperature wave, quasi-transverse wave, quasi-longitudinal wave, and surface wave. Rotation’s effects on the reflection angle, velocity, attenuation, and energy coefficients of the reflected wave are presented.     

海洋涡旋地震成像的时域有限差分仿真

传统的水声建模方法只考虑水中声波的折射影响,忽略了水层间的声反射,因此不能对反射波地震勘探的海水分层结构成像结果进行分析。文章首先建立了基于时域有限差分的低频宽带脉冲信号传输预报模型,该模型考虑海水分层结构的声反射影响,通过数值求解波动方程计算低频宽带脉冲信号近距离传播过程中的时域波形;其次将某次海上多道地震测量的水文条件作为输入环境参数,计算了近海面地震勘探接收阵所接收的气枪低频脉冲信号时域波形;最后按照反射波地震勘探处理流程,对接收阵信号在共反射点进行相干累加和地震成像,所得到的海水分层结构成像结果与海上多道测量成像结果符合较好。仿真结果验证了水层声反射对海水分层结构反射波地震成像的影响。     

板状粘接结构中对称和反对称纵波与界面的相互作用

为了激发粘接结构中的导波或界面波,通常需要将声波从两半无限介质同相位或反相位地同时入射多层系统。针对此问题,基于矩阵方法,推导了界面处于理想连接的情况下,对称或反对称纵波从上下半无限空间入射时,三层板状粘接结构中纵、横波的反射与透射系数表达式。分析了入射角度、粘接层厚度以及基体材料等对声波反射(或透射)特性的影响。结果表明,对称或反对称纵波垂直入射时不发生波型转换。粘接结构中声波的反射(或透射)特性与入射角度、频率以及粘接层厚度等参数密切相关。在相同的粘接层厚度(或频率)范围内,随着声波频率(或粘接层厚度)的增加,谐振频率曲线向低频漂移。该方法可作为粘接结构中体波或导波传播特性研究的重要理论基础。