基于“方程解耦”算法的各向异性介质纵横波分离方法

各向异性介质纵横波耦合的特性,使得纵波信息的获取对于各向异性非常规储层地震数据采集和处理具有重要意义.常规方法主要包括基于散度旋度场的Helmholtz分解和基于频散关系的声波近似等两大类,但这两类方法都改变了纵波波场的振幅和相位信息,并进一步影响正演数值模拟和纵波偏移成像的最终结果.本文基于方程解耦的思想,通过将弹性刚度系数分量中的纵横波耦合项近似为纵波模量和横波模量的线性函数,推导得到单独的纵波和横波方程,从而实现各向异性介质的纵横波波场分离.与常规方法相比,“方程解耦”方法得到的纵波波场的振幅和相位信息都更为准确,且波场信息也更为完整,能够为各向异性介质的纵波数据处理提供重要的保障.

TTI介质弹性波近似解耦波动方程

借助Christoffel方程可求解出各向异性介质弹性波精确频散关系.利用近似方法进行处理,再通过傅里叶逆变换将频率波数域算子变换为时空域算子,可导出解耦的qP波或qS波波动方程.本文在TTI介质弹性波精确频散关系的基础上,利用近似配方法推导了qP波和qSV波近似频散关系,通过傅里叶逆变换推导了TTI介质qP波和qSV波解耦的波动方程.为了验证近似频散关系的有效性,利用两组模型参数对其进行数值计算,分析了相对误差在不同传播方向上的分布.随后使用有限差分方法分别对均匀、层状及复杂TTI介质弹性波近似解耦波动方程进行数值模拟,结果显示qP波和qSV波完全解耦,并且在各向异性参数η<0以及介质对称轴倾角变化较大的情况下,纯qP波和纯qSV波近似波动方程依然可以保持稳定.

矩形中厚板的解耦方程

从矩形中厚板弯曲问题的基本方程出发,利用数学的方法,把弹性厚板的基本方程组转化成为解耦的相互独立的偏微分方程.进而可以简化这类问题的求解过程.

微振动力学系统模型构造微分方程系数矩阵方法

对于多自由度定常约束微振力学系统的数学建模有许多方法 ,但这些方法不是受到使用条件限制就是计算繁琐 ,并且不适合于计算机建模。根据系统的动能、势能、耗散能量与运动方程决定的动能、势能、耗散能量分别相等的原理 ,提出了构造微分方程系数矩阵方法 (下称能量偏导法 )。论证了直接法[1] 、视察法[2 ,7] 是能量偏导法的特例。能量偏导法的优点是 :在建立运动方程的过程中 ,设有对时间求导的过程 ,也没有对方程整理和化简的过程。该方法既适用于单自由度系数又适合于多自由度系统 ,既适用于手工建模又方便于计算机建模。在该方法的基础上 ,本文又提出了运动方程解耦的数学条件 ,为广义坐标的选取指明了方向。文中也给出了能量偏导法的应用和结论。

基于声辐射模态的有源控制解耦

在声辐射模态有源噪声控制策略框架下,选择压电陶瓷片作为控制作动器。根据前四阶声辐射模态形状特点提出了四种压电作动器位置布置方法。理论分析及数值计算表明,以这种方式布放的压电作动器不仅能有效地降低结构辐射的声功率,而且控制过程中这四组作动器分工明确,从而将控制方程解耦。在控制前几阶声辐射模态声功率时可以将复杂的多输入/多输出控制系统转变为几个简单的、互相独立的单输入/单输出控制系统。

模态阻尼不解耦时的处理方法及其收敛性的证明

求解有阻尼多自由度结构系统的振动微分方程,常用实模态分析方法。但对于实模态矩阵不能使结构系统阻尼阵解耦的情况,势必去掉模态阻尼耦合项才可继续求解。有时求得结果误差太大。或者转而用复模态方法求解,但这将大大增加计算难度和计算工作量,往往必须在大容量计算机上求解。本文针对以上问题,指出在一定条件下,可避免用复模态求解,仍用实模态,而又计入了模态阻尼耦合项对结构振动响应的影响,因而可保证有较好的计算精度。本文方法的收敛性在数学上给予了证明,且具有计算简便,易于编程,占用计算机内存少,节省计算费用的特点。对一些不很复杂的结构,可在容量有限的计算机上求解。

