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1.
Existing analytical procedures for nonsteady flow in a leaky confined aquifer assume that the aquifer system is areally infinite. A technique is presented that treats a leaky confined aquifer system of finite configuration. By means of a discrete space continuous time (DSCT) modeling approach, the partial differential equation governing the flow system is transformed into a set of ordinary differential equations that can be easily integrated numerically on a high speed digital computer using available scientific subroutines. The finite difference formulation is in effect an explicit scheme. A criterion is developed for which the scheme is computationally stable. A numerical example is presented. 相似文献
2.
A non-Gaussian closure scheme based on the Edgeworth expansion of the probability density function is used to study the response of a hysteretic structure under random parametric excitation. The system considered consists of a weightless mass supporting a concentrated mass and it is subjected to the vertical and horizontal components of the ground acceleration modeled as nonstationary Gaussian white noise processes. The material of the structure exhibits bilinear hysteretic behaviour. The equation governing the motion of the system is transformed into an Itô stochastic differential equation. A set of ordinary differential equations governing the response statistics are obtained. These form an infinite hierarchy of equations which must be truncated in order to solve for moments of any order. The Edgeworth expansion of the joint density is used to truncate this infinite hierarchy. Such a closure scheme appears desirable since for hysteretic systems an explicit expression of the probability density is required. A frequently used closure scheme based on Gaussian assumption underestimates the response. The non-Gaussian density can be used in reliability studies. 相似文献
3.
The scaled boundary finite‐element method is extended to simulate time‐harmonic responses of non‐homogeneous unbounded domains with the elasticity modulus and mass density varying as power functions of spatial coordinates. The unbounded domains and the elasticity matrices are transformed to the scaled boundary coordinates. The scaled boundary finite‐element equation in displacement amplitudes are derived directly from the governing equations of elastodynamics. To enforce the radiation condition at infinity, an asymptotic expansion of the dynamic‐stiffness matrix for high frequency is developed. The dynamic‐stiffness matrix at lower frequency is obtained by numerical integration of ordinary differential equations. Only the boundary is discretized yielding a reduction of the spatial dimension by one. No fundamental solution is required. Material anisotropy is modelled without additional efforts. Examples of two‐ and three‐dimensional non‐homogeneous isotropic and transversely isotropic unbounded domains are presented. The results demonstrate the accuracy and simplicity of the scaled boundary finite‐element method. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
4.
A convection-diffusion equation arises from the conservation equations in miscible and immiscible flooding, thermal recovery, and water movement through desiccated soil. When the convection term dominates the diffusion term, the equations are very difficult to solve numerically. Owing to the hyperbolic character assumed for dominating convection, inaccurate, oscillating solutions result. A new solution technique minimizes the oscillations. The differential equation is transformed into a moving coordinate system which eliminates the convection term but makes the boundary location change in time. We illustrate the new method on two one-dimensional problems: the linear convection-diffusion equation and a non-linear diffusion type equation governing water movement through desiccated soil. Transforming the linear convection diffusion equation into a moving coordinate system gives a diffusion equation with time dependent boundary conditions. We apply orthogonal collocation on finite elements with a Crank-Nicholson time discretization. Comparisons are made to schemes using fixed coordinate systems. The equation describing movement of water in dry soil is a highly non-linear diffusion-type equation with coefficients varying over six orders of magnitude. We solve the equation in a coordinate system moving with a time-dependent velocity, which is determined by the location of the largest gradient of the solution. The finite difference technique with a variable grid size is applied, and a modified Crank-Nicholson technique is used for the temporal discretization. Comparisons are made to an exact solution obtained by similarity transformation, and with an ordinary finite difference scheme on a fixed coordinate system. 相似文献
5.
This paper deals with the lower order (first four) nonstationary statistical moments of the response of linear systems with random stiffness and random damping properties subject to random nonstationary excitation modeled as white noise multiplied by an envelope function. The method of analysis is based on a Markov approach using stochastic differential equations (SDE). The linear SDE with random coefficients subject to random excitation with deterministic initial conditions are transformed to an equivalent nonlinear SDE with deterministic coefficients and random initial conditions subject to random excitation. In this procedure, new SDE with random initial conditions, deterministic coefficients and zero forcing functions are introduced to represent the random variables. The joint statistical moments of the response are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vectors and the random variables of the structural system. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. The statistical moment equations are ordinary nonlinear differential equations where hierarchy of moments appear. The hierarchy is closed by the cumulant neglect closure method applied at the fourth order statistical moment level. General formulation is given for multi-degree-of-freedom (MDOF) systems and the performance of the method in problems with nonstationary excitations and large variabilities is illustrated for a single-degree-of-freedom (SDOF) oscillator. 相似文献
6.
