An explicit representation of steady state response of a beam on an elastic foundation to moving harmonic line loads

A closed‐form deflection response of a beam rest is presented in this paper using the integral transform method. The theory of linear partial differential equations is used to represent the deflection of beam subjected to a moving harmonic line load in integration form. The solution is finally carried out using the inverse Fourier transform. To evaluate the integration analytically, poles of the integrand are identified with the help of algebraic equation theory. Residue theorem is then utilized to represent the integration as a contour integral in the complex plane. Closed‐form deflections and numerical results are provided for different combinations of load frequency and velocity. Copyright © 2002 John Wiley & Sons, Ltd.     

Hamiltonian perturbation theory on a manifold

This paper deals with Hamiltonian perturbation theory for systems which, like Euler-Poinsot (the rigid body with a fixed point and no torques), are degenerate and do not possess a global system of action-angle coordinates. It turns out that the usual methods of perturbation theory, which are essentially local being based on the construction of normal forms within the domain of a local coordinate system, are not immediately usable to study perturbations of these systems, since degeneracy makes impossible to control that the system does not fall into a singularity of the coordinates. To overcome this difficulty, we develop a global formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The key for this study lies in the geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system, which is described by some generalizations of the Liouville-Arnol'd theorem and is reviewed in the paper. As an application, we provide a global formulation of Nekhoroshev's theorem on the stability for exponentially long times.     

Applicability of a Backprojection Algorithm to Reconstruct Images of Subsurface Horizontal Planes for Laboratory Experiments in Electrical Resistance Tomography

This paper describes the use of a backprojection algorithm to reconstruct subsurface images of the electrical resistivity in horizontal planes parallel to the surface. The algorithm can be applied to detect buried objects such as tanks or pipes and possible leakages from them. Two imaging strategies are compared: juxtaposition of vertical planes, and 3D reconstruction from the sensitivity matrix corresponding to the entire volume whose surface is explored. The electrode arrays used for voltage measurement are the dipole–dipole array and a modified Schlumberger array. A personal computer controls current injection, electrode switching, and voltage detection. The system injects 1 kHz, 20 V peak-to-peak square waveforms, thus avoiding electrode polarization effects. Experimental laboratory measurements show that the algorithm detects localized objects such as an insulating sphere and a conductive cylinder immersed in water. Furthermore, covering half of the cylinder by a rubber sleeve to simulate a nonconductive leak, yields a distinct image for the leak. The backprojection algorithm does not need any regularization parameter and it is very fast in inverting the sensitivity matrix because it approximates the inverse matrix by its transposed. The dipole–dipole array usually yields a lower overall pixel error than the modified Schlumberger array but both allow the detection of simulated underground leaks.     

四阶奇异边值问题无穷多个正解存在性的一个注记

本文考虑四阶奇异边值问题x( 4 ) =λa(t) f (t,x(t) ) ,0 相似文献   

正交直墙前直立圆柱的波浪绕射的解析研究

应用镜像原理,将正交直墙前单个圆柱的波浪绕射问题,转化为4个对称布置圆柱的4向入射波浪的绕射问题。然后应用速度势的特征展开方法和Graf加法定理,建立了正交直墙前垂直圆柱的波浪绕射解析解。通过数值计算研究了圆柱与正交直墙间距离大小、波浪入射角等因素与圆柱上总波浪作用力的解析关系。     

Quantitative perturbation theory by successive elimination of harmonics

We revisit some results of perturbation theories by a method of successive elimination of harmonics inspired by some ideas of Delaunay. On the one hand, we give a connection between the KAM theorem and the Nekhoroshev theorem. On the other hand, we support in a quantitative fashion a semi-numerical method of analysis of a perturbed system recently introduced by one of the authors.     

Characterizing mixed-use buildings based on multi-source big data

To-date few research has successfully integrated big data from multiple sources to characterize urban mixed-use buildings. In this paper, we introduce a probabilistic model to integrate multi-source and geospatial big data (social network data, taxi trajectories, Points of Interest and remote sensing images) to characterize urban mixed-use buildings. The usefulness of our model is demonstrated with a case study of the Tianhe District in megacity Guangzhou, China. The model predicted building functions at 85% accuracy based on ground truth data from field surveys. We further explored the spatial patterns of the identified building functions. Most mixed-use buildings are located along major streets. Our proposed model can identify mixed-use buildings in a city; information is useful for planning evaluation and urban policymaking.     

NWP 模式热量系统误差的动力诊断分析

文章证明了模式在预报时段的位温误差,是由于在模式大气和真实大气中,该时段内位温变化过程的不同而造成的。还证明了原始方程的无加速定理对各强迫因子的线性分解同样适用于研究NWP模式热量误差的成因。对国家气象中心T42L9模式1992年1月和7月预报结果的动力诊断表明,模式对纬向位温分布具有较好的预报能力,但在各纬带也存在明显的误差。通过无加速定理的分解分析,研究了这些误差的成因及改善模式的可能途径。     

分数阶混合随机泛函微分方程的能控性

主要研究了分数阶混合随机泛函微分方程的能控性.在无限维空间下,假设所考虑方程线性部分生成半群不是紧的,使用非紧性测度技术和Mönch不动点定理,给出了方程能控性充分条件,并通过一个例子说明了结论的有效性.     

斜交型不稳定谱点分布侧半圆定理及其增长率上界的估计

本对斜交型扰动不稳定谱点的分布做了理论分析，得到了该谱点分布的半圆定理一该谱点分布在复一面上以原点为圆心以R0为半径的上半平面上，同时还对该不稳定增长率的上界作了估计。发现水平永度越小，模式顶越高则该估计值越大；垂直风切变的增大和纬度的增高对该增长率的增大有正贡献；当层结稳定度减小时，最大增长率随相对最大增长率得增大而减小。