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基于外行简谐波动模型、多项式插值理论和具有解析表达式的外插序列,导出了N阶透射边界及其误差项与收敛的充分条件。利用外插序列的时空坐标满足同一直线方程的几何特征,完成了简谐波动N阶透射边界向任意外行波动阶透射边界的推广。依据外插序列的解析表达式,导出了后者误差项的近似表达式和收敛性的充分条件。N阶透射边界的主部与N阶多次透射公式相同,但误差项的表达式不同,精度与收敛性的分析方法与结果也不同。提出了与虚拟透射边界相关的频率放大倍数概念,认为它们是影响虚拟透射边界精度的关键因素。 相似文献
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本文以紧凑形式给出了可以直接用于波动有限元计算的透射人工边界公式。为了阐明离散化误差和由人工边界引起的振荡失稳的基本概念,作者利用简单的一维模型详细分析了波动有限元模拟中遇到的这两个主要问题。基于在离散和连续模型中波动规律差别的分析,首先研究了离散化误差。这一研究导致对可能实现波动有限元模拟的频段的识别,以及采用一种兼备有限差和有限元优点的集中质量离散模型的建议。根据波在人工边界的放大效应和在有限离散模型中多次反射的概念在频域内阐明了这一常见的振荡失稳的机制。在此基础上提出了在保证数值计算精度的条件下通过对人工边界附近节点运动的修正来消除振荡失稳的措施。本文还以一维模型为例给出了人工边界条件的稳定性准则。 相似文献
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一种基于多项式外推的局部透射边界位移解(外行波为平面波情形) 总被引:3,自引:4,他引:3
基于外行波局部法向透射概念,从多项式外推的角度,结合一维和广义二维几何解释,推导建立了外行波为平面波时,人工边界节点位移解的计算公式。对该位移解的精度进行了时域分析,论证了该位移解收敛于数值精确解的必要条件和线性外推位移解的精度与数值精确解匹配的充要条件。在此基础上提出了一次“精确”透射的概念和相应的数学方法,实现了该位移解逼近于数值精确解的优化计算。 相似文献
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一种基于多项式外推的局部透射边界位移解(外行波为非平面波情形) 总被引:3,自引:3,他引:3
一般情况下,通过人工边界向外透射的波动常为非平面波。对于近场非平面波在人工边界上的透射问题,不能采用简单的平面波透射方法。本文针对近场非平面波在人工边界上的透射特点,分析了非平面波沿人工边界法向视波速的变化规律及其近场失稳机制,推导了适合近场非平面波的、人工边界点位移解的不等步距线性外推公式。 相似文献
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推导出了分析二维粘及弹性场地地形对地震动影响的显式有限元-有限差分方法.这一方法中,首先利用人工边界及有限元离散方法,给出问题分析的有限元离散网格计算力学模型,并利用一种类似于差分方法的有限元方法,建立局部网格节点的动力方程,而后利用笔者提出的有阻尼体系动力方程求解的显式差分格式,及推广的多次透射边界公式,给出网格节点运动量计算的时域显式逐步积分公式.利用计算机程序实现这一方法的计算具有所需计算机内存量小及计算时间量小的优势,而且,这一方法适用于任意地形情况,具有较高的计算精度及较好的计算稳定性. 相似文献
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多次透射公式实用形式稳定性分析 总被引:1,自引:1,他引:0
景立平 《地震工程与工程振动》2004,24(4):20-24
本文以二维出平面波动方程为例,利用数值方法研究了多次透射公式的实用形式的稳定问题,结果表明:多次透射公式的实用形式与波动方程的集中质量显式有限元结合,不但存在零频漂移,而且同样存在高频振荡失稳,而与中心差分方法结合仅存在零频漂移失稳。 相似文献
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暂态弹性波分析中人工边界的研究 总被引:14,自引:2,他引:14
本文提出一种应用于有限离散模型计算暂态弹性波时人工边界处理的新方法——多次透射法。它的误差与(ΔX)~N同量级,N为透射次数,ΔI为离散模型的空间步距。初步数值结果表明它对近场弹性波有良好的透射能力。这一方法为研究三维波传播问题提供了新的前景。 相似文献
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John L. Tassoulas 《地震工程与结构动力学》2011,40(5):531-550
A half‐space finite element and a transmitting boundary are developed for a water‐saturated layered half‐space using a paraxial boundary condition. The exact dynamic stiffness of a half‐space in plane strain is derived and a second‐order paraxial approximation of the stiffness is obtained. A half‐space finite element and a transmitting boundary are then formulated. The development is verified by comparison of the dynamic stiffness of impermeable and permeable rigid strip foundations with other published results. The advantage of using the paraxial boundary condition in comparison with the rigid boundary condition is examined. It is shown that the paraxial boundary condition offers significant gain and the resulting half‐space finite element and transmitting boundary can represent the effects of a water‐saturated layered half‐space with good accuracy and efficiency. In addition, the numerical method described herein maintains the strengths and advantages of the finite element method and can be easily applied to demanding problems of soil–structure interaction in a water‐saturated layered half‐space. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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The paper outlines the most important results of the paraxial complex geometrical optics (CGO) in respect to Gaussian beams
diffraction in the smooth inhomogeneous media and discusses interrelations between CGO and other asymptotic methods, which
reduce the problem of Gaussian beam diffraction to the solution of ordinary differential equations, namely: (i) Babich’s method,
which deals with the abridged parabolic equation and describes diffraction of the Gaussian beams; (ii) complex form of the
