热弹性波在偶应力固体界面上的反射和透射

基于广义热弹性无能量耗散的G-N理论,研究了两种不同偶应力固体界面上弹性波的反射和透射.首先,建立偶应力弹性固体中的运动方程和边界条件.然后,根据非传统界面条件推导出弹性波反射和透射的振幅比.最后,用法向能量守恒验证了数值计算结果,根据数值计算结果,讨论了微结构参数和热力学参数对弹性波反射和透射的影响.结果显示,偶应力热弹性固体界面处存在三种体波和一种表面波;微结构参数对所有波的传播都有影响,而热力学参数只对热波的影响显著.     

横观各向同性含液饱和多孔介质中应力波传播的特征分析

根据广义特征理论,对横观各向同性含液饱和多孔介质中应力波传播特性进行了特征分析．给出了特征曲面的微分方程以及沿次特征线的相容条件,得到了波阵面的解析表达式．详细地讨论了应力波在横观各向同性含液饱和多孔介质中传播时,其速度曲面和波阵面的形状及性质．分析结果亦表明,纯固体中应力波传播的特征方程,是含液饱和多孔介质中应力波特征方程的特例．     

弹性波在应变梯度固体界面上的反射与透射

研究了弹性波在应变梯度固体界面上的反射和透射.首先,通过应变能密度推导出应变梯度固体中的运动方程和界面条件.然后,根据非传统界面条件推导出弹性波反射和透射的振幅比.最后,用法向能量守恒验证了数值计算结果,根据数值计算结果,讨论了微结构参数对弹性波反射和透射的影响.结果发现,应变梯度固体中不仅存在体波而且还存在表面波,尤其是入射波波长越接近材料微结构的特征长度,微结构效应就会越显著.     

团簇取样法计算六方晶系GaN晶体中N K-edge电子能量损失谱近阈精细结构

利用多重散射自洽场方法,通过团簇取样计算了晶体的电子能量损失谱精细结构. GaN晶体中N K-edge 近阈结构的计算结果与实验谱线符合得很好.由于理论结果可以对不同能量损失区间的透射电子给出清楚标识,讨论了有关能量过滤像的实验.     

分离折叠波导慢波线的理论分析与实验研究

本文提出了一种多波导传输线模型,用以分析分离折叠波导慢波线,用场论方法分析了多波导系统,导出了它的特性导纳,进而推导了以此导纳函数描述的色散方程,并对输入阻抗与耦合阻抗进行了分析。相应于慢波线每一主要尺寸的改变,就色散与阻抗进行了计算,色散特性理论与实验值吻合较好,其差别在最低通带内一般小于5％,在正常工作频率范围内则不超过1％。     

弹塑性杆在刚性块轴向撞击下的动力屈曲

基于能量原理,对弹塑性杆在刚性块轴向撞击下的动力屈曲问题进行了讨论．用特征线法分析了刚性块轴向撞击弹塑性直杆时应力波传播的过程．考虑了弹塑性应力波传播对屈曲的影响,建立了该问题横向扰动方程．用幂级数解法,理论上给出了该问题的级数解．分析解的性质,得到了发生屈曲时的临界条件．通过理论分析和数值计算,得到了临界速度与冲击质量、临界长度及线性强化模量间的关系．     

浅水中群桩受力状况的理论研究

本文研究了两类浅水波:Cnoidal波和弧立波对圆柱群的绕射问题.采用Bessel坐标变换方法统一坐标系,并通过散射波解中系数的确定来满足各柱面零法向速度条件.对几种柱分布情况,用两类入射波分别计算了若干实例.对计算结果进行了讨论并与实验数据进行了比较,结果令人满意.     

微极热弹性无限板的轴对称自由振动

研究了在应力自由和刚性固定边界条件下,无能量耗散的均匀、各向同性微极热弹性无限板的轴对称自由振动波的传播,导出了相应的对称和斜对称模态波传播的闭合式特征方程和不同区域的特征方程.对短波的情况,应力自由热绝缘和等温板中对称和斜对称模态波传播的特征方程退化为Rayleigh表面波频率方程.根据导出的特征方程得到了热弹性、微极弹性和弹性板的结果.在对称和斜对称运动中计算了板的位移分量幅值、微转动幅值和温度分布,给出了对称和斜对称模式的频散曲线,并示出了位移分量和微转动幅值和温度分布的曲线.能够发现理论分析和数值结论是非常一致的.     

具有微极弹性构架的流体-饱和多孔固体中波在边界面处的传播

通过研究匀质非黏性液体半空间和微极流体饱和多孔固体半空间交界面处平面波的反射与透射,得到不同角度入射波的反射和透射系数.计算出反射波与透射波的振幅比数值,并用图表示出微极性和多孔性对反射和透射的影响.最后根据公式对一些特例进行了推导.     

爆炸作用下钢板层裂的数值分析

用一维运动模型对高能炸药在钢板表面接触爆炸时钢板中应力波的传播及其在钢板自由面上反射后引起的层裂现象进行了数值分析,并和前几年在我国进行的实验结果作了比较.发现当钢板采用流体弹塑性模型,并采用损伤积累层裂准则的情况下,计算所得的主裂片厚度是和实验结果合理地符合的.提出了一个计算主裂片厚度的近似公式,对实验中出现的多层的呈云母状结构的次裂片现象也作出了较满意的解释.     

