共查询到19条相似文献，搜索用时 179 毫秒
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本文应用包括地壳破裂发震过程中具有激发及衰减的非线性Rayleigh阻尼,用Voigt粘弹性模型表示地壳,它能更全面地反映地壳介质分子之间的内摩擦造成的粘滞性阻尼,在数学方法上,用解非线性问题解析法的摄动理论结合动坐标的富氏级数,把问题的非线性控制方程组化为各阶线性化的控制方程组后,再简化为标准的Mathieu方程构成的耦连方程组,再用WKBJ方法,给出其在稳定区域的近似解,从而得出了问题的解析解。 相似文献
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把所有的参数都无量纲化,然后在证明了无量纲的非线性项的阻尼(与运动速度立方正比)系数B<1为小参数之后,把待求解的振幅函数展成B的收敛幂级数,再代入动力方程或方程组,得到一系列线性化的逼近方程或方程组,用以动坐标表示的广义富氏级数代入各级逼近方程或方程组,对Ⅰ、Ⅱ、Ⅲ型破裂的弹性断裂动力学问题和Voigt模型的粘弹性断裂动力学问题,都化为含时间自变量的Mathieu方程或方程组,用WKBJ方法得出其在稳定区域的渐近解。还用此法解了一个三维问题。 相似文献
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大气方程组的惯性流形 总被引：3，自引：0，他引：3
从一类非线性演化方程出发 ,得到其全局吸引子 ,并利用截断技巧讨论了它的惯性流形 .然后 ,根据大气方程组算子的性质 ,证明强迫耗散非线性大气算子方程即为这类非线性演化方程 ,从而在耗散算子满足谱间断条件下得到大气方程组的惯性流形的存在 ,为进一步研究大气方程组全局吸引子上的动力性质及设计性能良好的数值格式提供了基础 . 相似文献
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本文利用MHD二维不可压模式,研究了地球磁层顶边界区剪切流引起的Kelvin-Helmholtz（K-H）不稳定性问题,得到了一个新的非线性微分方程组.理论和数值分析表明:该问题的非线性演化对初值非常敏感,而且在雷诺数和磁雷诺数给定的条件下,Alfven马赫数（MA）对K-H不稳定性的非线性演化起决定性作用.这组方程蕴含几个吸引子,如不动点,极限环和奇异吸引子等,这体现了磁层顶非线性系统的复杂性.文中还发现背景磁场在磁层顶K-H不稳定性的非线性演化过程中起很重要的作用. 相似文献
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本文研究了磁层顶等离子体的一个基本模型,得到了一新的非线性常微分方程组.数值分析表明,在一定的磁Reynolds数范围内,系统呈现混沌行为,相轨道趋向于奇异吸引子. 相似文献
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朱镜清 《地震工程与工程振动》1983,(3)
本文根据文献〔1〕中的前两个定理,证明了Newmark法当且仅当2β≥γ≥1/2时对带有阻尼项的线性结构动力学方程组形成的积分格式是无条件稳定的,同时也完整地研究了此法的条件稳定问题。接着进一步讨论了包括弹塑性和非线性弹性情形在内的结构动力分析中的相应问题,指出文献〔1〕中的第三个定理也适用于非线性弹性情形;此外,对阶梯法应用于非线性弹性情形时间能发生的不稳定现象作了一定的分析,并介绍了一个减少不稳定性出现的可能性的方法。 相似文献
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本文用具有非线性Ｒａｙｌｅｉｇｈ阻尼的断裂动力学的控制方程组或方程来研究水平强震地面运动或垂直强震地面运动，并得出其解析解，数值计算结果显示，本文得出的结果与任意选择的两个强震记录是很相似的。 相似文献
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CHAO JiPing & LIU Fei National Marine Environmental Forecasting Center Beijing China The First Institute of Oceanography SOA Qingdao China Key Laboratory Regional Climate-Environment for Temperate East Asia Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China Graduate University of Chinese Academy of Sciences Beijing China 《中国科学D辑(英文版)》2007,50(1):153-160
Based on the developed Anderson and Moore's theory about cross-equatorial inertial jets and a nonlinear equivalence shallow water model, new universal functions are determined by the characters of the vortical large-scale air flow (atmosphere) or ocean current (ocean) related to the jet, then the potential vorticity and energy conservation equations along the streamline in the cross-equatorial in-ertial jets can be obtained. Because the governing equations are nonlinear, some limited multiple equi-libria of cross-equatorial inertial jets may exist. According to the character of large-scale air flow or ocean current outside the jets, the existent criterion for multiple eqnilibria in cross-equatorial inertial jets is discussed, and two examples for multiple equilibia of nonlinear governing equations are given. 相似文献
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《Advances in water resources》1996,19(5):297-315
The contamination of groundwater by various hazardous materials has emerged as a primary environmental issue. The pollution of oil reservoirs is a closely related problem in that microorganisms are involved in the contaminant process. The mathematical models that describe these phenomena involve a set of nonlinear advective-diffusive-reactive transport equations, which may involve reactions with all the species and are themselves coupled to growth equations for the subsurface bacterial population. In this article, we discuss and compare different mathematical models, present Eulerian-Lagrangian localized adjoint methods (ELLAM) and combine them with specific linearization techniques to solve these nonlinear transport systems. The derived numerical schemes systematically adapt to the changing features of governing equations. The relative importance of advection, diffusion and reaction is directly incorporated into the schemes by judicious choice of the test functions in the variational formulations. Numerical experiments are presented to show the potential of these methods. 相似文献
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A Taylor basis for kinematic nonlinear real-time simulations. Part I: The complete modal derivatives
