Errors in response calculations for non-classically damped structures

The classical normal mode method of determining response is extremely useful for practical calculations, but depends upon the damping matrix being orthogonal with respect to the modal vectors. Approximations that allow the method to be used when this condition is not satisfied have been suggested; the simplest approach is to neglect off-diagonal terms in the triple matrix product formed from the damping and modal matrices. In this paper the errors in response caused by this approximation are determined for several simple structures for a wide range of damping parameters and different types of excitation. Based on these results a criterion, relating modal damping and natural frequencies, is formulated; if this is satisfied, the errors in response caused by this diagonalization procedure are within acceptable limits.     

Errors in response calculations for extensional vibrations of bars

The transient extensional vibrations of a slender and uniform bar, which is clamped at one end and is subjected to an axial force at the other free end, are investigated by applying three methods: the Laplace transform method, the normal mode and Newmark β methods in conjunction with the finite element method (FEM); the errors caused by the spatial discretization of the FEM and the direct integration of the Newmark β method are studied and compared with those of the previous paper where the flexural vibrations of a cantilever beam were considered. The reason why the extensional vibration problem is investigated here is that the condition seems to be severe due to the closeness of adjacent natural frequencies, the larger values of natural frequencies and the smaller number of nodal variables of the FEM in comparison with those of the flexural vibration problem. The numerical results show that the errors in response of the extensional vibration problem are large. However, if one follows the criterion proposed in this paper, accurate response is obtainable by the Newmark β method, which requires less computer time than either of the other methods mentioned above.     

欧拉梁动力反应初边值问题的微分求积解

动荷载作用下欧拉梁动响应的计算是一个初边值问题,通常很难得到解析解,传统数值方法一般是把空间和时间分别离散进行求解,计算相对复杂,效率也不高.针对分布动荷载作用下欧拉梁的振动偏微分方程,采用传统微分求积法,在空间和时间上同时进行离散;对于所有非0阶的初/边值条件,采用嵌入法在权系数计算中予以考虑.算例的数值结果与精确解的对比证明采用传统微分求积法处理此问题是可行的,而且是高效的.对于实际工程中的其他类似问题,该方法同样适用.     

Towards an optimum model for the response of reinforced concrete beams to cyclic loads

The paper describes the development of a mathematical model to predict the flexural response of reinforced concrete beams to severe cyclic loading. The model is constructed with the aid of System Identification, which permits the coefficients in it to be so tuned as to replicate with the maximum possible accuracy the results of physical experiments. The uniaxial constitutive behaviour of the concrete and steel are considered separately, and they are then combined through a bond-slip relationship to form a global model for the composite material. The cyclic stress-strain law for the steel proves to be critical to the overall accuracy, and a suitable formulation is developed for it. Comparisons between observed and predicted behaviour are presented, both for the steel alone and for the composite material.     

Errors in time delay measurements

Summary Simple delay and sum of sensors in a seismic array is an effective method for noise suppression. However, unless we have precise steering delays, much of the signal energy is lost during the beam forming process too. We have investigated possible error sources in time delay measurements, using a computerized cross-correlation procedure. Parameters perturbed are correlation window length and positioning, signal frequency content and signal to noise ratio (SNR). Our results indicate that relative low frequency waves and using the very first part of theP-signals give the most reliable and stable time delay values. High frequency bandpass filtering improves SNR, but signal correlation and the precision in beam steering corrections decrease. Significant loss of high frequency energy during beamforming seems to be unavoidable.     