A small time solutions for the KdV equation using Bubnov-Galerkin finite element method

A Bubnov-Galerkin finite element method with quintic B-spline functions taken as element shape and weight functions is presented for the solution of the KdV equation. To demonstrate the accuracy, efficiency and reliability of the method three experiments are undertaken for both the evolution of a single solitary wave and the interaction of two solitary waves. The numerical results are compared with analytical solutions and the numerical results in the literature. It is shown that the method presented is accurate, efficient and can be used at small times when the analytical solution is not known.     

基于拟Shannon小波浅水长波近似方程组的数值解

本文研究了浅水长波近似方程组初边值问题的数值解.利用小波多尺度分析和区间拟Shannon小波,对浅水长波近似方程组空间导数实施空间离散,用时间步长自适应精细积分法对其变换所的非线性常微分方程组进行求解,得到了浅水长波近似方程组的数值解,并将此方法计算的结果与其解析解进行比较和验证.     

The inverse scattering problem for a partially coated cavity with interior measurements

We consider the interior inverse scattering problem of recovering the shape and the surface impedance of an impenetrable partially coated cavity from a knowledge of measured scatter waves due to point sources located on a closed curve inside the cavity. First, we prove uniqueness of the inverse problem, namely, we show that both the shape of the cavity and the impedance function on the coated part are uniquely determined from exact data. Then, based on the linear sampling method, we propose an inversion scheme for determining both the shape and the boundary impedance. Finally, we present some numerical examples showing the validity of our method.     

非线性反应扩散方程的数值解

本文采用Petrov-Galerkin有限元法构造了非线性反应扩散方程的数值格式,既适用于全场性的初值,也适用于局部性的初值,利用全场性初值求得的进波数值解与精确解高度吻合,证明本方法与其它数值方法比较,有更高的精度和稳定性,利用各种局部性初值所算出的数值解表明,任何局部的扰动都会得到充分的发展,且当时间充分长后,演变为向左、右传播的行波,其波前的形状及传播速度完全由系统本身所决定,而与初值的类型无关.     

Shape identification of anisotropic diffraction gratings for TM-polarized electromagnetic waves

This paper concerns the shape identification problem of anisotropic periodic structures which are known as diffraction gratings. We study the so-called Factorization method as a tool for reconstructing the anisotropic periodic media from measured spectral data involving scattered electromagnetic waves in TM modes. This sampling method provides a simple criterion to compute a picture of shape of diffraction gratings in a rapid way. We propose a rigorous analysis for the method as well as numerical experiments to examine its performance.     

On the Computation of Nonlinear Planetary Waves

A numerical method is developed to solve a class of nonlinear, nonlocal eigenvalue problems defined in an infinite strip, and is applied to compute solitary planetary waves in a sheared zonal current on the beta-plane. This method, an iterative procedure derived from the natural variational structure of these problems, is implemented in the physical case when the ambient parallel flow has a linear or a quadratic velocity profile. The results of the numerical experiments establish rigorous limits on the range of validity of the formal asymptotic theory of weakly nonlinear long waves, and also reveal some new phenomena involving strongly nonlinear waves. The iterative procedure is analyzed in a general setting, and is shown to be globally convergent without restriction on the wave amplitude.     

The inverse scattering problem for a partially coated penetrable cavity with interior measurements

In this paper we consider the inverse scattering problem for a cavity that is bounded by a partially coated penetrable inhomogeneous medium of compact support and recover the shape of the cavity and the surface conductivity from a knowledge of measured scattered waves due to point sources located on a curve or surface inside the cavity. First, we prove that both the shape of the cavity and the surface conductivity on the coated part can be uniquely determined from a knowledge of the measured data. Next, we establish a linear sampling method for determining both the shape of the cavity and the surface conductivity. A central role in our justification is played by an eigenvalue problem which we call the exterior transmission eigenvalue problem. Finally, we present some numerical examples to illustrate the validity of our method.     

有限深两层流中内孤立波的高阶解*

本文研究有限水深两层流中孤立波的三阶近似理论,并考虑了自由表面对孤立波的影响,运用坐标变形方法得到了三阶内孤立波的发展方程,求得波速的解析表达式。对方程进行了数值计算,得到了几种参数下三阶解曲线,指出自由表面对波型和波速的影响是二阶的。计算表明三阶解对一阶、二阶解有明显的改进,使其更加接近试验结果。     

Numerical solutions and stability analysis for solitary waves of complex modified Korteweg–de Vries equation using Chebyshev pseudospectral methods

In this research article, the authors investigate the interaction of solitary waves for complex modified Korteweg–de Vries (CMKdV) equations using Chebyshev pseudospectral methods. The proposed method is established in both time and space to approximate the solutions and to prove the stability analysis for the equations. The derivative matrices are defined at Chebyshev–Gauss–Lobbato points and the problem is reduced to a diagonally block system of coupled nonlinear equations. For numerical experiments, the method is tested on a number of different examples to study the behavior of interaction of two and more than two solitary waves, single solitary wave at different amplitude parameters and different polarization angles. Numerical results support the theoretical results. A comprehensive comparison of numerical results with the exact solutions and other numerical methods are presented. The rate of convergence of the proposed method is obtained up to seventh-order.     

Interacting dromions for electron acoustic waves

Analytical and numerical investigation of electron acoustic waves shows the existence of interacting dromions solutions. Using the asymptotic perturbation (AP) method, based on Fourier expansion and spatio-temporal rescaling, it is found that the amplitude slow modulation of Fourier modes is described by a system of nonlinear evolution equations. This system is C-integrable, i.e. can be linearized through an appropriate transformation of the dependent and independent variables. We demonstrate the existence of dromion solutions, which propagate with their own group velocity and during a collision maintain their shape, the only change being a phase shift. Numerical results are used to check the validity of the AP method.