dynamic ray tracing method, which generalizes paraxial ray approximation on Gaussian beams and (iii) paraxial WKB approximation
by Pereverzev, which gives the results, quite close to those of Babich’s method. For Gaussian beams all the methods under
consideration lead to the similar ordinary differential equations, which are complex-valued nonlinear Riccati equation and
related system of complex-valued linear equations of paraxial ray approximation. It is pointed out that Babich’s method provides
diffraction substantiation both for the paraxial CGO and for complex-valued dynamic ray tracing method. It is emphasized also
that the latter two methods are conceptually equivalent to each other, operate with the equivalent equations and in fact are
twins, though they differ by names.
The paper illustrates abilities of the paraxial CGO method by two available analytical solutions: Gaussian beam diffraction
in the homogeneous and in the lens-like media, and by the numerical example: Gaussian beam reflection from a plane-layered
medium. 相似文献
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A half-space finite element and a consistent transmitting boundary in a cylindrical coordinate system are developed for analysis of rigid circular (or cylindrical) foundations in a water-saturated porous layered half-space. By means of second-order paraxial approximations of the exact dynamic stiffness for a half-space in plane-strain and antiplane-shear conditions, the corresponding approximation for general three-dimensional wave motion in a Cartesian coordinate system is obtained and transformed in terms of cylindrical coordinates. Using the paraxial approximations, the half-space finite element and consistent transmitting boundary are formulated in a cylindrical coordinate system. The development is verified by comparison of dynamic compliances of rigid circular foundations with available published results. Examination of the advantage of the paraxial condition vis-á-vis the fixed condition shows that the former achieves substantial gain in computational effort. The developed half-space finite element and transmitting boundary can be employed for accurate and effective analysis of foundation dynamics and soil–structure interaction in a porous layered half-space. 相似文献
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General absorbing boundary conditions based on Biot's two-phase mixture theory and paraxial approximation is presented for the dynamic analysis of fluid-saturated porous media with isotropic, transverse isotropic, and anisotropic properties. For the last two cases, the equivalent Lame's constants, under conditions of uniqueness, are introduced to facilitate the analytical solutions. The numerical results show that the proposed absorbing boundary can greatly suppress spuriously reflected waves and efficiently model the far field of the system with sufficient accuracy. 相似文献
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本文给出了有限离散点或周期离散点的新的傅氏变换计算法。它与经典的用周期性Diracδ抽样理论之纯离散变换的算法不同,而是根据抽样点的原曲线情况,采用任意幂多项式甚至无限幂(理想光滑化)曲线来模拟的新算法。它计算简便,只要在原FFT计算结果上乘上一个本文导出的简单的βn或β∞因子即可。 文中给出算例,阐述了该算法之优点。在理论上它不仅给出全频域的连续变换值,并且也避免了过去DFT计算中在高频处出现的混迭误差。这对信息的合理抽样,提高计算精度等方面,具有理论和实际意义。 相似文献
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The concept of polynomial‐fraction approximation is explored in this article to develop a nested type of systematic lumped‐parameter model for unbounded soil. Based on the optimal coefficients determined from the flexibility formulation, the reciprocal of the polynomial‐fraction is first taken to represent the dynamic stiffness function of foundation and then decomposed into a linear polynomial and another polynomial‐fraction. The nested division introduced in this study is operated to generate a nested form for this decomposed polynomial‐fraction, which directly corresponds to a nested discrete‐element model. The nested type of lumped‐parameter model is then easily constructed by connecting this nested discrete‐element model in series with another simple discrete‐element model corresponding to the linear polynomial. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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Jianguo Sun 《Geophysical Prospecting》1996,44(3):351-374
