变形三重介质三渗模型的压力动态分析

在应力敏感油藏的试井分析中,常岩石特性的假设对于确定传导率和储存系数可能引起较大的误差。研究了应力敏感地层中三孔三渗流动模型的压力响应,不仅考虑了储层的三孔三渗特征,而且考虑了井筒储集效应和应力敏感地层中介质的变形,引入了渗透率模数,建立了应力敏感地层三孔三渗流动的数学模型,渗透率依赖于孔隙压力变化的流动方程是强非线性的,因而采用数值方法求解数学模型,并探讨了变形参数和三重介质参数变化时压力的变化规律,给出了典型的压力曲线图板,这些结果可用于试井分析。     

变形介质双渗模型非线性流动模拟

在碳酸盐油藏和低渗油藏的渗流问题研究中,传统的研究方法都是假设地层渗透率是常数,然而对于地层渗透率是压力敏感的,这样的假设,对压力的变化将导致较大的误差。研究了应力敏感地层中双渗流动模型的压力不稳定响应,不仅考虑了储层的双渗特征,而且考虑了应力敏感地层中介质的变形,建立了应力敏感地层双孔隙度、双渗透率流动的数学模型,渗透率依赖于孔隙压力变化的流动方程是强非线性的,采用Douglas-Jones预估-校正法获得了圆井定产量生产和定压生产时无限大地层情况下的数值解,并探讨了变形参数和双重介质参数变化时压力变化规律,给出了典型压力曲线图版和应用实例。     

计及结构阻尼的等截面梁纯弯曲振动的非线性分析

针对考虑挠度微分方程中高阶项所引起的几何非线性及材料阻尼所引起的阻尼非线性的梁，建立了梁纯弯曲振动时的非线性运动方程。利用非线性理论对该非线性问题进行了研究，得到了周期解稳定和不稳定区域的分界线方程和频率响应方程，得到忽略梁非线性因素的条件，得到了梁挠度微分方程中高阶项所引起的几何非线性项具有软特性效应等四点结论。     

等截面梁纯弯曲振动的几何非线性分析

在讨论梁纯弯曲微幅振动时，考虑在材料力学的讨论中梁的挠度微分方程忽略项后，线性问题变为非线性问题。利用非线性理论对该非线性问题进行了讨论，得到了周期解稳定和不稳定区域的分界线方程和频率响应方程，得到忽略挠度几何非线性因素的条件。     

一类具有非线性边界流的双重退化抛物型方程的临界指标

本文研究了一类具有非线性边界流的双重退化抛物型方程,该方程可用来描述多孔介质中的非牛顿渗流现象,可以描述气体或液体在多孔介质中的流动,具有广泛的实际背景.通过构造不同的自相似上、下解得到了方程的临界指标,即整体存在指标po和临界Fujita指标pc.主要结果为:当0＜p≤po时,方程存在整体解;当po＜p＜pc时,方程...     

浸液轴向运动板的非线性自由振动和内共振分析

以竖直浸没于液体中的轴向运动矩形板作为研究模型,根据经典薄板理论以及von Kámán非线性几何关系,得到流-固耦合系统的非线性振动微分方程。假定液体为无黏、无旋、不可压缩的理想流体,流体对板的动压力采用速度势函数及Bernoulli方程描述。然后应用直接多尺度法求解系统的非线性偏微分方程,根据可解性条件,获得系统的非线性频率。分析了浸液轴向运动板的1:1内共振及1:3内共振现象,并讨论了系统参数对该流-固耦合系统非线性动力学特性的影响。     

粉末注射成形喂料充模层状二维流动的基本方程

将粉末注射成形喂料在薄壁模腔中的流动视为层状二维流动,以喂料流动的守恒方程组为基础,建立了描述粉末注射成形喂料充模流动的数学模型。推导了喂料熔体流导率的计算公式,得出压力场的控制方程是一非线性椭圆偏微分方程。使模型的计算成为可能,为进一步对粉末注射成形进行计算机模拟和数值分析奠定了数学基础。     

非线性粘弹性梁方程的整体动力学

考虑具有介质阻尼及非线性粘弹性本构关系的梁方程，证明了它的有界吸收集和有限维惯性流形的存在性，并由此得到在一定的条件下所给偏微分方程等价于-常微分方程组的初值问题。     

