关于自由面压力脉动与摇板造波的等价性

考虑了一个逆问题，即在浮体运动和自由面压力分布之间是否存在某种等价性？作为这一方向努力的一部分，从二维半无限长水槽摇板造波的特例出发考察了这个问题．基于线性势流理论，导出了自由面压力分布应满足的带复数核的第一类Ｆｒｅｄｈｏｌｍ积分方程，并用正则化方法得到了这类不适定的积分方程的近似正则解．结果表明，自由面压力脉动与摇板造波之间的等价性可以通过解相应的逆问题来解决．     

Hertz接触问题的解的唯一性条件

讨论了接触面为圆面的Ｈｅｒｔｚ接触问题。若压力分布是轴对称的，则该接触问题的解必是唯一的。且在上述条件下，该接触问题的积分方程可化为两个推广的Ａｂｅｌ积分方程组，此方程组的解便给出此接触问题的解。     

受压固、气两相介质一维膨胀运动

本文讨论受压固、气两相介质向真空膨胀这一基本的非定常运动,用渐近法得到了早期和晚期自模拟解,在气体绝热指数为3的情形下用数值法得到了过渡期解。结果说明:三阶段的解互相衔接,连续过渡;质量及动量分布由稀到密的变化是急剧的;当自由面运动了大约50倍粒径后,运动基本上可以用晚期自模拟解描写。     

翼型空化绕流数值研究

空化是发生在流体机械上的复杂过程，理论研究遇到很大困难。本文引入合适的空化数值模型，将空腔界面近似为自由面，用界面构造精度较高的流体体积方法求解空腔位置，通过直接求解原始变量的NavuerStokes方程，数值模拟了无界域中空化在翼型上发生、发展和脱落的周期过程；并分析了空化产生对翼型表面的压力分布、翼型收到的阻力和升力的影响。结果表明，空化出现在翼型上表面；由于空化的产生，翼型表面压力分布不稳定，导致升力、阻力和流场压力出现波动，这是实际中产生噪声和损失的主要原因。     

生物芯片中周期性电渗驱动液体薄膜的流动特性

研究了二维周期性电渗驱动液体薄膜的流动特性. 以Debye-Hückel 假设近似下线性化的Poisson-Boltzmann方程描述双电层电动势分布和电荷密度的分布关系, 与黏性不可压缩流体Navier-Stokes方程相耦合, 得到流体在自由面与固壁之间的周期电渗流流场的精确解. 结果显示, 薄膜内速度振幅与流体黏性密切相关, 雷诺数越大, 速度振幅就越小. 该文还细致分析了雷诺数和自由面ζ电势对自由面的流速振幅和薄膜内速度相位差的影响.     

近自由面水下爆炸冲击载荷特性三维数值模拟

基于三维SPH 方法,对传统链表搜索算法进行了变光滑长度改进,并提出了具有较好稳定性的多 相物质交界面的处理方法,模拟了三维无限域水下爆炸问题,验证了改进的三维SPH 方法模拟水下爆炸问题 的可行性和有效性。在此基础上,建立了水下爆炸三维数值模型,模拟了近自由面水下爆炸过程,研究了冲击 波传播特征、自由面下压力场和能量场特性以及水柱的产生过程。结果表明:自由面可将冲击波压力峰值和 压力冲量最大衰减到1/3和1/7;爆深的增加会导致压力比和冲量比的等值柱面曲率变小,产生的水柱也逐 渐由破碎的喷柱向高而窄的水冢过渡。     

具有小密度差的两层流体中运动点源的二阶内波解

在具有自由面的两层流体中，运动点源生成的Kelvin船波存在两种模式，即表面波模式和内波模式。当上、下层流体密度比趋于1时，由内波模式计算的界面波幅趋于无穷大，这与实验事实相违背。为克服此困难，在自由面和界面作小波幅运动的假设，引入一个小密度差参数。研究了运动点源在无粘、不可压且具有小密度差的两层有限深流体中生成的高阶波动。首先利用摄动方法推导了各阶小参数满足的边值问题；其次，给出了小密度差情形下的可解性条件。证明了在密度比趋于1的极限情形，不存在导致界面波幅无穷大的内波模式；最后，利用Phillips的非线性共振相互作用理论，构造了具有自由面的两层有限深流体中Kelvin船波系的二阶一致有效波动解，并证明了该解在深水情形下退化为Newman关于均匀流体中自由面的二阶波动解。     

无单元法在有自由面渗流计算中的应用

针对有自由面渗流分析中的有限元固定网各法存在的不足，利用无单元法中积分网格和结点相互独立的优点，提出了有自由面渗流的无单元法。计算结果表明，无单元法可以方便地解决迭代计算中的自由面变化问题，实现了真正意义上的网格固定。     

