Gaussian beams in inhomogeneous media: A review

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.     

A non‐baseline algorithm for damage locating in flexural structures using dynamic distributed macro‐strain responses

The concept of distributed strain‐sensing techniques has been proposed in our recent research, which was dedicated to utilizing the strain distributions throughout the full or partial areas of structures to detect arbitrary and unforeseen damage. An algorithm not requiring a detailed analytical model is presented for damage locating in flexural structures through the direct use of dynamic responses recorded by distributed long‐gauge strain sensors. The modal macro‐strain vector (MMSV), which has been proven to have a mapping relation with displacement mode shape, can be extracted directly from macro‐strain time‐series data, from which a damage evaluating index can be derived and used as an indicator for locating damage. Numerical examples are simulated to verify the sensitivity and effectiveness of the index in different cases. Furthermore, experimental investigations on a cantilevered beam with various long‐gauge fibre optic sensors placements are carried out to examine the feasibility and applicability of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of the weightiness of site effects on reinforced concrete (RC) building seismic behaviour: The Adra town example (SE Spain)

The damage distribution in Adra town (south‐eastern Spain) during the 1993 and 1994 Adra earthquakes (5.0 magnitude), that reached a maximum intensity degree of VII (European Macroseismic Scale (EMS scale)), was concentrated mainly in the south‐east zone of the town and the most relevant damage occurred in reinforced concrete (RC) buildings with four or five storeys. In order to evaluate the influence of ground condition on RC building behaviour, geological, geomorphological and geophysical surveys were carried out, and a detailed map of ground surface structure was obtained. Short‐period microtremor observations were performed in 160 sites on a 100m × 100m dimension grid and Nakamura's method was applied in order to determine a distribution map of soil predominant periods. Shorter predominant periods (0.1–0.3 s) were found in mountainous and neighbouring zones and larger periods (greater than 0.5 s) in thicker Holocene alluvial fans. A relationship T = (0.049 ± 0.001)N, where T is the natural period of swaying motion and N is the number of storeys, has been empirically obtained by using microtremor measurements at the top of 38 RC buildings (ranging from 2 to 9 storeys). 1‐D simulation of strong motion on different soil conditions and for several typical RC buildings were computed, using the acceleration record in Adra town of the 1993 earthquake. It is noteworthy that all the aforementioned results show the influence of site effects in the degree and distribution of observed building damage. Copyright © 2007 John Wiley & Sons, Ltd.     

Impedance of flexible suction caissons

The dynamic response of offshore wind turbines is affected by the properties of the foundation and the subsoil. The aim of this paper is to evaluate the dynamic soil–structure interaction of suction caissons for offshore wind turbines. The investigations include evaluation of the vertical and coupled sliding–rocking vibrations, influence of the foundation geometry and examination on the properties of the surrounding soil. The soil is simplified as a homogenous linear viscoelastic material and the dynamic stiffness of the suction caisson is expressed in terms of dimensionless frequency‐dependent coefficients corresponding to different degrees of freedom. The dynamic stiffness coefficients for the skirted foundation are evaluated using a three‐dimensional coupled boundary element/finite element model. Comparisons with known analytical and numerical solutions indicate that the static and dynamic behaviours of the foundation are predicted accurately using the applied model. The analysis has been carried out for different combinations of the skirt length, Poisson's ratio of the subsoil and the ratio of the soil stiffness to the skirt stiffness. Copyright © 2007 John Wiley & Sons, Ltd.     

Prediction of the median IDA curve by employing a limited number of ground motion records

A methodology has been proposed which can be used to reduce the number of ground motion records needed for the reliable prediction of the median seismic response of structures by means of incremental dynamic analysis (IDA). This methodology is presently limited to predictions of the median IDA curve only. The reduction in the number of ground motion records needed to predict the median IDA curve is achieved by introducing a precedence list of ground motion records. The determination of such a list is an optimization problem, which is solved in the paper by means of (1) a genetic algorithm and (2) a proposed simple procedure. The seismic response of a simple, computationally non‐demanding structural model has been used as input data for the optimization problem. The presented example is a three‐storey‐reinforced concrete building, subjected to two sets of ground motion records, one a free‐field set and the other a near‐field set. It is shown that the median IDA curves can be predicted with acceptable accuracy by employing only four ground motion records instead of the 24 or 30 records, which are the total number of ground motion records for the free‐field and near‐field sets, respectively. Copyright © 2007 John Wiley & Sons, Ltd.     