Abstract The problem of identifying and reproducing the hydrological behaviour of groundwater systems can often be set in terms of ordinary differential equations relating the inputs and outputs of their physical components under simplifying assumptions. Conceptual linear and nonlinear models described as ordinary differential equations are widely used in hydrology and can be found in several studies. Groundwater systems can be described conceptually as an interlinked reservoir model structured as a series of nonlinear tanks, so that the groundwater table can be schematized as the water level in one of the interconnected tanks. In this work, we propose a methodology for inferring the dynamics of a groundwater system response to rainfall, based on recorded time series data. The use of evolutionary techniques to infer differential equations from data in order to obtain their intrinsic phenomenological dynamics has been investigated recently by a few authors and is referred to as evolutionary modelling. A strategy named Evolutionary Polynomial Regression (EPR) has been applied to a real hydrogeological system, the shallow unconfined aquifer of Brindisi, southern Italy, for which 528 recorded monthly data over a 44-year period are available. The EPR returns a set of non-dominated models, as ordinary differential equations, reproducing the system dynamics. The choice of the representative model can be made both on the basis of its performance against a test data set and based on its incorporation of terms that actually entail physical meaning with respect to the conceptualization of the system. Citation Doglioni, A., Mancarella, D., Simeone, V. & Giustolisi, O. (2010) Inferring groundwater system dynamics from hydrological time-series data. Hydrol. Sci. J. 55(4), 593–608. 相似文献
7.
The objective of this research is to study the dynamic response characteristics of a three-beam system with intermediate elastic connections under a moving load/mass-spring. In this study, the finite Sine-Fourier transform was performed for the dynamic partial differential equations of a simply supported three-beam system (SSTBS) under a moving load and a moving mass-spring, respectively. The dynamic partial differential equations were transformed into dynamic ordinary differential equations relative to the time coordinates, and the equations were solved and the displacement Fourier amplitude spectral expressions were obtained. Finally, based on finite Sine-Fourier inverse transform, the expressions for dynamic response of SSTBS under the moving load and moving mass-spring were obtained. The proposed method, along with ANSYS, was used to calculate the dynamic response of the SSTBS under a moving load/mass-spring at different speeds. The results obtained herein were consistent with the ANSYS numerical calculation results, verifying the accuracy of the proposed method. The influence of the load/mass-spring’s moving speed on the dynamic deflections of SSTBS were analyzed. SSTBS has several critical speeds under a moving load/mass-spring. The vertical acceleration incurred by a change in the vertical speed of SSTBS due to the movement of mass-spring and the centrifugal acceleration produced by the movement of massspring on the vertical curve generated by SSTBS vibration could not be neglected. 相似文献
8.
Xingzhong Shi Richard T. McNider M. P. Singh David E. England Mark J. Friedman William M. Lapenta William B. Norris 《Pure and Applied Geophysics》2005,162(10):1811-1829
Previous studies of the stable atmospheric boundary layer using techniques of nonlinear dynamical systems (MCNIDER et al., 1995) have shown that the equations support multiple solutions in certain parameter spaces. When geostrophic speed is used as a bifurcation parameter, two stable equilibria are found—a warm solution corresponding to the high-wind regime where the surface layer of the atmosphere stays coupled to the outer layer, and a cold solution corresponding to the low-wind, decoupled case. Between the stable equilibria is an unstable region where multiple solutions exist. The bifurcation diagram is a classic S shape with the foldback region showing the multiple solutions. These studies were carried out using a simple two-layer model of the atmosphere with a fairly complete surface energy budget. This allowed the dynamical analysis to be carried out on a coupled set of four ordinary differential equations. The present paper extends this work by examining additional bifurcation parameters and, more importantly, analyzing a set of partial differential equations with full vertical dependence. Simple mathematical representations of classical problems in dynamical analysis often exhibit interesting behavior, such as multiple solutions, that is not retained in the behavior of more complete representations. In the present case the S-shaped bifurcation diagram remains with only slight variations from the two-layer model. For the parameter space in the foldback region, the evolution of the boundary layer may be dramatically affected by the initial conditions at sunset. An eigenvalue analysis carried out to determine whether the system might support pure limit-cycle behavior showed that purely complex eigenvalues are not found. Thus, any cyclic behavior is likely to be transient. 相似文献
9.