基于格子Boltzmann两相模型的粘弹流体挤出胀大分析

挤出胀大的数值模拟是非牛顿流体研究中具有挑战性的问题．本文运用格子Boltzmann方法(LBM)分析Oldroyd-B和多阶松弛谱PTT粘弹流体的挤出胀大现象，采用颜色模型模拟出口处粘弹流体和空气的两相流动，通过重新标色获得两种流体的界面，并最终获得胀大的形状．Navier-Stokes方程和本构方程的求解采用双分布函数模型．将胀大的结果与解析解、实验解和单相自由面LBM结果进行了比较，发现格子Boltzmann两相模型结果与解析解和实验结果相吻合，相比于单相模型，收敛速度更快，解的稳定性更高．研究了流道尺寸对胀大率的影响，并对挤出胀大的内在机理进行了分析．     

自由面对爆破振动信号能量分布特征的影响

基于爆破振动实测数据, 通过小波分析方法, 得到不同数量自由面爆破振动信号的总能量、各频带的峰值质点振动速度(PPV)及各频带能量, 进而对不同数量自由面爆破振动信号的能量分布特性进行研究。结果表明:开(掏)槽爆破, 由于受单一自由面限制, 大部分炸药爆炸的能量都将作为地震能量消耗掉;自由面越多, 爆破振动信号总能量越少;自由面的数量可影响各频带振动分量分布, 随自由面数量的增加, 爆破振动能量更趋向高频分布, 中低频能量有减少趋势, 振动速度降低;同一振动信号中的高频带PPV虽比低频带PPV高, 但振动持续时间短, 能量衰减较快。建议在工程爆破的减振设计中, 优化起爆方案, 尽量利用多个自由面, 这将比仅仅减少单段起爆药量更有效。     

EFFECTS OF A TRANSLATING LOAD ON A FLOATING PLATE—STRUCTURAL DRAG AND PLATE DEFORMATION

The elastic deformation of a structural plate floating on water caused by a translating three-dimensional load is investigated. The problem is akin to the landing and take-off of aircraft on a structural or ice sheet. The initial-boundary-value problem is solved analytically using a free-surface condition that incorporates the flexural rigidity of the plate. The three-dimensional load is modeled as an axisymmetric, translating pressure distribution. The time-dependent analytical solution is used to obtain the unsteady drag of this moving pressure, if it exists, as well as its asymptotic behavior at large time. The behavior of the transition of the drag near a critical speed related to the minimum celerity of the free waves of the hydroelastic system is examined. Asymptotic analysis shows that the drag attains a discontinuous but finite value as the translation speed approaches the critical speed, an essential difference from some existing two-dimensional results. The growth rate of the plate slope is found to be weakly singular, like log t, for large time. Comparisons with published experimental data for plate deformation are made for the case of an ice sheet. The agreement is very favorable. Implications on the operation of floating runways are discussed.     

Impact of an ideal fluid jet on a curved wall: the inverse problem

This paper analyzes an ideal fluid jet impinging a wall. The usual two-dimensional model of jet flow uses an ideal, incompressible, weightless fluid, and maps this flow in a way that reduces it to a problem of complex analysis that cannot be solved analytically. An efficient procedure is presented here for solving the inverse problem numerically in the case of an arbitrary wall shape, i.e. the design of a wall corresponding to a prescribed velocity (or pressure) distribution. In similar studies, as in airfoil design, important constrains have to be applied to the prescribed distribution in order to ensure the existence of a solution. Not only is this not the case here, but also a constraint must be added to impose the uniqueness of the solution.     

不同发射深度下导弹水下点火气水流体动力计算

从流体动力角度研究了不同发射深度下，导弹水下点火这一非定常非线性过程。整个系统分为外部水流场、喷管流场和燃气泡流场三个区域加以考虑。水流场采用不可压势流模型，用边界元方法求解；喷管内流场采用非定常一元流动模型，用特征线差分法求解，并设置了激波检测功能；燃气泡采用基于质量和能量守恒的零维计算模型。在时间域中用步进方法实现了三个流场的耦合求解。给出了四种发射深度下的数值计算结果，展示了导弹水下点火的一     

岩质滑坡的时间预报与水力启动模型

摘  要  岩质滑坡发生时间的适时超前预报是一个世界性难题,之所以长期不得其解,主要是缺乏对滑坡成生机理的明晰认识和未建立正确的量化模型。本文根据我国长江三峡工程库岸和西南山区积累的大量滑坡实例调查资料并参考国外的一些研究成果,排除了地形控制论与地层控制论观点,阐明了滑坡形成的必要条件是斜坡具有易滑结构;滑坡发生的充分条件是有一定强度的诱发因素作用。故而诱发因素的动态变化对滑坡发生的时间具决定意义。
鉴于地下水诱发的岩质滑坡分布最广,为建立正确的水力启动模型,本文归纳了近代典型岩质滑坡的主要特征：（1）滑面是导水性差异最大的贯通面;（2）滑体长度大而厚度小,长厚比多在20左右;（3）滑坡前缘段先启动;（4）临滑前在前缘段有渗水、冒水或喷水现象;（5）出水宽度之和远小于前缘段总宽度。根据这些特征和水力学、水文地质学的成熟理论指出jennings（1970）等人提出的岩质斜坡稳定性模型存在下列问题：（1）未表明贯通面上岩体重力分布状况;（2）空隙水压力的分布特征与前述滑坡现象和水力学原理相悖;（3）未考虑通水率问题。然后,本文按顺向坡中的易滑超倾坡和椅状坡两个类型建立了斜坡稳定性模型和滑坡水力启动临界值（基本）计算公式。提出潜滑面的综合内摩擦角和通水率的确定方法：（1）滑坡反算;（2）对无水压滑坡滑面倾角和渗水边坡通水率进行观测统计;（3）剪切试验和简易水文地质试验;（4）物探方法。
本文还讨论了新模型的实用意义和应用范围,并对解决这类复杂地质灾害问题的研究途径发表了作者的认识,强调了积累经验的重要性。     

