Stokes波在铅垂圆柱上绕射的二阶分析

在势流假设下,利用摄动原理,求解 Stokes 波中铅垂圆柱的二阶绕射势,得到完整的二阶波浪压力和波浪力。根据铅垂圆柱的几何特性,采用两种求解方法。一是直接利用外场解析表达式求解;二是设置控制面,外场用解析表达式,内场用简单 Green 函数方法求解。两种方法得到的结果吻合良好,验证了计算方法的有效性,可为求解任意三维物体的二阶绕射问题提供参考。     

求解三维物体波浪荷载的边界元模型

建立了求解规则波中任意形状三维物体绕射问题的边界元模型。设置辐射面将流场分为内、外场,外场中的绕射势用特征函数展开式解析表达,内场则由边界积分方程求解,所取的Green 函数为简单的1/r 形式。内场边界采用四边形面元和轴对称面元混合布置的划分方式,轴对称面元上奇点强度沿周向为Fourier 级数展开的高次分布,提高了求解三维绕射问题的精度和效率。经与直立圆柱绕射的线性理论解比较,验证了数值方法的可靠性。利用谱分析原理,将规则波中的结果拓展,得到多向不规则波中绕射物体所受波浪力的统计特性。     

畸形波作用下二阶波浪载荷对张力腿平台动力响应的影响

畸形波易对海上的建筑物造成极大的危害。为研究畸形波作用下张力腿平台的动力响应特性,考虑张力腿平台的六自由度运动与张力腿非线性恢复刚度,建立非线性耦合运动方程。结合随机频率相位角调制法生成的畸形波波面时历,计算在畸形波条件下平台所受的一阶及二阶和、差频波浪载荷,并采用数值方法求解平台六自由度的运动。结果表明,在畸形波作用下,一阶、二阶波浪载荷均受到畸形波的影响,但各波浪载荷成分的增幅在不同自由度上并不相同。以纵荡为代表的低频运动主要受二阶差频波浪载荷影响,以垂荡、纵摇为代表的高频运动受二阶和频波浪载荷的影响。而由平台水平面内运动引发的下沉运动在二阶差频波浪载荷的作用下显著增大,从而诱发了垂荡运动产生了显著增加,因此在畸形波作用下垂荡运动同时受到二阶和频及差频波浪载荷的影响。此外,由于畸形波具有冲击载荷的特性,不同自由度运动幅值出现时刻并不相同。     

卷破波冲击新型桩板桥梁结构水动力特性试验研究

依托福建省滨海国道涉海浅滩段新型桩板桥梁结构工程,通过波浪水槽开展卷破波冲击桩板桥梁结构水动力特性试验,研究了三个阶段卷破波冲击作用下波浪爬高和桩板桥梁结构所受波浪力水动力特征,并与规则波冲击作用试验结果进行对比,分析了入射波高、波浪周期、水深对波浪爬高和波浪力的影响规律。结果表明：三个阶段卷破波冲击新型桩板桥梁结构的水动力特性显著不同,破碎前阶段和破碎中阶段卷破波会出现明显的波浪爬高现象,破碎前阶段卷破波爬高后的波面高程可达规则波的1.99倍;破碎前阶段的水平波浪力最强,是同阶段竖向波浪力幅值的4.48倍,可达规则波水平波浪力的3.08倍。波浪特征参数和水深对三个阶段卷破波冲击水动力特性影响显著,入射波高和水深的增加会使破碎中阶段卷破波的波面高程和竖向波浪力超过其他阶段;波浪周期的增加会使破碎后阶段卷破波冲击前波面高程和破碎前阶段的竖向波浪力超过破碎中阶段卷破波。     

柱形地形上单浮体的辐射和散射问题

在有限水深、同轴但半径大于或等于浮体半径的圆柱体障碍物地形条件下，基于特征函数展开法，推导了垂直放置的圆柱形浮体由于波的辐射和散射作用所表现的动力学和运动学特征表达式，涉及浮体做垂荡、横荡和横摇运动所产生的辐射势，以及在入射波的作用下，由于浮体固定不动而产生的散射势，并推导了激励力、附加质量和阻尼系数表达式。采用与同轴、同半径圆柱体障碍物地形上单浮体水动力学特性相比的方式和激励力计算两种方法验证了推导的表达式，最后分析了障碍物几何尺寸对浮体水动力学特性的特有影响。     