We present a theoretical weakly nonlinear analysis of the dynamics of an inviscid flow submitted to both rotation and precession of an unbounded cylindrical container, by considering the coupling of two Kelvin (inertial) waves. The parametric centrifugal instability known for this system is shown to saturate when one expands the Navier–Stokes equation to higher order in the assumed small precession parameter (ratio of precession to rotation frequencies) with the derivation of two coupled Landau equations suitable to describe the dynamics of the modes. It is shown that an azimuthal mean flow with differential rotation is generated by this modes coupling. The time evolution of the associated dynamical system is studied. These theoretical results can be compared with water experiments and also to some numerical simulations where viscosity and finite length effects cannot be neglected. 相似文献
10.
The one-dimensional dynamic column and borehole problems of soil mechanics formulated on the basis of the poroelastic theory of Vardoulakis and Beskos are solved analytically-numerically. The quasi-static counterparts of these problems are analysed as special cases of the dynamic ones. Use of Laplace transform with respect to time reduces the column and borehole problems to ordinary differential equations with constant and variable coefficients, respectively. The transformed solution of these problems is obtained analytically for the column and by finite differences for the borehole problem, and after, a numerical Laplace transform inversion produces the time domain response. Both a suddenly applied and a harmonically varying with time load are considered. It is concluded that the significance of inertial effects depends on the kind of loading and that the degree of saturation for the nearly saturated case greatly affects the response. 相似文献
11.
Nicos Makris 《地震工程与结构动力学》1994,23(3):251-264
A new rigorous approach in modelling mechanical behaviour is developed. The dynamic response of a rigid disc resting on an elastic half-space is approximated by a macroscopic force-displacement relationship, where not only the coefficients but also the order of time derivatives are complex valued. It is shown that comlex-parameter constitutive models are not simply an elegant alternative in modelling mechanical behaviour, but are the outcome of rigorous non-linear regression analysis on complex-valued functions, like the dynamic stiffness of dissipative systems. Complex-parameter constitutive models are very attractive since a minimum number of parameters is required to obtain a satisfactory fit of the ‘exact’ response. A two-parameter generalized Kelvin model reproduces closely the ‘exact’ dynamic stiffness of the disc for all three vertical, horizontal and rocking modes studied herein. Frequency- and time-domain algorithms to solve complex-order differential equations are developed, validated and used to calculate the foundation–response under earthquake excitation. It is the excellent agreement of results and the economy in number of parameters that make complex-parameter models so attractive in constitutive modelling. 相似文献
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13.
Mathematical modelling of overland flow is a critical task in simulating transport of water, sediment and other pollutants from land surfaces to receiving waters. In this paper, an overland flow routing method is developed based on the Saint‐Venant equations using a discretized hillslope system for areas with high roughness and steep slope. Under these conditions, the momentum equation reduces to a unique relationship between the flow depth and discharge. A hillslope is treated as a system divided into several subplanes. A set of first‐order non‐linear differential equations for subsequent subplanes are solved analytically using Chezy's formula in lieu of the momentum equation. Comparison of the analytical solution of the first‐order non‐linear ordinary differential equations and a numerical solution using the Runge‐Kutta method shows a relative error of 0·3%. Using runoff data reported in the literature, comparison between the new approach and a numerical solution of the full Saint‐Venant equations showed a close agreement. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
14.
Summary In problems of linear flow of heat in inhomogeneous media, the governing equation is a second order ordinary differential equation with variable coefficients. When transformed into a set of first order ordinary differential equations with variable coefficients, the problem becomes amenable to an elegant method of propagator matrices. In this paper the propagator matrices for some steady and unsteady heat conduction problems (including a case of heat generation by an irreversible first order reaction) having conductivity and heat generation functions as piecewise continuous, have been described. 相似文献
15.
