非保守弹性动力系统两类变量的广义拟变分原理及其应用

按照广义力和广义位移之间的对应关系,将弹性动力学的各基本方程分别乘上相应的虚量,然后在相应的体积域和面积域上积分,将积分式代数相加,再将代数和在时间域上积分,代入本构关系,并考虑到体积力和面积力均为伴生力,进而建立了非保守弹性动力系统的第1类两类变量的广义拟变分原理;再应用类似的方法,通过代入另一类本构关系,建立了非保守弹性动力系统的第2类两类变量广义拟变分原理.应用第1类两类变量广义拟余能原理给出同时求解1个典型的非保守弹性动力系统的固有频率、变形和内力的计算方法.最后,讨论了有关问题.     

新增大楼对地倾斜观测的影响

根据弹性力学的基本理论,建立了水平矩形薄板模型,推导了计算此类薄板影响地倾斜的基本公式,通过该模型的模拟计算,分别得出了由大楼质量造成的附加引力位对观测点水平摆的偏转角度和大楼负荷产生的地倾斜,并针对厦门地震台的实际情况,讨论了大楼对地倾斜观测的影响。     

应用混合变量法求解均布谐载作用下的矩形板的受迫振动

应用混合变量法求解了矩形板在均匀谐载作用下的受迫振动问题，给出了三边固定一边自由矩形板在均匀谐载作用下的受迫振动的稳态解。所获得的计算结果，不仅具有重要的理论价值。而且可以为工程实际直接采用。     

利用攀枝花仁和台压容应变资料预测强震

20世纪90年代中后期，攀枝花仁和钻孔应变台RZB－1型压容应变仪记录了数次强震。通过计算该台的主应变方向，并结合强震进行分析，发现强震发生的该台的最大或最小主应变方向附近；计算了该台单位体积应变势能值，发现强震发生在应变势能值升至峰值后回落的过程中。这两种方法对于强震预测有重要意义。对于这些现象给出弹性力学解释，并总结出了预报三要素判据。     

横向非均匀介质中弹性地震波传播的数值模拟

应用混合变量弹性动力学方程和线性常微分方程组的矩阵指数解法，将层状介质中广泛应用的弹性波传播矩阵解法推广至横向非均匀介质，给出了一种可计算复杂地质体中弹性波传播的广义传播矩阵数值解法。该方法可模拟任意震源及所产生的各种体波、面波，数值结果表明具有很高的计算精度。     

非弹性反应谱计算的一个改进算法

本文就非弹性地震反应谱的计算问题（运动方程的形式，谱参量的选取，方程解算中恢复力模型上拐折点的处理和时间积分方法），给出了几点理论考虑，介绍了一个改进的算法。这一算法具有精度好和效率高的优点，这对做好结构抗震设计和其它地震工程问题中需要处理大量强震动数据的分析研究工作是有利的。文中还就双线型恢复力模型具体计算了2个例子（一个为屈服强化情形，另一个为理想弹塑性情形）。最后联系计算工作和计算结果，对非弹性反应谱计算中的其它有关事项做了补充讨论和说明。     

建筑变形后幕墙结构屈曲破坏临界荷载研究

为解决传统建筑沉降变形中存在的幕墙结构易发生变形、稳定性较差等问题,提出建筑沉降变形中幕墙结构屈曲稳定临界荷载的研究。选取框架玻璃幕墙作为研究对象,建立玻璃面板的有限元模型,分别从X、Y、Z三个方向对玻璃面板施加平动自由度约束力,进行幕墙结构屈曲稳定临界荷载的模拟;然后在建筑底部不同节点处设置竖向弹簧,通过调节弹簧刚度模拟建筑沉降变形的竖向作用力,在此基础上,采用能量法分别计算玻璃肋的应变势能、外力势能和弹性约束势能,根据势能驻值原理计算得出建筑沉降变形中幕墙结构屈曲稳定临界荷载;最后设置不同的玻璃肋参数,选取单一变化因素进行实验。实验结果表明:在不同玻璃肋跨度和截面厚度对比下,所提方法的计算结果较为准确,且所提方法的临界荷载计算耗时低于其他方法,具有较高的实际应用价值。     