基于声辐射模态的有源控制解耦在固定支承板上的研究

基于声辐射模态的主动控制理论,以固定支承板为例,通过四组作动器在固定支承板上的布放,使其能分别控制不同阶声辐射模态辐射的声功率,来使控制方程解耦,从而设计了比较简单与稳定的单输入/单输出控制系统,模拟计算取得了较好的控制效果。同时本文对控制过程中的溢出等问题进行了一定的探讨。

感应电动机中三相不对称绕组

对具有三相不对称交流绕组的感应电动机进行研究,对已有的研究成果进行分析与对比。在对称分量变换下建立了采用序阻抗表达的对称绕组相电压方程,得到了相绕组的自漏阻抗和互漏阻抗与等效阻抗和零序阻抗之间的关系。根据不对称绕组的实际情况,将等效阻抗和零序阻抗分别乘上不同的系数,建立了新的电压方程。采用磁动势分量进行了坐标变换,实现了电压方程的解耦,使计算得到简化。最后,通过实验对计算数据进行了验证。

车辆作用下的公路简支梁桥测试频率

应用达朗伯(D'Alembert)原理和欧拉-柏努利梁(Euler-Bernoulli)假设,建立了多个车辆-桥梁系统相互作用的理论模型。利用模态分析方法,使车辆-桥梁系统方程解耦,基于广义坐标的自由振动理论,对用广义坐标矩阵形式表示的解耦后的运动方程用固有振动理论求解,从而得出多个车辆作用下的桥梁有载频率。对于中小跨径的公路桥梁,往往采用单个车辆激振桥梁,激振后停于桥上,因此推导出了单个车辆作用下的桥梁有载频率解析表达式。讨论了车辆的位置、弹簧刚度、簧上质量、簧下质量和桥梁有载频率与桥梁固有频率差值之间的关系。

不稳定飞机气动参数辨识的一种实用方法

输出误差法是飞行器气动参数辨识最广泛采用的一种方法。但对于气动高度不稳定的飞机 ,辨识算法往往因状态方程组和灵敏度方程组积分发散而无法进行。为克服这一数值困难 ,将方程解耦技术引入输出误差法 ,发展了高度不稳定飞机气动参数辨识的一种实用方法——基于方程解耦的输出误差法。并对某鸭式布局飞机的纵向机动仿真数据进行了辨识仿真计算 。

Explicit Solutions for a New (2+1)-Dimensional Coupled mKdV Equation

An integrable （2＋1）-dimensional coupled mKdV equation is decomposed into two （1 ＋1）-dimensional soliton systems, which is produced from the compatible condition of three spectral problems. With the help of decomposition and the Darboux transformation of two （1＋1）-dimensional soliton systems, some interesting explicit solutions of these soliton equations are obtained.

Two-Soliton Solutions and Interactions for the Generalized Complex Coupled Kortweg-de Vries Equations

Kortweg-de Vries （KdV）-typed equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Generalized complex coupled KdV （GCCKdV） equations are investigated in this paper. Through the dependent variable transformations and symbolic computation, GCCKdV equations are transformed into their bilinear forms, based on which the one- and two-soliton solutions are obtained. Through the interactions of two solitons, the regular elastic collision are shown. When the wave numbers are complex, three kinds of solitonie collisions are presented： （i） two solitons merge and separate from each other periodically; （ii） two solitons exhibit the attraction and repulsion nearly twice, and finally separate from each other after such type of interaction; （iii） two solitons are ftuctuant in the central region of the collision. Propagation features of solitons are investigated with the effects of the coefficients in the GCCKdV equations considered. Velocity of soliton increase with the a increasing. Amplitude of v increase with the a increasing and decrease with the β increasing.

Nonequivalent Similarity Reductions and Exact Solutions for Coupled Burgers-Type Equations

Using the machinery of Lie group analysis,the nonlinear system of coupled Burgers-type equations is studied.Using the infinitesimal generators in the optimal system of subalgebra of the said Lie algebras,it leads to two nonequivalent similarity transformations by using it we obtain two reductions in the form of system of nonlinear ordinary differential equations.The search for solutions of these systems by using the G'/G-method has yielded certain exact solutions expressed by rational functions,hyperbolic functions,and trigonometric functions.Some figures are given to show the properties of the solutions.

