谱方法与开路边条件

谱方法精度较高,开路边条件能保证出了计算区域的波不再回来.但谱方法对边条件的限制较多,一般不允许开路边条件.为统一两者,本文进行了特殊处理.试算的结果表明,方法是有效的.     

用Symbolic Computation计算毛细重力波六阶解

本文首先运用Symbolic Computation在半物理平面(x,)上计算了毛细重力波的六阶解,得到了波形与色散关系,低阶解与 Hogan 结果一致。     

圆柱运动的内波渐近解

本文提供一个二维内波的渐近解法,对水平圆柱在无粘、稳定的密度连续分层流体中任意倾角运动的问题,得到了伴随的色散关系式,结合倾角α=90°圆柱垂直运动情况,给出了圆柱面上的边界条件和无穷远衰减条件。用渐近展开的方法求出內波的渐近解;对内波传布的规律作了讨论并与內波流场显示结果进行了比较,计算结果合理,运用本解法可望在求解分层流体中圆柱任意方向运动的问题,其它形状物体分层绕流的内波问题、非定常色散以及三维的内波问题中得到推广应用。     

一种考虑虚拟质量力的井筒气液两相压力波色散经验模型

考虑虚拟质量力、管道特性、频率、空隙率等因素,建立气液双流体压力波速模型,结合小扰动理论,提出了一种新的考虑虚拟质量力的两相压力波色散经验模型,与前人气液两相流（12.5%空隙率）中波色散实验测试数据对比是一致的,且经验公式也可达到准确求解压力衰减系数的目的．对控压钻井两相压力波进行计算,结果表明：(1)随系统压力的增大,压力波衰减系数呈现减小趋势,随节流阀动作频率增大、温度增大,压力波衰减系数呈现增大趋势;(2)随空隙率增大,压力衰减呈现先增大后减小趋势,空隙率在8%≤φ≤40%区间,两相压力衰减系数存在最大峰值,当压力为0.2 MPa时,空隙率在19.5%时达到峰值2.78 dB/m;(3)在低频下,波色散主要受相间机械及热力学平衡机制的制约,波色散现象明显;在高频下,相间来不及进行动量及能量交换,气液状态达不到有序的状态,因而波色散现象不明显;(4)不考虑虚拟质量力,两相压力衰减系数呈现增大趋势,波色散现象显著性下降．     

基于复数矢径的波叠加法解声辐射问题

利用波叠加法与结构动力分析中的相似性，提出了一种在波叠加法中克服解非唯一的通用方法，即在虚拟源强系统中加入一定的虚拟阻尼从而能获得全波数域内的唯一解，并以此为基础提出了一种新的加入虚拟阻尼的方法——复数矢径波叠加法。文中给出了脉动球和摆动球两个数值算例，计算结果表明：本文方法不仅能有效解决数值求解过程中解非唯一的问题，且计算时间只与标准波叠加法相当，计算精度却比同类方法高。     

外磁场调控下弹性波的反射和透射

本文应用麦克斯韦电磁学理论研究了在外磁场调控下弹性波的反射和透射问题．首先根据麦克斯韦方程组推导出洛伦兹力,其次根据运动方程推导出P波、SV波和SH波的色散关系,然后根据连续的界面条件推导出反射波和透射波相对于入射波的振幅比以及能流比．通过数值计算结果,详细分析了洛伦兹力对弹性波反射和透射的影响,结果发现,洛伦兹力不改变波动模式和色散性质,只改变弹性波的传播速度大小．最后,通过法向能量守恒验证了数值计算结果的可靠性．     

任意叠层球壳内的应力波传播

提出一种有效求解方法，求解了任意叠层球壳在动载荷作用下的应力波传播。首先，利用有限Ｈａｎｋｅｌ变换和Ｌａｐｌａｃｅ变换求解了每一单层的弹性动力学解。然后，利用叠层球壳的内、外边界条件和层与层之间的连接条件确定每一单层解中的待定常数。从而，我们可以得到应力波在叠层球壳内传播的精确解。最后，我们计算了在一个突加内压作用下的两层球壳（Ｓｔｅｅｌ／Ａｌ）和三层球壳（Ｓｔｅｅｌ／Ａｌｌｏｙ／Ａｌ）内的应力波传播。求解过程和计算结果表明文中提出的求解方法是简便可行的。     

爆轰波与惰性介质相互作用的迭代收敛计算

爆轰波与惰性介质相互作用的计算。可以用解析解和作图法求解。但在解析解求解中会遇到迭代发散问题。本文利用解反函数的办法进行计算,使迭代过程收敛。文中分别给出反射冲击波和反射稀疏波两种情况的迭代收敛计算公式。公式是按强爆轰的形式给出的,其中包括了C-J爆轰的特殊情况。     

两种高分辨率数值方法计算波前有非均匀流的变截面管内激波传播规律的比较

本文采用两种对间断解具有高分辨率的数值方法基于推广Riemann问题解的二阶Godunov型有限差分法和分裂算子的随机选取法,计算了微波在波前有非均匀定常流的一维变截面管道中的传播和波后流场特征,得到一致结果,用数值模拟方法揭示了这类运动的一些特殊规律。对比两种方法的计算过程和结果,可以看出,二阶Godunov型方法明显优于随机选取法。     

含孔平板弹性波散射问题的复变函数方法

本文采用平板弯曲波动理论及复变函数方法，对平板开孔弹性波的散射及动应力集中问题进行了分析研究，得到了传播急剧记波时此种平板弯曲波动问题的分析解。若同时采用保角射技术，就为主解平板任意形状开孔弹性波的散射及动应力集中问题提供了一种统一规范的方法。作为算例，本文给出了平板开圆孔和椭圆孔附近的动应力集中系数的数值结果，并对其进行了讨论。     

The high precision open boundary conditions designed for transient waves

ＴＨＥＨＩＧＨＰＲＥＣＩＳＩＯＮＯＰＥＮＢＯＵＮＤＡＲＹＣＯＮＤＩＴＩＯＮＳＤＥＳＩＧＮＥＤＦＯＲＴＲＡＮＳＩＥＮＴＷＡＶＥＳＺｏｕＧｕａｎｇ－ｙｕａｎ（邹光远）（ＤｅｐａｒｔｍｅｎｔｏｆＭｅｃｈａｎｉｃｓ．ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙＢｅｉｊｉ...     