Conventionally, the Fresnel zone and the geometrical spreading factor are investigated separately, because they belong to different theories of wave propagation. However, if the paraxial ray method is used for establishing the Fresnel–Kirchhoff diffraction formula for a laterally inhomogeneous multilayered medium, it can be shown that the normalized geometrical spreading factor is inversely proportional to the area of the first Fresnel zone associated with the reflection point. Therefore, if no diffracting edge cuts the first Fresnel zone, the geometrical optics approximation represents the principal part of the wavefield obtained by Fresnel–Kirchhoff diffraction theory. Otherwise, the geometrical optics approximation has to be corrected by adding edge diffractions. It is also shown that Kirchhoff-type migration and geometrical spreading factor correction both reduce the first Fresnel zone to a zone with unit area. 相似文献
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In this paper, a finite element model of a soil island is coupled to both a consistent transmitting boundary and a paraxial boundary, which are then used to model the propagation of waves in semi-infinite elastic layered media. The formulation is carried out in the frequency domain while assuming plane strain conditions. It is known that a discrete model of this type, while providing excellent results for a wide range of physical parameters in the context of a half-space problem, may deteriorate rapidly at low frequencies of excitation. This is so because at low frequencies the various waves in the model eventually attain characteristic wavelengths which exceed the distance of the bottom boundary, which then causes that boundary to fail. Also, the paraxial boundaries themselves break down at very low frequencies. In this paper, this difficulty is overcome and the model׳s performance is improved upon dramatically by incorporating an artificial buffer layer sandwiched between the bottom of the soil medium and the underlying elastic half-space. Applications dealing with rigid foundations resting on homogenous or layered half-space media are shown to exhibit significant improvement. Following extensive simulations, clear guidelines are provided on the performance of the coupled model and an interpretation is given on the engineering significance of the findings. Finally, clear recommendations are provided for the practical use of the proposed modelling strategy. 相似文献
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T. AkiyoshiK. FuchidaH. L. Fang 《Soil Dynamics and Earthquake Engineering》1994,13(6):387-397
Based on Biot's two-phase mixture theory and the paraxial approximation, the absorbing boundary conditions in the time domain for u-w, u-U and u-p formulations are presented for the dynamic analysis of fluid-saturated porous media. These absorbing boundaries are equivalent to the viscous boundaries in the fundamental mode. The expressions for the energy ratio and reflection coefficient between the reflected and incident waves along the absorbing boundary are given. The numerical results show that the proposed absorbing boundaries can greatly suppress the spuriously reflected wave and model the far field of the system. These results also dynamic analysis of infinite fluid-saturated porous media. for the transient dynamic analysis of infinite fluid-saturated porous media. 相似文献