Subsidence history and forming mechanism of anomalous tectonic subsidence in the Bozhong depression, Bohaiwan basin

The Bozhong depression of the Bohaiwan basin belongs to a family of extensional basins in East China, but is quite different from other parts of the basin. The Cenozoic subsidence of the depression is controlled by a combination of lithospheric thinning and polycyclic strike-slip movements. Three episodic rifts have been identified, i.e. Paleocence-early Eocene, middle-late Eocene and Oligocene age. The depression underwent syn-rift and post-rift stages, but two episodic dextral movement events of the strike-slip faults modify the subsidence of the Bozhong depression since the Oligocene. The early dextral movement of the Tan-Lu fault associated with crustal extension resulted in accelerated subsidence during the time of deposition of the Dongying Formation with a maximum thickness of 4000 m. A late reactivation of dextral movement of the Tan-Lu fault began in late Miocene (about 12 Ma), which resulted in the intense subsidence of Minghuazhen Formation and Quaternary. In addition, dynamic mantle convection-driven topography also accelerated the post-rift anomalous subsidence since the Miocene (24.6 Ma). Our results indicate that the primary control on rapid subsidence both during the rift and post-rift stages in the Bozhong depression originates from a combination of multiple episodic crustal extension and polycyclic dextral movements of strike-slip faults, and dynamic topography.     

Robust H∞ control for aseismic structures with uncertainties in model parameters

This paper presents a robust H∞ output feedback control approach for structural systems with uncertainties in model parameters by using available acceleration measurements and proposes conditions for the existence of such a robust output feedback controller. The uncertainties of structural stiffness, damping and mass parameters are assumed to be norm-bounded. The proposed control approach is formulated within the framework of linear matrix inequalities, for which existing convex optimization techniques, such as the LMI toolbox in MATLAB, can be used effectively and conveniently. To illustrate the effectiveness of the proposed robust H∞ strategy, a six-story building was subjected both to the 1940 El Centro earthquake record and to a suddenly applied Kanai-Tajimi filtered white noise random excitation. The results show that the proposed robust H∞ controller provides satisfactory results with or without variation of the structural stiffness, damping and mass parameters.     

地形RSG模型的动态构网算法

论述了一种基于规则格网地形模型的动态构网算法。通过定义模型中顶点间的约束关系以及顶点误差的继承方法，利用四叉树构建出顶点的层次结构，有效解决了不同分辨率网络间接边的裂缝问题，实现在模型误差控制下的多分辨网络的实时正确构网。实验证明，该方法对于实时控制地形模型的细节层次，增强地形模型的绘制效率是非常有效的。     

大跨度斜拉桥变形监测研究

系统地介绍现代大跨度桥梁变形监测的内容、变形监测的方案与资料分析，结合武汉长江二桥的监测实践，指出利用现代测量仪器和技术，如GPS定位系统、测量机器人等不仅完全可以满足大跨度桥梁管理部门提出的要求，而且还可以提高测量速度，其测量成果也具有很高的精度。     

大气中对称不稳定机制的动力学分析及暴雨的分析与预报

用气块法从力学角度对对称不稳定机制及在对称不稳定条件下产生的环流进行分析，更全面地定义了对称不稳定及它的产生机制和中尺度环流形成的过程。对暴雨个例诊断分析表明，有些强降水区在降水前和降水过程中存在着不对称不稳定，说明对称不稳定条件下形成的环流对暴雨有引发和加强作用。在以往研究原基础上，总结出了利用常规观测资料分析对称不是否存在，及其能量大小的方法，用它来预报是否降水及降水的强度，从而提高降水预报准确率。