Solitary Elastic Waves and Elastic Wavelets

A new group of wavelets that have the form of solitary waves and are the solutions of the wave equations for dispersive media is proposed to call elastic wavelets. That this group includes well-known Mexican-hat wavelets is proved. It is proposed to use elastic wavelets to study local features of the profile evolution of a solitary wave in an elastic dispersive medium     

Wave propagation in periodic buckled beams. Part I: Analytical models and numerical simulations

Periodic buckled beams possess a geometrically nonlinear, load–deformation relationship and intrinsic length scales such that stable, nonlinear waves are possible. Modeling buckled beams as a chain of masses and nonlinear springs which account for transverse and coupling effects, homogenization of the discretized system leads to the Boussinesq equation. Since the sign of the dispersive and nonlinear terms depends on the level of buckling and support type (guided or pinned), compressive supersonic, rarefaction supersonic, compressive subsonic and rarefaction subsonic solitary waves are predicted, and their existence is validated using finite element simulations of the structure. Large dynamic deformations, which cannot be approximated with a polynomial of degree two, lead to strongly nonlinear equations for which closed-form solutions are proposed.     

Surface waves propagation in shallow water: A finite element model

A two-dimensional (in-plane) numerical model for surface waves propagation based on the non-linear dispersive wave approach described by Boussinesq-type equations, which provide an attractive theory for predicting the depth-averaged velocity field resulting from that wave-type propagation in shallow water, is presented. The numerical solution of the corresponding partial differential equations by finite-difference methods has been the subject of several scientific works. In the present work we propose a new approach to the problem: the spatial discretization of the system composed by the Boussinesq equations is made by a finite element method, making use of the weighted residual technique for the solution approach within each element. The model is validated by comparing numerical results with theoretical solutions and with results obtained experimentally.     

Oblique interactions of weakly nonlinear long waves in dispersive systems

Studies on the oblique interactions of weakly nonlinear long waves in dispersive systems are surveyed. We focus mainly our concentration on the two-dimensional interaction between solitary waves. Two-dimensional Benjamin–Ono (2DBO) equation, modified Kadomtsev–Petviashvili (MKP) equation and extended Kadomtsev–Petviashvili (EKP) equation as well as the Kadomtsev–Petviashvili (KP) equation are treated. It turns out that a large-amplitude wave can be generated due to the oblique interaction of two identical solitary waves in the 2DBO and the MKP equations as well as in the KP-II equation. Recent studies on exact solutions of the KP equation are also surveyed briefly.     

Acoustics of Rotating Deformable Saturated Porous Media

We investigate wave propagation in elastic porous media which are saturated by incompressible viscous Newtonian fluids when the porous media are in rotation with respect to a Galilean frame. The model is obtained by upscaling the flow at the pore scale. We use the method of multiple scale expansions which gives rigorously the macroscopic behaviour without any prerequisite on the form of the macroscopic equations. For Kibel numbers A A(1), the acoustic filtration law resembles a Darcys law, but with a conductivity which depends on the wave frequency and on the angular velocity. The bulk momentum balance shows new inertial terms which account for the convective and Coriolis accelerations. Three dispersive waves are pointed out. An investigation in the inertial flow regime shows that the two pseudo-dilatational waves have a cut-off frequency.     

Nonlinear travelling waves in a hyperelastic rod composed of a compressible Mooney-Rivlin material

In this paper, we study strongly nonlinear axisymmetric waves in a circular cylindrical rod composed of a compressible Mooney-Rivlin material. To consider the travelling wave solutions for the governing partial differential system, we first reduce it to a nonlinear ordinary differential equation. By using the bifurcation theory of planar dynamical systems, we show that the reduced system has seven periodic annuluses with different boundaries which depend on four parameters. We further consider the bifurcation behavior of the phase portraits for the reduced one-parameter vector fields when other three parameters are fixed. Corresponding to seven different periodic annuluses, we obtain seven types of travelling wave solutions, including solitary waves of radial contraction, solitary waves of radial expansion, solitary shock waves of radial contraction, solitary shock waves of radial expansion, periodic waves and two types of periodic shock waves. These are physically acceptable solutions by the governing partial differential system. The rigorous parameter conditions for the existence of these waves are given.     

Dispersion and Attenuation of Surface Waves in a Fluid-Saturated Porous Medium

An investigation is conducted of propagation of surface waves in a porous medium consisting of a microscopically incompressible solid skeleton in which a microscopically incompressible liquid flows within the interconnected pores, and particularly the case where the solid skeleton deforms linear elastically. The frequency equations of Rayleigh- and Love-type waves are derived relating the dependence of wave numbers, being complex quantities, on frequency, as a result those waves are dispersive as well as inhomogeneous. Nevertheless, the amplitudes of both surface waves attenuate along the surface of the porous medium, whereas they decay exponentially receding from the surface of the medium.