A tale of two beams: an elementary overview of Gaussian beams and Bessel beams

An overview of two types of beam solutions is presented, Gaussian beams and Bessel beams. Gaussian beams are examples of non-localized or diffracting beam solutions, and Bessel beams are example of localized, non-diffracting beam solutions. Gaussian beams stay bounded over a certain propagation range after which they diverge. Bessel beams are among a class of solutions to the wave equation that are ideally diffraction-free and do not diverge when they propagate. They can be described by plane waves with normal vectors along a cone with a fixed angle from the beam propagation direction. X-waves are an example of pulsed beams that propagate in an undistorted fashion. For realizable localized beam solutions, Bessel beams must ultimately be windowed by an aperture, and for a Gaussian tapered window function this results in Bessel-Gauss beams. Bessel-Gauss beams can also be realized by a combination of Gaussian beams propagating along a cone with a fixed opening angle. Depending on the beam parameters, Bessel-Gauss beams can be used to describe a range of beams solutions with Gaussian beams and Bessel beams as end-members. Both Gaussian beams, as well as limited diffraction beams, can be used as building blocks for the modeling and synthesis of other types of wave fields. In seismology and geophysics, limited diffraction beams have the potential of providing improved controllability of the beam solutions and a large depth of focus in the subsurface for seismic imaging.     

Control of the seismic response of a composite tall building modelled by two interconnected shear beams

The possibility of controlling the seismic response of tall buildings by use of a structural system consisting of a stiff and lightly damped external structure and a very flexible and moderately damped internal structure connected by stiff links at a few elevations is explored. Optimal damping values for the internal structure are obtained by consideration of the response on the composite structure in the vicinity of its fundamental mode. The resulting optimal damping values depend on the relative stiffness of both structures. Numerical results in the frequency and time domain are used to illustrate the advantages of such a system for seismic excitation. The possibility of using flexible links between the internal and external structures to moderate the required reduction of stiffness in the internal structure is also explored. © 1998 John Wiley & Sons, Ltd.     

Approximate methods for explicit calculations of non-Gaussian moments

We present theoretical tools from statistical physics for the calculation of non-Gaussian moments. In particular, we focus on the variational approximation and the cumulant expansion. These methods enable approximate but explicit moment calculations with non-Gaussian probability density functions (pdfs). Their use is illustrated by calculating the variance and the excess kurtosis for a univariate non-Gaussian pdf. We comment on the potential application of these methods in estimating the parameters of the recently proposed Spartan spatial random fields.     

Effects of Location Errors in Pattern Informatics

The effect of location errors in the performance of seismicity-based forecasting methods was studied here using one particular binary forecast technique, the Pattern Informatics (PI) technique (Rundle et al., Proc Nat Acad Sci USA 99, 2514–2521, 2002; Tiampo et al., Pure Appl Geophys 159, 2429–2467, 2002). The Southern Californian dataset was used to generate a series of perturbed catalogs by adding different levels of noise to epicenter locations. The PI technique was applied to these perturbed datasets to perform retrospective forecasts that were evaluated by means of skill scores, commonly used in atmospheric sciences. These results were then compared to the effectiveness obtained from the original dataset. Isolated instances of decline of the PI performance were observed due to the nature of the skill scores themselves, but no clear trend of degradation was identified. Dependence on the total number of events in a catalog also was studied, with no systematic degradation in the performance of the PI for catalogs with events in the cases studied. These results suggest that the stability of the PI method is due to the invariance of the clustering patterns identified by the TM metric (Thirumalai and Mountain, Phys Rev A 39, 3563–3573, 1989) when applied to seismicity.     

混凝土梁纯扭加载装置研制

为满足教学实验要求,特研制了一种混凝土梁纯扭加载装置。该装置不仅设计简约,而且安装方便和操控简单。建立了试验加载的力学模型,利用已有条件,设计了该纯扭加载装置及其测量方法。在试验加载过程中,加载装置的位移将会引起试件受力状态和测量结果的变化;文中介绍了测量扭矩及扭转角与实际情况的偏差,混凝土梁会产生的附加弯矩,讨论了偏差及附加弯矩对试验的影响程度。通过若干试件梁的纯扭试验,可以认为该装置符合设计要求。     