空沟对平面纵波隔离效果的理论解答

借助复变函数的保角变换法将有限长度的空沟映射变换为单位圆,根据空沟四周完全自由的边界条件,运用波动函数展开法得到了空沟对纵波(P波)和剪切波(SV波)隔离的理论解答。引入位移比值(屏障后某点由入射波波、散射波产生的总位移与入射波单独产生的位移之比),以入射P波为例,计算了沟宽0.4 m、沟长分别为3.0 m、4.0 m、5.0 m和6.0 m共4条空沟的位移比值,通过比较发现:随着空沟长度的增加,最佳隔振效果明显提高,区域明显增大;当空沟长度达到6.0 m时,靠近空沟的区域的隔振效果超过了70%,隔振效果比较理想。最后对比了空沟和单排柱腔列的隔振效果,结果表明:由于单排柱腔列产生波的透射和绕射,而空沟仅产生波的绕射,6.0 m长空沟的最佳隔振效果与8根半径1.0 m的单排柱腔列相当,因此在场地和施工条件都允许的前提下,宜优先考虑空沟进行隔振。     

爆炸冲击荷载下相邻巷道裂隙扩展机理模拟试验

为探究邻近巷道裂纹缺陷受爆炸荷载作用的扩展机理,采用透射式动态焦散线实验系统进行模拟实验。结果表明,对迎爆侧隐性裂纹,当裂纹与巷道左壁相对距离10 mm时,裂纹右尖端扩展因巷道的存在使预制裂纹导向作用更显著,引导爆生主裂纹与预制裂纹左尖端贯穿,衍射后作用于右尖端反射拉伸引起;对背爆侧隐性裂纹,当裂纹与巷道右壁相对距离4 mm时,裂纹扩展源于薄弱的巷道临空面将绕射的应力波能传递并导向裂纹缺陷,裂纹受拉扩展贯穿。巷道存在会增加其围岩裂纹缺陷处动应力集中,在爆炸应力波作用下会诱发裂纹扩展。     

正高程差下边坡爆破对X70钢管振速的影响

为了探究正高程差边坡爆炸施工对邻近埋地管道振速的影响,基于商用有限元软件ANSYS/LS-DYNA采用数值模拟方法研究了炸药量相同(30 kg),正高程差不同(2.1、2.6、3.1、3.6、4.1、4.6和5.1 m)时,边坡爆破振动对既有X70管道振速的影响,并与平面地形结果作对比分析。研究表明：相较于平面地形,在水平距离不变的条件下,管道Y方向上会出现振速放大现象,且随着高程增大,振速加快衰减。管道振速放大系数随着高程差的增大呈现先增大后减小的趋势。当高程差为3.1 m时,管道迎爆面测点的振速放大系数最大,为1.998;当高程差为3.6 m时,管道背爆面测点的放大系数最大,为1.622。爆炸地震波在不同的介质界面发生折射和反射所形成的叠加效应以及在坡脚发生绕射,是产生高程放大效应的主要原因。     

在平面波的作用下地下洞室的振动加速度分布规律研究

利用模型试验和理论研究了在平面应力波的作用下,地下洞室振动加速度分布规律.结果表明:当洞室受到拱顶正上方平面波作用时,拱顶径向振动加速度是4个测量数据中最大的,是振动最激烈的地方;当入射方向从拱顶向左侧偏移至水平方向,迎爆侧的径向加速度都比背爆侧的径向加速度大;当入射方向在拱顶时,切向振动加速度从拱顶至侧墙是先增加后减小,入射方向在拱腰处,拐角的切向振动加速度应该注意;对比洞室的径向加速度和切向振动加速度,洞室的振动加速度允许峰值是由径向加速度控制.这将对实际工程进行抗爆设计非常有意义.     

