饱和土中球空腔的瞬态动力响应

采用工程上通用的饱和土力学模型,考虑流体与固全之间的耦合作用,利用Ｌａｐｌａｃｅ变换求解了饱和土中球空腔的瞬态动力响应问题,得到了变换域内的解析解,借助数值Ｌａｐｌａｃｅ换求解了饱和土中球空腔瞬态动力响应的位移、应力及孔压的变化规律,为分析地下结构瞬态动力响应提供了一种有效的方法,模型符合工程实际,有一定的工程应用价值。     

圆锥壳自由振动传递函数解

本文在线性弹性理论基础上，给出了一种求解圆锥薄壳自由振动的渐进传递函数解法，壳体的三个位移分量，外力和边界条件首先沿环向展开的Ｆｏｕｒｉｅｒ级数，然后关于时间变量进行Ｌａｐｌａｃｅ变换，这样就将壳体的控制方程化为一系列含复参数ｓ的变系数常微分方程组，通过定义状态变量。得到了壳体动力学问题的状态空间控制微分方程，引入一小参数，并利用摄动技术就可以得到微分方程的渐进传递函数解，将各于锥段的解进行综合，     

弹性基础上简支方板在阻尼介质中的塑性动力响应

通过Ｌａｐｌａｃｅ 变换,用矩量法求解弹性基础上简支方板在阻尼介质中的塑性动力响应,得出解析表达式。     

粘弹性矩形板的稳定性分析

根据动力系统的观点研究了四边简支粘弹性矩形板的稳定性，利用Ｌａｐｌａｃｅ变换得到了蠕变临界载荷λｃｒ和瞬时临界载荷λｃｓ。同时采用Ｌａｐｌａｃｅ变换和Ｇａｌｒｋｉｎ方法计算了时间相关载荷λ（ｔ）的峰值λ满足条件λｅｒ〈λ〈λｃｓ时，线性和非线性问题的挠度随时间的变化规律。     

论半无限长杆对有限长梁的横向弹性冲击问题

研究了半无限长弹性杆对有限长弹性梁的横向冲击问题，采用小高——中原对受冲击接触面的准静态处理方法，给出了描述这一问题的基本方程，并用Ｌａｐｌａｃｅ变换方法对它进行了求解，文中通过数值的Ｄｕｒｂｉｎ反演结果展示了杆梁间冲击问题的一些特点     

弹／粘塑性柱体扭转问题的函数Laplace变换解

在应力Ｌａｐｌａｃｅ变换分析粘塑性轴对称问题基础上，对弹性－弹／粘塑性圆柱体扭转全过程进行分析，根据柱体扭转的应力分布，构造应力函数与位移函数，并对函数进行Ｌａｐｌａｃｅ变换。相应求出圆柱体、空心圆柱体的Ｌａｐｌａｃｅ变换解，以及圆柱体的弹性－粘塑性交界线值     

正交各向异性层状弹性半平面动力奇异解及其应用

本文采用Ｌａｐｌａｃｅ－Ｆｏｕｒｉｅｒ联合变换及传递矩阵方法导出了正交各向异性层状弹性半平面动力问题的时域奇异解的解析表达式，讨论了奇异解的数值实施，并把奇异解应用于边界元，计算了地下直墙拱结构的动力响应问题。     

刚粘塑性强化球形薄壳在撞击体作用下的大变形动力分析

本文研究了在平头圆柱体的冲击下，薄球形壳的动力大变形。通过等度量变换，给出了球壳的变形模态。在Ｐｅｒｚｙｎａ和Ｓｙｍｏｎｄｓ的粘塑性本构模型基础上，设材料从Ｍｉｓｅｓ屈服条件，并假定弯矩的膜力不耦合。根据刚粘塑性强化材料的变分原理。给出球壳的运动方程结果与实验进行了比较，二者吻合较好。     

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。     

正交各向异性层状弹性半平面动力奇异解及其应用

本文采用Ｌａｐｌａｃｅ－Ｆｏｕｒｉｅｒ联合变换及传递矩阵方法导出了正交各向异性层状弹性半平面动力问题的时域奇异解的解析表达式，讨论了奇异解的数值实施。并把奇异解应用于边界元，计算了地下直墙拱结构的动力响应问题。     

Nonlinear flexural waves in fluid–filled elastic channels

Nonlinear waves on liquid sheets between thin infinite elastic plates are studied analytically and numerically. Linear and nonlinear models are used for the elastic plates coupled to the Euler equations for the fluid. One-dimensional time-dependent equations are derived based on a long-wavelength approximation. Inertia of the elastic plates is neglected, so linear perturbations are stable. Symmetric and mixed-mode travelling waves are found with the linear plate model and symmetric travelling waves are found for the nonlinear case. Numerical simulations are employed to study the evolution in time of initial disturbances and to compare the different models used. Nonlinear effects are found to decrease the travelling wave speed compared with linear models. At sufficiently large amplitude of initial disturbances, higher order temporal oscillations induced by nonlinearity can lead to thickness of the liquid sheet approaching zero.     

Application of the Discrete Fourier Transform to Study the Dynamics of Wave Packets

A method for solving equations that describe the dynamics of wave packets of the Tollmien–Schlichting waves in the boundary layer is proposed. The method of splitting the initial problem into the linear and nonlinear parts at each time step is used. The linear part is resolved by using an equation for spectral components of the wave packet with a subsequent Fourier transform from the space of wavenumbers to the physical space. A system of ordinary differential equations is solved in the physical space. The Fourier transform is performed by means of the library procedure of the fast Fourier transform. As examples, the problems solved were the linear dynamics of the wave packet concentrated in the vicinity of the instability region (i.e., a set of wave vectors in the space of wavenumbers for which the imaginary part of the eigenfrequency of the Tollmien–Schlichting waves is positive) and the nonlinear dynamics of the wave packet overlapping the instability region.     