Despite todays computational power, only small nonlinear numerical substructures may be simulated in real time. The size restriction on the substructures in nonlinear finite element analysis is primarily due to the time-consuming evaluation of the internal restoring forces, which is performed element-by-element in every iteration step. The present work constitutes the first of two papers presenting a method to simulate kinematic nonlinear structures more efficiently. It involves applying a reduced basis with modal derivatives representing the nonlinearities of the system in an efficient way. Previously, the modal derivatives have been determined from a set of approximate governing equations. In the present paper, a novel set of equations governing the complete modal derivatives is derived. This is done by introducing a Taylor series into the free undamped kinematic nonlinear equations of motion. Also, the approximate governing equations are improved by introducing a novel geometric restriction. By way of an example, it is shown that only the modal derivatives determined from the complete set of equations are consistent with the Taylor series. In the second paper, it is shown that the novel modal derivatives may be used in a so-called Taylor basis and that they improve the computational time and stability significantly. 相似文献
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Second-order exact ensemble averaged equation for linear stochastic differential equations with multiplicative randomness and random forcing is obtained by using the cumulant expansion ensemble averaging method and by taking the time dependent sure part of the multiplicative operator into account. It is shown that the satisfaction of the commutativity and the reversibility requirements proposed earlier for linear stochastic differential equations without forcing are necessary for the linear stochastic differential equations with forcing when the cumulant expansion ensemble averaging method is used. It is shown that the applicability of the operator equality, which is used for the separation of operators in the literature, is also subjected to the satisfaction of the commutativity and the reversibility requirements. The van Kampen’s lemma, which is proposed for the analysis of nonlinear stochastic differential equations, is modified in order to make the probability density function obtained through the lemma depend on the forcing terms too. The second-order exact ensemble averaged equation for linear stochastic differential equations with multiplicative randomness and random forcing is also obtained by using the modified van Kampen’s lemma in order to validate the correctness of the modified lemma. Second-order exact ensemble averaged equation for one dimensional convection diffusion equation with reaction and source is obtained by using the cumulant expansion ensemble averaging method. It is shown that the van Kampen’s lemma can yield the cumulant expansion ensemble averaging result for linear stochastic differential equations when the lemma is applied to the interaction representation of the governing differential equation. It is found that the ensemble averaged equations given for one the dimensional convection diffusion equation with reaction and source in the literature obtained by applying the lemma to the original differential equation are restricted with small sure part of multiplicative operator. Second-order exact differential equations for the evolution of the probability density function for the one dimensional convection diffusion equation with reaction and source and one dimensional nonlinear overland flow equation with source are obtained by using the modified van Kampen’s lemma. The equation for the evolution of the probability density function for one dimensional nonlinear overland flow equation with source given in the literature is found to be not second-order exact. It is found that the differential equations for the evolution of the probability density functions for various hydrological processes given in the literature are not second-order exact. The significance of the new terms found due to the second-order exact ensemble averaging performed on the one dimensional convection diffusion equation with reaction and source and during the application of the van Kampen’s lemma to the one dimensional nonlinear overland flow equation with source is investigated. 相似文献
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Jian-Fei Lu Dong-Sheng Jeng Tsung-Lin Lee 《Soil Dynamics and Earthquake Engineering》2007,27(9):875-891