论不同模式大气中的静力适应过程

为了研究大气静力平衡适应过程的本质,利用波动理论和能量转换角度,分别对完全可压缩的等温大气模型、滞弹近似下的等温大气模型和层结中性大气模型进行研究比较.结果表明：大气静力平衡适应过程的本质是声波和混合声重力波对扰动能量的频散过程,滞弹近似模型和层结中性模型均不能完全描述此适应过程;在波动假设下,此三类大气模型中扰动物理量之间的偏振关系同波动的性质有关,气团的运动方程均为椭圆方程,声波和混合声重力波对气团运动的作用差异较显著.
大气静力平衡适应过程中扰动能量以有效势能、有效弹性势能、动能或波动能量的形式存在并相互转换;扰动有效势能与其他形式能量之间的转换与混合声重力波或者重力内波有关,扰动有效弹性势能与其他形式能量之间的转换与声波有关.在完全可压缩的等温大气模型中,扰动有效势能增加1个单位,其中69.9%来自扰动垂直动能,其余30.1%来自扰动有效弹性势能.     

基于能量密度的自解耦互相关成像条件

基于能量密度构建的弹性波能量成像条件,可以准确提取弹性波场的能量信息,并可以有效压制背向散射.但是该成像条件得到的成像结果将所有弹性波场能量信息耦合在一起,难以区分纯波模式的能量信息.为此,我们从势能及动能两方面将能量场解耦,得到纯纵波（PP）、纯横波（SS）、转换波（C）能量场.根据能量守恒定律,基于Helmholtz原理对位移场的空间导数进行因式分解,将弹性势能自解耦得到纯纵波、纯横波及转换波势能;引入体应力构建得到P波及S波速度,将弹性动能分解为纯纵波、纯横波和转换波动能.从而,构建基于能量密度自解耦得到纯波能量互相关成像条件.数值实验表明自解耦成像条件可实现弹性波场能量的分解,并得到背向散射压制、振幅有效保持的PP波、SS波和C波成像结果.     

变分法在结构抗震验算中的应用

本文介绍了利用变分原理推导的拟势能原理和拟余能原理，把拟势能原理和拟余能原理应用到结构抗震分析中，从而对结构受地震惯性力大小的范围问题进行研究，可以看出拟势能原理和拟余能原理可分别求解结构竖向地震压力的近似上、下限值。     

Vibration of vertical rectangular plate in contact with water on one side

In this paper, the vibratory characteristics of a rectangular plate in contact with water on one side are studied. The elastic plate is considered to be a part of a vertical rectangular rigid wall in contact with water, the edges of which are elastically restrained and parallel to those of the rigid wall. The location and size of the plate on the rigid wall may vary arbitrarily. The water with a free surface is in a rectangular domain infinite in the length direction. The effects of free surface waves, compressibility of the water and the hydrostatic water pressure are neglected in the analysis. An analytical‐Ritz method is developed to analyse the interaction of the plate–water system. First of all, by using the method of separation of variables and the method of Fourier series expansion, the exact expression of the motion of water is derived in the form of integral equations including the dynamic deformation of the plate. Then the Rayleigh–Ritz approach is used to derive the eigenfrequency equation of the system via the variational principle of energy. By selecting beam vibrating functions as the admissible functions of the plate, the added virtual mass incremental (AVMI) matrices for plate vibration are obtained. The convergency studies are carried out. The effects of some parameters such as the depth and width of water, the support stiffnesses, location and aspect ratio of the plate and the plate–water size and density ratios on the eigenfrequencies of the plate–water system are investigated. Several numerical examples are given. The validity of AVMI factor approach is also confirmed by comparing the AVMI factor solutions with the analytical‐Ritz solutions. The results show that the approach presented here can also be used as excellent approximate solutions for rectangular plates in contact with water of infinite width and/or infinite depth. Copyright © 2000 John Wiley & Sons, Ltd.     

A new kind of optimal second-order symplectic scheme for seismic wave simulations

Here we introduce generalized momentum and coordinate to transform seismic wave displacement equations into Hamiltonian system. We define the Lie operators associated with kinetic and potential energy, and construct a new kind of second order symplectic scheme, which is extremely suitable for high efficient and long-term seismic wave simulations. Three sets of optimal coefficients are obtained based on the principle of minimum truncation error. We investigate the stability conditions for elastic wave simulation in homogeneous media. These newly developed symplectic schemes are compared with common symplectic schemes to verify the high precision and efficiency in theory and numerical experiments. One of the schemes presented here is compared with the classical Newmark algorithm and third order symplectic scheme to test the long-term computational ability. The scheme gets the same synthetic surface seismic records and single channel record as third order symplectic scheme in the seismic modeling in the heterogeneous model.     