多孔介质中两相可混溶驱动问题的特征-混合动态有限元方法(英文)

数学上,多孔介质中一种不可压流体对另一不可压流体的相溶驱动由两个耦合的非线性偏微分方程组成,其中一个是关于压力的椭圆方程,另一个是关于浓度的抛物方程。本文用特征有限元方法结合动态有限元空间来逼近浓度,而压力和达西速度则由混合元方法来同时逼近。通过采用负模估计,我们给出了收敛性分析与误差估计。     

光纤中两个高阶变系数薛定谔方程的精确解

本文创造性地运用辅助方程方法研究了高阶变系数非线性偏微分方程的求解,其实质是基于常微分方程的解构造非线性偏微分方程的精确解。文章借助几个辅助常微分方程构造了两个高阶变系数非线性薛定谔方程的多个新型精确解,包括亮孤子、暗孤子以及单周期波解等,并推广了其中一个方程,给出了该方程的一些新型精确解。     

Magnetofluiddynamic flow with a pressure gradient and fluid injection

Summary The nonlinear partial differential equation of motion for an incompressible fluid flowing over a flat plate under the influence of a magnetic field and a pressure gradient, and with or without fluid injection (or ejection) through the plate is transformed to a nonlinear, third order ordinary differential equation by using a stream function and a similarity transformation.The necessary boundary conditions are developed for flow with and without fluid injection (or ejection), and an example is presented to illustrate the solution to the flow problem.The controlling equation reduces to the well known Falkner-Skan equation when the magnetic field is zero, and if additionally the pressure gradient is zero, the equation reduces to the Blasius equation.     

Magnetohydrodynamic flow for a non-Newtonian power-law fluid having a pressure gradient and fluid injection

Summary The nonlinear partial differential equation of motion for an incompressible, non-Newtonian power-law fluid flowing over flat plate under the influence of a magnetic field and a pressure gradient, and with or without fluid injection or ejection, is transformed to a nonlinear third-order ordinary differential equation by using a stream function and a similarity transformation.The necessary boundary conditions are developed for flow with and without fluid injection (or ejection), and a solution for four different power-law fluids, including a Newtonian fluid, is presented.The controlling equation includes, as special cases, the Falkner-Skan equation and the Blasius equation.     

蛋白质气泡有限变形研究

根据粘弹性材料有限变形的应变能密度函数、Maxwell模型的松弛函数及气泡的变形梯度张量,推导出蛋白质气泡有限变形的应力方程。并结合气泡的平衡方程,得到气泡在动态压力作用下有限变形时内径相对变化率随时间变化的表达式。运用该表达式,通过数值模拟方法,对蛋白质气泡有限变形的非线性特性、径向变形随气泡内外压力差、膜的厚度以及膜的粘性的变化规律进行了计算分析。结果表明:在不同载荷作用下,蛋白质气泡径向变形不但具有明显的非线性特性,而且气泡变形达到平衡时的变形大小和时间也不相同。增加气泡膜的厚度和膜的粘性既可以延长气泡变形达到平衡的时间,又可以大大增强气泡承受载荷的能力。     

Linear and nonlinear parametric instability behavior of cylindrical sandwich panels subjected to various mechanical edge loadings

Linear and nonlinear dynamic instability behavior of cylindrical sandwich panels subjected to combined static and dynamic nonuniform in-plane loadings is studied in this article. The core compressibility effects are considered in the model by assuming fourth and fifth order expansions for the transverse and tangential displacement of the core. The exact stress distributions within the panel are determined by panel prebuckling analysis for the applied parabolic and partial edge loadings. Galerkin's method is used to reduce the governing partial differential equations of the shell panel into a set of nonlinear ordinary differential equations. Dropping the nonlinear term, dynamic instability regions are obtained by solving the Mathieu-type differential equation by the method of Fourier series. The characteristics feature of the stable and unstable regions are investigated by linear and nonlinear time history responses and phase plots of the shell panel in those regions using Newmark's time integration. Incremental harmonic balance (IHB) method is used to study the nonlinear frequency amplitude responses of the cylindrical sandwich panels.     