Recently, considerable efforts have been devoted to evaluation of seismic dynamic response of a circular tunnel. Conventional approaches have considered integral liners embedded in an elastic medium. In this study, we re-examine the problem with piecewise liners embedded in a porous medium. Surrounding saturated porous medium of tunnels is described by Biot's poroelastic theory, while the liner pieces and the connecting joints are treated as curved beams and characterized by curved beam theories. The scattered wave field in the porous medium is obtained by the wave function expansion method. The differential equations governing the vibration of a curved beam is discretized by the General Differential Quadrature (GDQ) method. The domain decomposition method is used to establish the global discrete dynamic equations for the piecewise tunnel. The surrounding soil and the tunnel are coupled together via the stress and the displacement continuation conditions which are implemented by the boundary collocation method. Numerical results demonstrate that the stiffness difference between the liner piece and the connecting joints has a considerable influence on the internal forces of the liner piece. 相似文献
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The lithosphere is known to deform under geologic loads such as those due to surface volcanoes and submerged magma chambers. The lithosphere is modelled here as a linear viscous circular plate supported on the underlying asthenosphere, which in turn is modelled as a Winkler foundation. A two-dimensional steady creep relation is used to derive the governing partial differential equations for deflection, stress and bending moment. The temperature variation through the thickness of the lithosphere is of major importance and is included in the analysis. Solutions to the governing equations are obtained both in general and for an illustrative set of geometric, loading, material and thermal parameters. 相似文献
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《Advances in water resources》2007,30(4):927-936
A nonlinear model for single-phase fluid flow in slightly compressible porous media is presented and solved approximately. The model assumes state equations for density, porosity, viscosity and permeability that are exponential functions of the fluid (either gas or liquid) pressure. The governing equation is transformed into a nonlinear diffusion equation. It is solved for a semi-infinite domain for either constant pressure or constant flux boundary conditions at the surface. The solutions obtained, although approximate, are extremely accurate as demonstrated by comparisons with numerical results. Predictions for the surface pressure resulting from a constant flux into a porous medium are compared with published experimental data. 相似文献
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An analytical approach is developed to study the dynamic response of a flexible plate on single-layered saturated soil. The analysis is based on Biot's two-phased theory of poroelasticity and also on the classical thin-plate theory. First, the governing differential equations for saturated soil are solved by the use of Hankel transform. The general solutions of the skeleton displacements, stresses, and pore pressures, derived in the transformed domain, are subsequently incorporated into the imposed boundary conditions, which leads to a set of dual integral equations describing the corresponding mixed boundary value problem. These governing integral equations are finally reduced to the Fredholm integral equations of the second kind and solved by standard numerical procedures. The accuracy of the present solution is validated via comparisons with existing solutions for an ideal elastic half-space. Furthermore, some numerical results are presented to show the influences of the layer depth, the plate flexibility, and the soil porosity on the dynamic compliances. 相似文献
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This paper considers the vertical dynamic response of a disk on a saturated poroelastic half-space. Firstly the pressure-solid displacement form of the harmonic equations of motion for a poroelastic solid are developed from the form of the equations originally presented by Biot. These equations are solved by a new method. Then the mixed boundary value problem for the vertical harmonic vibration of a disk on a poroelastic half-space is studied. The two types of drainage conditions at the surface of the poroelastic half-space are considered: (a) the surface of the poroelastic half-space is assumed to be completely pervious both within and exterior to the plate; (b) The interface between the plate and the poroelastic half-space is assumed to be impervious and the exterior region is assumed to be pervious. By using the Hankel transform techniques, the paper develops the governing dual integral equations. These governing integral equations are further reduced to systems of standard Fredholm integral equations of the second kind by Abel transform. 相似文献