基于扰动方程的超音速轴对称射流马赫波辐射研究

超音速不稳定波是导致剪切流失稳和转捩的主要不稳定模态,这种模态以马赫波的形式辐射到远场,从而产生强烈的声场。采用线性稳定性理论和非线性扰动方程(NLDE)分析,计算超音速轴对称射流不稳定波的扰动演化(Ma=2.1),对马赫波辐射进行研究,包括马赫波辐射方向、辐射源位置,以及随斯特劳哈尔数的变化情况。研究结果表明,在超音速轴对称射流中,马赫波沿固定方向辐射向远方,不稳定波相位沿另一方向传播,这两个方向相互正交;马赫波辐射源位置位于不稳定波压力幅值最大处;斯特劳哈尔数St越大,马赫波辐射的能力越强,辐射区域越集中。     

A method to recover water-wave profiles from pressure measurements

An operational formulation is proposed for reconstructing a time series of water surface displacement from waves using measurements of pressure. The approach is based on the fully nonlinear formulation for pressure below traveling-wave solutions of Euler’s equations developed by Oliveras, Vasan, Deconinck and Henderson. Its validity is tested using experiments in which both the pressure and the surface displacement are measured. The experiments include a wave system that is Galilean invariant – cnoidal waves, and wave systems that are not – reflected cnoidal waves and wave groups. We find that since the proposed formulation is nonlinear, it reproduces the amplitude spectrum of the measured surface displacements better than the hydrostatic model and better than the linear model that takes into account the pressure response factor due to small amplitude waves (the transfer function). Both the proposed formula and the transfer function reconstruct the surface reasonably well, with the proposed formula’s being about 5% more accurate.     

The influence of topography on the nonlinear interaction of Rossby waves in the barotropic atmosphere

ＴＨＥＩＮＦＬＵＥＮＣＥＯＦＴＯＰＯＧＲＡＰＨＹＯＮＴＨＥＮＯＮＬＩＮＥＡＲＩＮＴＥＲＡＣＴＩＯＮＯＦＲＯＳＳＢＹＷＡＶＥＳｉＮＴＨＥＢＡＲＯＴＲＯＰＩＣＡＴＭＯＳＰＨＥＲＥＸｉｏｎｇＪｉａｎ－ｇａｎｇ（熊建刚）ＹｉＦａｎ（易帆）ＬｉＪｕｎ（李钧）（...     

On the nonlinear dynamics of the traveling-wave solutions of the Serre system

We numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes a high-order finite-element method with smooth, periodic splines in space and explicit Runge–Kutta methods in time. Other forms of solutions such as cnoidal waves and dispersive shock waves are also considered. The differences between solutions of the Serre equations and the Euler equations are also studied.     

促进其线性频散特征另一种形式的Bousinesq方程

Ｂｏｕｓｉｎｅｓｑ方程能够用于模拟表面重力波传播过程中的折射、绕射、反射以及浅化，非线性作用等现象．用不同垂直积分方法所得到的二维Ｂｏｕｓｓｉｎｅｓｑ方程形式具有不同的线性频散特征．采用两个不同的水深层的水平速度变量组合，推导出一个新形式的Ｂｏｕｓｉｎｅｓｑ方程．通过对其参数的设置可得到精确的线性频散解Ｐａｄｅ近似４阶精度．其适用范围已由原来的浅水，向深水拓进．相速误差小于２％，其拓展适用范围可达到０８个波长水深．应用所得到的新型Ｂｏｕｓｉｎｅｓｑ方程，采用有限差分法，对经典工况进行了数值模拟，其计算结果表明，计算值与物模实验值吻合较好．这说明本文新形式的Ｂｏｕｓｓｉｎｅｓｑ方程对变水深非线性效应所产生的能量频散有着较为精确的描述     

Internal waves in a two‐layer system using fully nonlinear internal‐wave equations

In order to understand the nonlinear effect in a two‐layer system, fully nonlinear strongly dispersive internal‐wave equations, based on a variational principle, were proposed in this study. A simple iteration method was used to solve the internal‐wave equations in order to solve the equations stably. The applicability of the proposed numerical computation scheme was confirmed to agree with linear dispersion relation theoretically obtained from variational principle. The proposed computational scheme was also shown to reproduce internal waves including higher‐order nonlinear effect from the analysis of internal solitary waves in a two‐layer system. Furthermore, for the second‐order numerical analysis, the balance of nonlinearity and dispersion was found to be similar to the balance assumed in the KdV theory and the Boussinesq‐type equations. Copyright © 2009 John Wiley & Sons, Ltd.     

促进其线性频散特征另一种形式的Bousinesq方程

Ｂｏｕｓｉｎｅｓｑ方程能够用于模拟表面重力波传播过程中的折射、绕射、反射以及浅化，非线性作用等现象．用不同垂直积分方法所得到的二维Ｂｏｕｓｓｉｎｅｓｑ方程形式具有不同的线性频散特征．采用两个不同的水深层的水平速度变量组合，推导出一个新形式的Ｂｏｕｓｉｎｅｓｑ方程．通过对其参数的设置可得到精确的线性频散解Ｐａｄｅ近似４阶精度．其适用范围已由原来的浅水，向深水拓进．相速误差小于２％，其拓展适用范围可达到０８个波长水深．应用所得到的新型Ｂｏｕｓｉｎｅｓｑ方程，采用有限差分法，对经典工况进行了数值模拟，其计算结果表明，计算值与物模实验值吻合较好．这说明本文新形式的Ｂｏｕｓｓｉｎｅｓｑ方程对变水深非线性效应所产生的能量频散有着较为精确的描述