Theory of reconstructing the spatial distribution of the filtration coefficient in vascularized soft tissues: Exact and approximate inverse solutions

We formulate and solve an inverse poroelastic problem to reconstruct the spatial distribution of the filtration coefficient for soft vascularized tissue from a collection of displacement fields obtained during its relaxation. We present two solutions for the inverse problem, both developed using direct non-iterative approach. The first is a simple closed form approximate solution. It depends upon the approximation that the interstitial pressure is spatially homogeneous. The second solution relaxes this assumption. It requires the solution of a Poisson equation to reconstruct the pressure distribution. The inversion thus obtained is exact in the limit of negligible percolation. We present inversion results from computational experiments to validate and compare the two approaches. The closed form solution provides accurate results in favorable circumstances. The exact-pressure approach accommodates inhomogeneous loading easily. Both approaches are somewhat sensitive to noise. Our results suggest that it may be possible to image the filtration coefficient using this approach. Future work would include further test with noisy data and experimental validation.     

Interaction of viscous wakes with a free surface

The interaction of laminar wakes with.free-surface waves generated by a moving body beneath the surface of an incompressible viscous fluid of infinite depth was investigated analytically. The analysis was based on the steady Oseen equations for disturbed flows.The kinematic and dynamic boundary conditions were linearized for the small-amplitude free-surface waves. The effect of the moving body was mathematically modeled as an Oseenlet.The disturbed flow was regarded as the sum of an unbounded singular Oseen flow which represents the effect of the viscous wake and a bounded regular Oseen flow which represents the influence of the free surface. The exact solution for the free-surface waves was obtained by the method of integral transforms. The asymptotic representation with additive corrections for the free-surface waves was derived by means of Lighthill‘s two-stage scheme. The symmetric solution obtained shows that the amplitudes of the free-surface waves are exponentially damped by the presences of viscosity and submergence depth.     

均匀分布荷载作用下压电悬臂梁弯曲问题解析解

对由横观各向同性电介质构成的悬壁梁在均匀分布荷功作用下的弯曲问题进行了研究，采用逆解法，建立了问题的应力函数与电势分布函数，进而得到问题的精确多项式解析解。     

准饱和黄土中暗穴水动力扩展响应的研究

为分析强降水过程中暗穴扩展机理,在野外调查资料的基础上,建立了准饱和黄土暗穴的扩展计算模型,概化为弹性准饱和土层中无限长圆柱形孔洞表面受水压力的动力响应问题。通过引入势函数,得到了Lap lace变换域中的应力、位移及孔隙水压力的解析表达式,并利用数值逆变换方法求得时域解,分析了降雨历时及饱和度等因子对暗穴动力响应的影响。结果表明,水动力是引起黄土暗穴扩展的主要因素,水压力作用历时对位移及应力有较大的影响,同时饱和度的细微变化对径向位移有显著影响。     

Uncertainty quantification for dynamics of geometrically nonlinear structures coupled with internal acoustic fluids in presence of sloshing and capillarity

In this paper, we propose an uncertainty quantification analysis, which is the continuation of a recent work performed in a deterministic framework. The fluid–structure system under consideration is the one experimentally studied in the sixties by Abramson, Kana, and Lindholm from the Southwest Research Institute under NASA contract. This coupled system is constituted of a linear acoustic liquid contained in an elastic tank that undergoes finite dynamical displacements, inducing geometrical nonlinear effects in the structure. The liquid has a free surface on which sloshing and capillarity effects are taken into account. The problem is expressed in terms of the acoustic pressure field in the fluid, of the displacement field of the elastic structure, and of the normal elevation field of the free surface. The nonlinear reduced-order model constructed in the recent work evoked above is reused for implementing the nonparametric probabilistic approach of uncertainties. The objective of this paper is to present a sensitivity analysis of this coupled fluid–structure system with respect to uncertainties and to use a classical statistical inverse problem for carrying out the experimental identification of the hyperparameter of the stochastic model. The analysis show a significant sensitivity of the displacement of the structure, of the acoustic pressure in the liquid, and of the free-surface elevation to uncertainties in both linear and geometrically nonlinear simulations.