采用弱非线性近似得出中层耗散大气连续谱Ｒｏｓｓｂｙ波包的非线性时空演化方程，讨论了Ｒｏｓｓｂｙ波包的三波相互作用问题．数值计算表明，耗散和非线性的共同效应决定了Ｒｏｓｓｂｙ波包的演变．当一个Ｒｏｓｓｂｙ波包通过大气传播时，它的振幅若超过某个阈值，空间尺度分别比它大和比它小的两个次级Ｒｏｓｓｂｙ波包的振幅会随时间增长．特别当这两个次级波包同时随时空变化时，仅当主波的振幅超过一个更大的阈值，且其群速度介于两次级波包的群速度之间时，两次级波包的振幅才会随时空同时增长，即出现绝对不稳定现象，耗散和３个波包的频率失配都会增大不稳定的阈值． 相似文献
16.
基于中高层大气重力波动力学是由非线性过程和损耗过程共同决定的物理思想,本文采用弱非线性相互作用近似,推导出损耗大气中重力波的非线性相互作用方程.这组方程是研究固定相位和随机相位重力波相互作用问题的出发点.通过引入平均振幅,我们得到了损耗情况下离散重力波的三波相互作用方程,该方程描述了重力波波包非线性时空演变的规律.作为该方程的一个具体应用,我们考虑了由于波-波相互作用产生的不稳定性.当一大尺度大振幅的主重力波通过大气传播时,非线性相互作用可能导致两个次级波振幅随时间指数增长.由于分子损耗和频率失配,主波的振幅必须大于一个阈值,这种指数增长才可能出现.共振条件满足时,阈值变为最小.频率失配还会导致次级波本征频率发生改变,改变的大小是频率失配值的一半. 相似文献
17.
B. G. Verma 《Pure and Applied Geophysics》1971,88(1):146-153
Summary In this paper, an attempt has been made to study the non-uniform self progagation of cylindrical imploding shocks in an electrically conducting gas. The similarity solution has been extended to earlier times in the implosion process when the shock strength is finite and Oshima's quasi similar approximation method is applied to reduce the equations of motion to a set of ordinary differential equations in order to discuss the regularity of the solution. 相似文献
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19.
Abstract A finite element model to simulate runoff and soil erosion from agricultural lands has been developed. The sequential solutions of the governing differential equations were found: Richards' equation with a sink term for infiltration and soil water dynamics under cropped conditions; St Venant equation with kinematic wave approximation for overland and channel flow; and sediment continuity equation, for soil erosion. The model developed earlier has been improved to simulate erosion/deposition in impoundments and predicted and observed soil loss values were in reasonably good agreement when the model was tested for a conservation bench terrace (CBT) system. The finite element model was extensively applied to study the hydrological behaviour of a CBT system vis-à-vis the conventional system of sloping borders. The model estimates runoff and soil loss reasonably well, under varying conditions of rainfall and at different crop growth stages. The probable reasons for discrepancies between observation and simulation are reported and discussed. Sensitivity analysis was carried out to study the effect of various hydrological, soil and topographical parameters, such as ratio of contributing to receiving areas, weir length, depth of impoundment, slope of contributing area, etc. on the flow behaviour in a CBT system. 相似文献
20.
A note on dynamic ray tracing in ray-centered coordinates in anisotropic inhomogeneous media 总被引：1，自引：0，他引：1
V. Červený 《Studia Geophysica et Geodaetica》2007,51(3):411-422
Dynamic ray tracing plays an important role in paraxial ray methods. In this paper, dynamic ray tracing systems for inhomogeneous
anisotropic media, consisting of four linear ordinary differential equations of the first order along the reference ray, are
studied. The main attention is devoted to systems expressed in a particularly simple choice of ray-centered coordinates, here
referred to as the standard ray-centered coordinates, and in wavefront orthonormal coordinates. These two systems, known from
the literature, were derived independently and were given in different forms. In this paper it is proved that both systems
are fully equivalent. Consequently, the dynamic ray tracing system, consisting of four equations in wavefront orthonormal
coordinates, can also be used if we work in ray-centered coordinates, and vice versa.
vcerveny@seis.karlov.mff.cuni.cz 相似文献