台阶爆破质点振速的高程效应研究

为了研究台阶爆破振动高程效应,采用NUBOX-6016对露天矿山爆破现场质点振动速度进行长时间监测。通过监测数据的对比分析发现,在正高差地形下,质点振速多表现为先衰减后放大的高程效应,而在负高差地形下,质点振速多表现为先放大后衰减的现象。研究结果表明:正高差边坡在爆破振动载荷作用下产生"鞭梢效应",使台阶突出部位岩体发生显著的高程放大效应;负高差边坡易使入、反射波叠加发生"坡面效应",导致振动速度局部放大。地震波的绕射对高程效应产生了重要影响,绕射叠加放大现象跟边坡形状及与爆区的相对位置有关。     

Ultrasonic Self-Focusing on the Edge of a Surface-Breaking Crack: Experiment and Modeling

An adaptive time-delay self-focusing technique has been used to focus ultrasound on the edge (tip) of a surface-breaking crack emanating from the opposite side of a plate. The diffraction of the focused signal has been measured with the array. Simulation of the self-focusing process and the diffraction by the crack edge has been carried out to obtain numerical results for the edge diffraction. Ray tracing has been used to determine the incident wave field in the plate. Comparisons between the numerical results and the measured data show good agreement. The results have been used to determine the depth of the crack.     

Wave radiation and diffraction by a two-dimensional floating rectangular body with an opening in its bottom

The radiation and diffraction problem of a two-dimensional rectangular body with an opening in its bottom floating on a layer of water of finite depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for the potentials are obtained by the method of separation of variables, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The hydrodynamic coefficients and wave excitation forces are obtained and verified using the near-field and far-field methods and the symmetry properties of coupled hydrodynamic coefficients. The effect of the opening on the wave excitation force and hydrodynamic coefficients is investigated. Piston resonant behaviour and sloshing resonant behaviour are also investigated and their effect on the wave excitation force and hydrodynamic coefficients is discussed.     

Numerical use of exterior singularities for computation of gravity waves in shallow water

This study examines the interaction of obliquely incident waves with a breakwater consisting of an infinite array of uniform multi-chamber perforated caissons with partition walls. Based on the linear potential theory, an analytical solution of the problem is developed by means of the matched eigenfunction expansion method. The periodicities of the breakwater and the incident waves are both incorporated into the solution. Several limiting cases are also examined to validate the newly developed solution. Three parameters of engineering interests, the reflection coefficient, the dimensionless total wave force in the normal direction of the breakwater and the dimensionless total wave force acting on the partition walls, are calculated and carefully examined. This study may give a better understanding of the hydrodynamic performance of multi-chamber perforated caissons. Some useful results are also presented to practical engineering.     

Theoretical and experimental investigations of the effect of diffractive multifocal focusing of radiation

The new optical effect of diffractive multifocal focusing of radiation, predicted earlier by theory, on a bicomponent diffraction system with small Fresnel numbers that consists of two plane screens with circular apertures on given optical axes, is confirmed experimentally. It is shown that the diffraction picture in the focal planes of such a system represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity in the experiment can exceed by six to ten times the value of the incident plane-wave intensity. Experimentally it is established that the diffractive multifocal focusing of radiation on real screens with axial circular apertures, whose diameters exceed the radiation wavelength, is insensitive to the rough external conditions: thickness of the screens, irregularities of the edges and nonideal form of the apertures, heterogeneity of the initial distribution of the incident-wave intensity, and changes in the medium of the wave propagation.     

多孔蝴蝶形钢板剪力墙的抗震性能试验研究

为了研究多孔蝴蝶形钢板剪力墙的抗震性能,对4个足尺多孔蝴蝶形钢板剪力墙试件进行了低周反复加载试验。在蝴蝶杆腰宽比控制在0.4的前提下,研究了钢板厚度和开孔率对多孔蝴蝶形钢板剪力墙滞回性能、承载力和耗能性能的影响。试验结果表明:多孔蝴蝶形钢板剪力墙具有良好的抗震性能,是一种较理想的抗侧力构件和耗能构件;多孔蝴蝶形钢板剪力墙的最终破坏模式为钢板最外侧蝴蝶杆端部撕裂;随着钢板墙厚度的增大和钢板开孔率的减小,试件的抗侧刚度及承载力增大,耗能量增多。     

5 × 5 Spot array based on two crossed single-groove gratings

Compared to the reported 5?×?5 spot arrays, we propose a way of generating a 5?×?5 spot array with much higher efficiency and better uniformity by using two crossed single-groove gratings. Normally, a single-groove grating cannot generate a 1?×?5 equal-intensity array by employing traditional Fourier optics theory. In this letter, we will show by vector diffraction theory that when the period of a single-groove grating is more than twice that of the incident wavelength, it may generate a 1?×?5 equal-intensity array. Based on this discovery, we expand the 1?×?5 array into a 5?×?5 spot array straightforwardly by using two crossed single-groove gratings. The dependence on the refractive index for producing a 1?×?5 equal-intensity array is interesting and we explain the phenomenon from the perspective of energy distribution by the simplified modal method.     

