两层流体中水波在垂直薄板上的反射与透射

研究在两层流体中表面波模态和内波模态的波浪与半潜式刚性垂直薄板 相互作用的问题. 基于特征函数展开理论,建立了两种模态入射波作用下,半潜式刚性垂直 薄板的反射与透射能量的计算方法,证明了对每一种模态的入射波,另一种模态波浪的反射 与透射能量是相等的. 对水面漂浮和座底半潜式薄板的反射与透射能量,以及作用在其上的 水平波浪力进行了数值计算分析,表明在某个频率范围内,流体的分层效应对这些水动力 量的影响是不可忽视的. 特别地,当薄板的一端位于两层流体的内界面上时,两种模态波浪 的能量转化是最大的.     

双介质耦合刚性基弹性层平面应变型导波模式及界面散射能量分配

过渡段动力稳定性问题已成为制约400 km/h及以上高铁路基设计的关键难题,亟需从波动和能量的角度探究由基础非均匀引发的线路系统动力响应放大机理.文章将轨下基础简化为上表面自由、底端固定的刚性基弹性层,将高铁过渡段车致弹性波传播问题提炼为非均匀介质刚性基弹性层中波的散射问题,建立双介质耦合刚性基弹性层平面应变模型,优化该类波导结构频散方程在复平面求根方法,并结合岩土类介质特征展开刚性基弹性层频散分析,以明确其多模式导波特性及散射能量分配,最后,围绕弹性层厚度、刚度比等影响因素开展对比分析.结果表明:刚性基弹性层各模式导波均具有截止频率,弹性层厚度越小,杨氏模量越大,各阶导波模式的截止频率越高;入射波在双介质刚性基弹性层发生散射后,透射场基阶模式导波会占据主体能量,随着高阶导波模式被逐一激发,反射场及透射场高阶模式能量占比会在全频率范围呈现“此消彼长”状态;交换两侧弹性层材料,改变弹性层厚度及两弹性层刚度比不会显著改变能量分布规律,但总体来看,能量更易集中在较软侧弹性层中,各模式导波在激发初始频段会更为活跃,可分配到更多能量.     

柔性圆柱涡激振动流体力系数识别及其特性

涡激振动是诱发海洋立管、浮式平台系泊缆和海底悬跨管道等柔性圆柱结构疲劳损伤的重要因素.目前,海洋工程中用于柔性圆柱涡激振动预报的流体力系数主要来源刚性圆柱横流向受迫振动的实验数据,存在一定缺陷和误差.本文综合考虑横流向与顺流向振动耦合作用,建立了柔性圆柱涡激振动流体力模型,运用有限元法和最小二乘法确定升力系数、脉动阻力系数和附加质量系数.为了准确识别柔性圆柱涡激振动流体力系数,设计并开展了拖曳水池模型实验,实验用柔性圆柱模型的质量比为1.82,长径比为195.5.通过与刚性圆柱流体力系数对比,深入分析了柔性圆柱流体力系数的特性.结果表明:柔性圆柱在一阶模态控制区,流体力系数随约化速度变化趋势与刚性圆柱大致相似;二阶模态控制区,升力系数和脉动阻力系数显著增大;附加质量系数在响应频率较低时与振动位移的相关性增强;当响应频率较低时,振动位移较大区域为能量耗散区,当响应频率较高时,振动位移较大区域为能量输入区.     

射流扩散火焰闪烁模态及频率特性的实验研究

层流扩散火焰的闪烁是一种经典的火焰不稳定性现象,然而现阶段对其不稳定性模态及频率特性的研究尚不充分.文章利用高速摄影和粒子图像测速同步测量技术,对宽工况下准静态环境中的浮力主控和动量主控圆口射流扩散火焰的不稳定性及其频率进行了实验研究.实验发现,燃料射流流量增大会导致火焰失稳,所引起的闪烁现象可分为varicose模态和sinuous模态.流场测量结果表明,闪烁火焰的主要流动结构表现为分别位于火焰面内外的两个剪切层.火焰外剪切层卷起形成的大尺度环形涡的周期性产生、增长和脱落是导致火焰面周期性形变(即火焰闪烁)的原因.闪烁火焰具有准周期性,其流场具有统一的主频率,且该频率与火焰脉动频率一致,说明闪烁火焰在本质上是种整体流动不稳定性的体现.浮力主控火焰sinuous模态的频率比varicose模态高3 Hz左右,并且在燃料流量较大的工况下存在varicose和sinuous模态间的切换.浮力主控火焰的频率符合经典的1/2标度律,但不同模态对应着不同的标度律系数.动量主控火焰的频率显著偏离1/2标度率,且偏离程度随射流动量增加而增强.研究表明了流动不稳定性模态对于射流扩散火焰频率特性具有不可...     