Equilibrium calculations in volcanic gaseous systems

Equilibria calculations of high-temperature volcanic gases from lava lakes are carried out on the basis of best volcanic gas samples. The equilibrium gas composition at temperatures from 800° to 1400°K and pressures up to 25 kilobars (in ideal gas system) was calculated using the free energy minimization model as well as the Newton-Raphson methods. It is shown that the juvenile «magmatic gas » of basaltic magma consists of three components: H₂O, SO₂, CO₂; the water vapor being about 60%. The increase of temperature under constant pressure results in the increase of the SO₂ concentration and in the simultaneous decrease of H₂S. Under the same conditions the ratios CO/CO₂ and H₂/H₂O are found to increase. Methane cannot be a component of «magmatic gas» corresponding to the elemental composition of basaltic lava gases. The calculated values of \(P_{O_2 } \) are in good agreement with the experimental data obtained from direct measurements of \(P_{O_2 } \) in lava lakes and experiments with basaltic melts.     

新型可更换连梁研究进展

联肢剪力墙是高层建筑结构中广泛采用的抗侧力结构体系,而连梁是联肢剪力墙结构中重要的耗能构件。然而,不论是传统的钢筋混凝土连梁还是钢连梁或型钢混凝土组合连梁破坏后修复或更换都比较困难,代价昂贵。近年来,国内外的部分学者开始研究可更换连梁,使连梁在受损后易于修复或更换,减小连梁修复费用。本文首先提出了可更换连梁的定义和分类,然后对目前国内外可更换连梁的研究现状进行了比较全面的总结,特别是介绍了2012年9月第15届世界地震工程会议上展示的相关研究成果,最后对可更换连梁的研究未来做了展望。     

地磁场模型误差分析中的几个问题

地磁场全球建模和局域建模理论是编绘全球地磁图和区域地磁图(如国家地磁图)的基础.区域磁场是全球磁场的一部分,因此,区域模型系数与全球模型系数之间存在着确定的关系.这些关系既是检验区域建模的分析方法是否合理,结果是否正确的判据,又是估计区域模型误差的出发点.全球建模的标准方法是球谐分析,而局域建模方法很多,大体可分为基于...     

Body force equivalent calculations for subsidence of the Po valley

Summary Body force equivalents can be computed for subsidence of the Po delta in the twentieth century. Their preferred location suggests that not all of the subsidence is caused by pumping of fluids or other processes occurring at shallow depths. Some of the deformation may be due to crustal response to a north-south compressive stress.     

Ferrous iron in post-perovskite from first-principles calculations

We investigate by first-principles calculations the effect of ferrous iron, Fe²⁺, on the structure and the equation of state of MgSiO₃ post-perovskite. We find that ferrous iron is high-spin over the pressure range of the mantle assuming a ferromagnetic structure. The bulk modulus and the specific volume increase with the addition of ferrous iron to MgSiO₃. We find that Fe partitions preferentially to post-perovskite and broadens the two-phase pressure range.     

Simple risk calculations in dependent hydrological series

Abstract

Various theoretical expressions are presented for determining risk in water resources systems design based on floods modelled by dependent processes. The effect of dependence on the simple risks involved in any engineering design is investigated on the basis of the lag-one Markov process. Asymptotically dependent process formulations reduce to independent case solutions that are already available in the literature. It is shown that a design risk value can be determined if the expected project life, serial correlation coefficient and simple risk are known. Necessary procedures and tables are presented for risk calculations when the variables concerned are serially correlated.     

钢筋混凝土框架梁的变形能力及基于性能的抗震设计方法

本文以Priestley改进的Mander约束混凝土模型为基础推导了RC梁截面λbv-ξn-μbψ关系的一般计算公式和简化计算公式λbv-ξ-μbψ,建立了配箍特征值λbv、相对受压区高度ξn及曲率延性μbψ三者之间的量化关系式,用于梁截面在目标曲率延性下的变形能力设计,给出了梁截面在目标曲率延性下的设计流程图.对所设计的梁截面进行变形能力验算,均可达到设定的目标曲率延性.在简化的λbv-ξ-μbψ公式基础上建立了框架梁的性能设计方程,即λbv-ξ-θplb关系式,给出了RC框架梁基于性能的抗震设计方法的一般步骤.设计者可灵活地根据性能要求设定可接受的破损指标DI进行梁的性能设计.