Diffracted radiance: a fundamental quantity in nonparaxial scalar diffraction theory

Most authors include a paraxial (small-angle) limitation in their discussion of diffracted wave fields. This paraxial limitation severely limits the conditions under which diffraction behavior is adequately described. A linear systems approach to modeling nonparaxial scalar diffraction theory is developed by normalization of the spatial variables by the wavelength of light and by recognition that the reciprocal variables in Fourier transform space are the direction cosines of the propagation vectors of the resulting angular spectrum of plane waves. It is then shown that wide-angle scalar diffraction phenomena are shift invariant with respect to changes in the incident angle only in direction cosine space. Furthermore, it is the diffracted radiance (not the intensity or the irradiance) that is shift invariant in direction cosine space. This realization greatly extends the range of parameters over which simple Fourier techniques can be used to make accurate calculations concerning wide-angle diffraction phenomena. Diffraction-grating behavior and surface-scattering effects are two diffraction phenomena that are not limited to the paraxial region and benefit greatly from this new development.     

Hydroelastic Behavior of a Floating Ring-Shaped Plate

The interaction between incident surface water waves and floating elastic plate is studied. This paper considers the diffraction of plane incident waves on a floating flexible ring-shaped plate and its response to the incident waves. An analytic and numerical study of the hydroelastic behavior of the plate is presented. An integro-differential equation is derived for the problem and an algorithm of its numerical solution is proposed. The representation of the solution as a series of Hankel functions is the key ingredient of the approach. The problem is first formulated. The main integro-differential equation is derived on the basis of the Laplace equation and thin-plate theory. The free-surface elevation, plate deflection and Green’s function are expressed in polar coordinates as superpositions of Hankel and Bessel functions, respectively. These expressions are used in a further analysis of the integro-differential equation. The problem is solved for two cases of water depth infinite and finite. For the coefficients in the case of infinite depth a set of algebraic equations is obtained, yielding an approximate solution. Then a solution is obtained for the general and most interesting case of finite water depth analogously in the seventh section. The exact solution might be approximated by taking into account a finite number of the roots of the plate dispersion relation. Also, the influence of the plate’s motion on wave propagation in the open water field and within the gap of the ring is studied. Numerical results are presented for illustrative purposes.     

Hydroelastic wave diffraction by a vertical cylinder

A linear three-dimensional problem of hydroelastic wave diffraction by a bottom-mounted circular cylinder is analysed. The fluid is of finite depth and is covered by an ice sheet, which is clamped to the cylinder surface. The ice stretches from the cylinder to infinity in all lateral directions. The hydroelastic behaviour of the ice sheet is described by linear elastic plate theory, and the fluid flow by a potential flow model. The two-dimensional incident wave is regular and has small amplitude. An analytical solution of the coupled problem of hydroelasticity is found by using a Weber transform. We determine the ice deflection and the vertical and horizontal forces acting on the cylinder and analyse the strain in the ice sheet caused by the incident wave.     

Effect of back pressure on impact and compression-after-impact characteristics of composites

Low velocity impact and compression-after-impact characteristics of a typical plain weave E-glass/epoxy composite are studied experimentally. Atmospheric pressure was maintained on the top surface and different pressures were applied on the rear side during impact experiments. Pressure on the rear side of the impacted plate is referred to as back pressure in further discussion. Effect of back pressure on the impact behavior is studied. It is observed that the variation in peak contact force and maximum central deflection are governed by two opposing phenomena. The parameters influencing the opposing phenomena are: induced curvature because of back pressure, effective pre-stressing and effective thickness. The incident impact energy was the same in all the experiments. Post-impact compressive strength was also investigated.