Vibration characteristics of moving sigmoid functionally graded plates containing porosities

This study investigates vibration characteristics of longitudinally moving sigmoid functionally graded material (S-FGM) plates containing porosities. Two types of porosity distribution, i.e., the even and uneven distributions, are taken into account. In accordance with the sigmoid distribution rule, the material properties of porous S-FGM plates vary smoothly along the plate thickness direction. The nonlinear geometrical relations are adopted by using the von Kármán non-linear plate theory. Based on the d’Alembert’s principle, the nonlinear governing equation of the system is derived. Then, the governing equation is discretized to a set of ordinary differential equations via the Galerkin method. These discretized equations are subsequently solved by using the method of harmonic balance. Analytical solutions are verified with the aid of the adaptive step-size fourth-order Runge–Kutta method. By using the perturbation technique, the stability of the steady-state response is highlighted. Finally, both natural frequencies and nonlinear forced responses of moving porous S-FGM plates are examined. Results demonstrate that the moving porous S-FGM plates exhibit hardening spring characteristics in the nonlinear frequency response. Moreover, it is shown that the type of porosity distribution, moving speed, porosity volume fraction, constituent volume fraction and in-plane pretension all have significant influence on the nonlinear forced responses of moving porous S-FGM plates.     

温度影响下Winkler-Pasternak弹性地基上多孔FGM矩形板的自由振动分析

基于经典薄板理论和Hamilton原理研究温度影响下Winkler-Pasternak弹性地基上多孔功能梯度材料(FGM)矩形板的自由振动特性。采用Voigt混合幂率模型和孔隙任意分布模型来表征多孔FGM矩形板的材料属性,并考虑多孔FGM矩形板内部均匀温升和材料具有温度依赖特性;应用物理中面推导弹性地基上多孔FGM矩形板自由振动的控制微分方程并进行无量纲化;采用微分变换法(DTM)对无量纲控制微分方程及其边界条件进行变换,引入典型的六种边界在MATLAB统一编程且保证计算精度一致,经过迭代收敛,求解出无量纲固有频率;通过算例研究了边界条件、梯度指数、升温、孔隙率、长宽比、边厚比、无量纲弹性刚度系数和无量纲剪切刚度系数对多孔FGM矩形板振动特性的影响。     

随从力作用下功能梯度矩形板的非线性振动

本文研究了切向均布随从力作用下简支FGM矩形板的非线性振动问题。按照材料组份体积分数的简单幂率分布规律,FGM板的材料常数仅沿厚度连续变化。由大挠度的von Karman理论建立了以应力函数和挠度函数表示的运动偏微分方程组,再由Galerkin法转化成非线性常微分方程。对随从力作用下的四边简支陶瓷/金属矩形板,讨论了随从力、梯度指标和边长比对板的动力特性的影响,得到了各种条件下板中心振幅与非线性基频的关系。     

非线性常微分方程高阶谐波平衡法傅里叶展开的简化

简化了一种求取非线性常微分方程高阶谐波解的近似解析计算方法。对平方和立方非线性项的傅里叶展开过程进行改进和简化，使计算过程变为两次矩阵运算即可完成展开过程，且两次矩阵运算过程一致，易于编程。以Duffing方程为算例，计算结果与数值方法一致，运算效率有所提高。     

Flutter of high-dimension nonlinear system for a FGM truncated conical shell

The nonlinear flutters of a truncated conical shell, which is subjected to aerodynamic pressure and aerodynamic heating, are researched. Material properties with gradient features along the radial direction depend on the temperature. The supersonic aerodynamic force is obtained by applying the first-order piston theory, including the correction factor for curvature. The temperature in the external surface of the functionally graded material truncated conical shell rises as a result of viscous aerodynamic heating, and the temperature distribution along the thickness can be described by polynomial series. Hamilton's principle is utilized to obtain the nonlinear partial differential equilibrium equation of the system. Using Galerkin's method, a high-dimensional nonlinear system can be derived. Without considering the parts of nonlinear terms and the external forcing excitation, the flutter boundaries are obtained by solving the eigenvalues problem. The influences of ratios of top radius to thickness, semi-vertex angle, and volume fraction index on nonlinear dynamic characteristics of functionally graded material truncated conical shell are studied in detail by the fourth-order Runge–Kutta algorithm.