基于动力学模态分解法的绕水翼非定常空化流场演化分析

空化是船舶和水下航行体推进器中经常发生的一种特殊流动现象,它具有强烈的非定常性,空化的发生往往会影响推进器的水动力性能和效率. 为探究绕水翼非定常空化流场结构,本文基于 Schnerr-Sauer 空化模型和 SST $k$-$\omega $ 湍流模型,开展绕二维水翼非定常空化流动数值预报与流场结构分析. 通过将数值预报的空泡形态演变和压力数据与试验结果对比,验证了建立的数值方法的有效性. 并基于动力学模态分解方法对空化流场的速度场进行模态分解,分析了各个模态的流场特征. 结果表明,第一阶模态对应频率为 0,代表平均流场;第二阶模态对应频率约为空泡脱落频率,揭示了空泡在水翼前缘周期性地生长与脱落,第三阶模态对应频率约为第二阶模态的 2 倍,揭示了两个大尺度旋涡在水翼后方存在融合行为. 第四阶模态对应频率约为第二阶模态的 3 倍,具有更高的频率,表征流场中存在一些小尺度旋涡的融合行为. 最后对不同空化数下的空化流场进行了模态分解分析,发现脱落空泡的旋涡结构随着空化数的减小而增大,第二阶模态频率随着空化数的减小而减小.      

三层流体中斜入射波作用下半无限板的水弹性响应

解析地研究了在三层流体中斜入射波浪与半无限弹性板的相互作用引起的波散射和板的水弹性响应. 三层流体在界面处的密度发生阶跃, 各层为一常数. 假设流体不可压缩、无黏、流体运动无旋. 在线性势流理论框架下, 使用本征函数展开法和内积式给出波板相互作用的半解析解. 根据色散关系分析, 得到了表面波模态和界面波模态入射时的临界入射角. 随着物理参数的变化, 临界角将随之发生变化. 临界角决定了当由开阔水域向板覆盖水域传播的表面波或界面波的存在性: (1)板覆盖水域入射界面上, 透射波能否存在; (2)入射界面之上界面中, 板覆盖水域中的透射波以及开阔水域中的反射波能否存在. 当下界面波入射时并且入射角足够大时, 开阔水域中的下界面波模态是整个流体域中唯一存在的模态.      

三层流体中斜入射波作用下半无限板的水弹性响应

解析地研究了在三层流体中斜入射波浪与半无限弹性板的相互作用引起的波散射和板的水弹性响应.三层流体在界面处的密度发生阶跃,各层为一常数.假设流体不可压缩、无黏、流体运动无旋.在线性势流理论框架下,使用本征函数展开法和内积式给出波板相互作用的半解析解.根据色散关系分析,得到了表面波模态和界面波模态入射时的临界入射角.随着物理参数的变化,临界角将随之发生变化.临界角决定了当由开阔水域向板覆盖水域传播的表面波或界面波的存在性:(1)板覆盖水域入射界面上,透射波能否存在;(2)入射界面之上界面中,板覆盖水域中的透射波以及开阔水域中的反射波能否存在.当下界面波入射时并且入射角足够大时,开阔水域中的下界面波模态是整个流体域中唯一存在的模态.     

分层流体中内孤立波在台阶上的反射和透射

基于匹配渐近展开和格林函数的方法,研究了两层流体系统中内孤立波在台阶地形上透射、 反射及其分裂的演化特征. 通过保角变换和求解奇异Fredholm积分方程,获得了反映地形 效应对Boussinesq方程影响的约化边界条件,藉此建立了KdV演化方程的``初值'问题, 根据散射反演理论获得了反射波和透射波的解析表达式. 分析结果表明：上下流体层的厚度 比、密度比以及台阶高度对于反射和透射波振幅及其分裂具有显著的影响. 尤其当上层流体 厚度小于下层厚度时,由于存在临界点,在其附近反射波的幅值随台阶高度的演化由单调增 变为单调减,透射波的幅值由单调减变为单调增;上台阶的反射波与入射波反相,其最大幅 值可达到入射波的数倍;此外,下台阶反射波也可发展为单支孤立波,它区别于单层流体中 反射波仅为衰减的振荡波列.     

基于Lamb波频散特性的薄板声发射源定位方法研究

声发射源时差定位方法中波速的确定是定位准确的关键问题,根据模态声发射理论,声发射信号在薄板内的传播过程中具有频散现象和多模态特性.不同频率不同模态的声波其传播速度不同.基于Lamb波频散特性和声发射检测技术,采取时频联合分析方法对铝薄板中声波模式进行识别;利用低频段频散不明显的扩展波的波速和同一频率同一模态波到达两传感器的时间差来实现声发射源的准确定位;通过铝薄板中AE源定位实验表明,采用S0模式,即扩展波的波速进行定位计算,可以比较准确地确定声发射源的位置,而且理论值与实际值相差很小.     