Analytic Expansion for Ground-State Wavefunction of Time-Dependent Strong-Coupling Schrodinger Equation

The new method proposed recently by Friedberg, Lee, and Zhao is extended to obtain an analytic expansion for the ground-state wavefunction of a time-dependent strong-coupling Schroedinger equation. Two different types of the time-dependent harmonic oscillators are considered as examples for application of the time-dependent expansion. It is show that the time-dependent strong-coupling expansion is applicable to the time-dependent harmonic oscillators with a slowly varying time-dependent parameter.

Existence and Regularity of Solution to a Thermally Coupled Nonstationary System

In this paper, a coupled elliptic-parabolic system modeling a class of engineering problems with thermal effect is studied. Existence of a weak solution is first established through a result of Meyers＇ theorem and Schauder fixed point theorem, where the coupled functions σ（s）,k（s） are assumed to be bounded in the C（IR×（0, T））. If σ（s）,k（s） are Lipschitz continuous we prove that solution is unique under some restriction on integrability of solution. The regularity of the solution in dimension n ≤ 2 is then analyzed under the assumptions on σ（s） ∈w^1,∞（Ω×（0, T）） and the boundedness of σ＇（s） and σ″（s）.

Mathematical Model and Intelligent Control of a Quadcopter, with Non-conventional Membership Functions

This paper shows detailed steps for modeling a quadcopter with Euler-Lagrange equations, followed by controlling it with intelligent control that includes states decoupling. In addition, this control shows non-conventional membership functions for the most instable states, in order to get a fast and effective response.

Temperature control for thermal treatment of aluminum alloy in a large-scale vertical quench furnace

The temperature control of the large-scale vertical quench furnace is very difficult due to its huge volume and complex thermal exchanges. To meet the technical requirement of the quenching process, a temperature control system which integrates temperature calibration and temperature uniformity control is developed for the thermal treatment of aluminum alloy workpieces in the large-scale vertical quench furnace. To obtain the aluminum alloy workpiece temperature, an air heat transfer model is newly established to describe the temperature gradient distribution so that the immeasurable workpiece temperature can be calibrated from the available thermocouple temperature. To satisfy the uniformity control of the furnace temperature, a second order partial differential equation(PDE) is derived to describe the thermal dynamics inside the vertical quench furnace. Based on the PDE, a decoupling matrix is constructed to solve the coupling issue and decouple the heating process into multiple independent heating subsystems. Then, using the expert control rule to find a compromise of temperature rising time and overshoot during the quenching process. The developed temperature control system has been successfully applied to a 31 m large-scale vertical quench furnace, and the industrial running results show the significant improvement of the temperature uniformity, lower overshoot and shortened processing time.

New Exact Solutions and Special Coherent Structures for Coupled Integrable Dispersionless Equation

Using improved homogeneous balance method, we obtain new exact solutions for the coupled integrable dispersionless equation. On the basis of these exact solutions, we find some new interesting coherent structures by selecting arbitrary functions appropriately.

Solutions of the Schrdinger Equation for PT-Symmetric Coupled Quintic Potentials in Two Dimensions

This paper deals with the solutions of time independent Schrodinger wave equation for a two-dimensional PT-symmetric coupled quintic potential in its most general form. Employing wavefunction ansatz method, general analytic expressions for eigenvalues and eigenfunctions for first four states are obtained. Solutions of a particular case are also presented.

The Filtration Problems of Fluid Containing Solute Through Layered Porous Media

In this paper, we consider the problem (θ(x,U))_t=(K(x,U)U_x)_x-(K(x,U))_x (x,t)∈G_T (θ(x,U)V(x,t))_t=(DθV_x)_x+(V(KU_x-K))_x,(x,t)∈G_T, u(x,0)=u_0(x),V(x,0),(x,0)=V_0(x),0≤x≤2, U(0,t)=h_0(t),U(2,t)=h_2(t),0≤t≤T, V(0,t)=g_0(t),V(2,t)=g_2(t),0≤t≤T. Where, θ(x,U)=θ_1(x,U) when (x,t)∈D_1={0≤x<1,0≤t≤T};θ(x,U)=θ_2(x,U),(x,t)∈D_2={1<x≤2,0≤t≤T}.K(x,U)=K_i(x,U),(x,t)∈D_i. θ_i, K_i are the Moisture content and hy draulic conductivity of porous Media on D_i respectively. V be the the concentration of solute in the fluid. In addition we also require that U, V, (K(x,U)U_x-1) and DθV_x+V(KU_x-K) are continu ous at x=1. We prove the exisence, uniqueness and large time behavior of the problem by the method of reg ularization.