Frequency analysis of rectangular plates continuous in one or two directions

The finite strip method is extended to the free vibration of rectangular plates continuous in one or two directions. A subroutine has been written for the computation of beam functions for continuous beams over any number of intermediate rigid supports and with simply supported or clamped end conditions. The standard finite strip method can thus be applied to plates continuous in both directions using the computed beam functions. The frequencies of 2 × 2 and 3 × 3 continuous panels with many different end conditions have been computed. The computations are also checked against published solutions and the accuracy is shown to be excellent.     

基于复阻尼理论的混合结构Rayleigh阻尼模型

混合结构的阻尼矩阵不满足经典阻尼条件,导致传统的模态叠加法无法适用。复阻尼理论无法适用于时域计算,其自由振动响应中存在发散现象。针对混合结构的阻尼矩阵非比例性和复阻尼理论的时域发散性,基于频域等效原则构建了求解Rayleigh阻尼系数的数学优化模型,进而得到与复阻尼理论等效的Rayleigh阻尼运动方程。算例分析表明:依据位移时程响应和结构等效阻尼比可证明Rayleigh阻尼运动方程的正确性。基于本文研究成果,等效复阻尼理论的混合结构Rayleigh阻尼运动方程可直接采用模态叠加法,结合其确定的结构等效阻尼比,为混合结构的振型分解反应谱法提供理论依据。     

Mantle flow with existence of plates and generation of the toroidal field

The observed plate velocities contain two types of motions. The poloidal component is related to the formation of ridges and subduction zones and the toroidal field expresses the shearing of surface plates. One very important consideration in modeling flow in the earth's mantle is the existence and motion of the lithospheric plates. The motion of plates represents a large-scale circulation with strong viscous coupling to the mantle underneath. The mantle flow probably is neither a purely free convection driven by buoyancy forces due to nonadiabatic temperature gradients in the mantle nor a forced convection generated by boundary forces, but a mixed convection that combines the effects of boundary and buoyancy forces. We present, in this paper, the mixed convection model resulting in a surface velocity field that contains both the observed poloidal and toroidal components.     

At‐a‐station hydraulic geometry relations, 1: theoretical development

This paper, the first of two, hypothesizes that: (1) the temporal variation of stream power of a river channel at a given station with varying discharge is accomplished by the temporal variation in channel form (flow depth and channel width) and hydraulic variables, including energy slope, flow velocity and friction; (2) the change in stream power is distributed among the changes in flow depth, channel width, flow velocity, slope, and friction, depending on the boundary conditions that the channels has to satisfy. The second hypothesis is a result of the principle of maximum entropy and the theory of minimum energy dissipation or its simplified minimum stream power. These two hypotheses lead to families of at‐a‐station hydraulic geometry relations. The conditions under which these families of relations can occur in the field are discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Problem on the vibrations of plates

Summary In this paper, the problem on the vibrations of rectangular, elliptical and circular plates of non-isotropic material have been solved by using Galerkin's method. With the help of this method, the same problem for an isotropic circular plate has also been considered at the end.     

超宽带天线矩形口径辐射特性研究

本文利用惠更斯等效原理，从时域和频域两方面研究了超宽带天线矩形口径的瞬态辐射特性，以及能量传播特性的解析解.最后利用二维模拟论证了激励脉冲在自由空间的传播特性与天线口径几何尺寸、形状和主辐射面、辐射波形之间的关系，得出轴线上的辐射波形与口径形状无关，与口径面积大小成正比的模拟结论，为设计超宽带天线口径和为进一步设计超宽带电磁辐射提供了理论依据.     

分段光滑曲线边界波动方程数值模拟研究

矩形网格有限差分法在地震波传播数值模拟方面具有计算速度快的显著优势,但该方法在处理复杂边界问题上存在着效率低的严重缺陷.本文针对分段光滑曲线边界定义了尖点处的一种正则导数,给出了矩形网格情形分段光滑曲线网格边界点法向导数的一种插值计算方法.采用矩形网格有限差分法对复杂边界地球介质模型进行地震波场数值模拟,并采用波场系列快照技术揭示地震波在起伏地表和复杂介质中的传播规律.模拟结果表明：法向导数插值计算方法为矩形网格有限差分法处理复杂边界提供了有效途径,采用波场系列快照技术可以清晰地展现地震波在反射界面的反射和透射规律、在尖点的绕射规律以及在自由表面的直达波和多次反射规律.