弯曲波彩虹捕获效应及其在能量俘获中的应用

弹性波在色散关系经过设计的梯度结构中传播时会产生空间分频现象和波场能量增强现象,即不同频率的弹性波会在结构的不同位置停止向前传播并发生能量聚集,这就是弹性波彩虹捕获效应.其相关研究成果可以促进结构健康监测、振动控制以及能量俘获等领域的发展.本文通过所设计的梯度结构梁,系统地研究了弯曲波彩虹捕获效应及其在压电能量俘获中的应用.首先,利用传递矩阵法获得了梯度结构梁元胞能带结构的解析解,进而分析了弯曲波彩虹捕获效应的产生机理:不同频率的弯曲波会在不同元胞附近群速度减小到零,从而停止向前传播并发生反射;入射波和反射波的叠加,以及群速度减小带来的能量聚集,会显著增强反射处的波场能量.其次,通过有限元仿真和实验验证了弯曲波彩虹捕获效应的空间分频现象和波场能量增强现象.最后,通过有限元多物理场耦合仿真和实验,研究了粘贴PVDF压电薄膜的梯度结构梁相对于均匀梁的弯曲波能量俘获效果及其随入射波频率的变化规律.结果表明,在弯曲波彩虹捕获效应发生频带内,粘贴在梯度结构梁上的PVDF压电薄膜的输出电压约为粘贴在均匀梁相应位置处的PVDF压电薄膜的输出电压的2倍.     

Wave propagation and reflection-transmission in a stratified viscoelastic solid

The paper investigates time-harmonic wave propagation in continuously stratified solids and provides the results of a reflection-transmission process generated by a layer sandwiched between homogeneous half-spaces. The layer is continuously stratified and allows for jump discontinuities at a finite number of planes. The dissipative effects are accounted for through the classical Boltzmann law of viscoelasticity. By using displacement and traction as convenient vector variables, the governing equations are considered in a vector Volterra integral equation and the solution is determined by means of a matricant. Next the matricant is applied to determine the reflection and transmission coefficients of a layer, with a generic piecewise continuous profile of the material properties. The reflection-transmission process produced by an obliquely incident wave, is considered for horizontally-polarized waves. The low-frequency approximation is derived for the reflection and transmission coefficients. Next, the high-frequency approximation is investigated by a WKB-like procedure which involves a complex valued frequency-dependent shear modulus. The displacement solution is obtained for the forward- and the backward-propagating waves in the layer along with the reflection and transmission coefficients.     

金属材料SHPB实验数据处理的三波校核法

通过自编程序调整入射波、透射波和反射波的相对位置。当移动波相对位置时,程序界面显示2 幅图:一幅显示入射波、透射波、反射波以及透射波与反射波之差;另一幅显示试样的3条应力应变。这3条 曲线分别由第1幅图中的入射波与透射波、入射波与反射波以及三波法求得。根据SHPB实验的基本假定, 这3条应力应变曲线的塑性段应该一致,同时透射波与入射波之差应等于反射波,把这2个等价的特点作为 正确处理SHPB实验数据标准的方法称为三波校核法。     

A note on the diffraction of an obliquely incident surface wave by a partially immersed fixed vertical barrier

The problem of the diffraction of surface waves, obliquely incident on a partially immersed fixed vertical barrier in deep water, is solved approximately by reducing it to the solution of an integral equation, for small angle of incidence of the incident wave. The corrections to the reflection and transmission coefficients over their normal incidence values for small angle of incidence are obtained and presented graphically for some intermediate values of wave numbers.     

A possible anomalous wave transformation in plasma

It is a familiar fact that in the approximation of geometrical optics the normal oscillations in a weakly inhomogeneous medium are independent. The approximation of geometrical optics is, however, violated close to those points where either the wave vector k(x) becomes zero (reversal point), or where the wave vectors corresponding to the different types of oscillation coincide (points of intersection of the solutions). In the immediate neighborhood of these points separation into normal oscillations is no longer possible, which in the case of “points of intersection of the solutions” leads to the possible appearance, in addition to the wave incident from infinity, of another new wave with different dispersive properties. However, cases so far considered of the “birth” of a new wave due to the passage of an incident wave with such properties have led to an exponentially small transformation coefficient, and also to the absence of reflected waves (see, for example, [1]; ibid. bibliography). In [2] the rules for going around points of “intersection” of the solutions were obtained for a system of two coupled oscillators, which also led to the appearance of the reflected solutions exp

$$\exp \left( {\int {\omega (t)dt} } \right) \to \exp \left( { - \int {\omega (t)dt} } \right),$$     

Scattering of water waves by vertical porous barriers: An analytical approach

An analytical approach is proposed here to study scattering of deep water waves by a submerged or a surface piercing vertical porous barrier. It involves a connection between two wave potentials of which one is the solution of a boundary value problem associated with wave scattering by the porous barrier and the other is the solution of a complementary type problem where barrier and gap positions are interchanged and solid barrier takes the position of the porous barrier. The connection also involves an auxiliary or a connection wave potential. The potential for the solid barrier problem involves incident wave forcing while the auxiliary potential describes a solid barrier type problem that involves a non-physical forcing. The solution procedure of Ursell (Ursell, 1947) is chosen to solve these boundary value problems explicitly in the case of normal wave incidence as it also determines necessary exact behavior of the potential at the barrier edge. The reflection coefficients are also connected and the reflection amplitudes of the normally incident wave against the vertical porous barriers are obtained analytically. Numerical results for reflection and transmission coefficients are presented.     

Transverse wave at a plane interface between isotropic elastic and unsaturated porous elastic solid half-spaces

Based on the poroelasticity theory, this article investigates the reflection and transmission characteristics of an incident plane transverse wave at a plane interface between an isotropic elastic half-space and an unsaturated poroelastic solid half-space. For this purpose, the effect of the saturation degree and frequency on the properties of the four bulk waves in unsaturated porous medium, i.e., three longitudinal waves and one transverse wave, are discussed at first. Two general cases of mode conversion are considered: (i) The initial transverse wave is incident from an unsaturated poroelastic half-space to the interface, and (ii) the initial transverse wave is incident from an elastic solid half-space to the interface. The expressions for the partition of energy at the interface during transmission and reflection process of waves are presented in explicit forms. At last, numerical computations are performed for these two cases and the results obtained are depicted, respectively. The variation of the amplitude ratios and energy ratios with the saturation degree and incident angle is illustrated in detail. It is also verified that, at the interface, the sum of energy ratios is approximately equal to unity as expected.     

A special solution of wave dissipation by finite porous plates

The reflection and transmission of water waves caused by a small amplitude incident wave through finite fine porous plates with equal spacing and permeability in an infinitely long open channel of constant water depth and zero slope are studied. A special solution is obtained when the distance between the two neighbouring plates is an integral multiple of the half-wavelength of the incident wave. It is found, that when the dimensionless porous-effect parameter G_0 is equal to half the total plate number, the wave dissipation reaches a maximum, and only 50% of the incident wave energy remains in the reflected and transmitted waves. Meanwhile, the reflected and transmitted waves have the same amplitude.     

The low frequency scatter of SH waves by a rough interface in an elastic plate

The study of the reflection and transmission of low frequency SH waves incident upon a rough interface in an elastic plate is undertaken by employing a theory of acoustic wave scattering from rough surfaces originally due to Biot and subsequently generalised to the case of elastic media. In this theory the interface is replaced by a distribution of voids/asperities whose individual size is small compared to the excitation wavelength. We plot the absolute values of the reflection and transmission coefficients versus frequency when a single symmetric SH plate mode is used as the input excitation. The different types of inclusions are used to simulate the rough surface are the hollow, fluid filled and aluminum spheres. Lastly, the loss of energy due to scattering is also estimated for the different inclusion distributions considered.     

Reflection and transmission of elastic waves at five types of possible interfaces between two dipolar gradient elastic half-spaces

Reflection and transmission of an incident plane wave at five types of possible interfaces between two dipo-lar gradient elastic solids are studied in this paper. First, the explicit expressions of monopolar tractions and dipolar trac-tions are derived from the postulated function of strain energy density. Then, the displacements, the normal derivative of displacements, monopolar tractions, and dipolar tractions are used to create the nontraditional interface conditions. There are five types of possible interfaces based on all possible combinations of the displacements and the normal derivative of displacements. These interfacial conditions with consid-eration of microstructure effects are used to determine the amplitude ratio of the reflection and transmission waves with respect to the incident wave. Further, the energy ratios of the reflection and transmission waves with respect to the incident wave are calculated. Some numerical results of the reflection and transmission coefficients are given in terms of energy flux ratio for five types of possible interfaces. The influences of the five types of possible interfaces on the energy parti-tion between the refection waves and the transmission waves are discussed, and the concept of double channels of energy transfer is first proposed to explain the different influences of five types of interfaces.