基于弯曲弹簧模型的裂纹混凝土梁动力特性分析

利用结构振动波传播理论,将含裂纹混凝土梁以裂纹为界划分为两段连续的波导体,为了表征由裂纹引起的梁中波传播的不连续特性,引入了模拟裂纹的弯曲弹簧模型。通过理论计算得到了裂纹简支梁的特征方程,并以一裂纹混凝土简支梁为例进行数值分析,讨论了裂纹的深度和位置对裂纹梁各阶固有频率的影响。     

Some aspects of floor spectra of 1DOF nonlinear primary structures

In this paper the influence of the nonlinear behaviour of the primary structure on floor spectra is investigated by means of simple models. The general trends of floor spectra for different types of nonlinear behaviour of one degree of freedom (1DOF) primary structure are shown and we point out their common futures and their differences. A special attention is given to the cases of elastoplastic and nonlinear elastic behaviours and methods to determine an equivalent linear oscillator are proposed. The properties (frequency and damping) of this equivalent linear oscillator are quite different from the properties of equivalent linear oscillators commonly considered in practice. In particular, in the case of elastoplastic behaviour, there is no frequency shift and damping is smaller than assumed by other methods commonly used. In the case of nonlinear elastic behaviour, the concept of an equivalent frequency which is a random variable is used. Finally, a design floor spectrum of primary structures, exhibiting energy dissipating nonlinear behaviour is proposed. Copyright © 2006 John Wiley & Sons, Ltd.     

Dynamics of elastic–plastic shear frames with secondary structures: shake table and numerical studies

Results from experimental and numerical studies of earthquake‐excited small‐scale primary–secondary structures are presented. The primary structure considered is a plane three‐storey shear frame with a fundamental frequency of 5.5 Hz. The columns of the first floor are built with soft aluminium and they are stressed beyond its linear range of behaviour. After each test the elastic–plastic columns are replaced by a new set of undeformed virgin aluminium bars. The elastic–plastic shear frame is tested with and without an attached secondary structure. The secondary structure is modelled as an elastic SDOF oscillator, and its natural frequency is tuned to the fundamental frequency of the shear frame. Alternatively, the oscillator is mounted on the horizontal beam of the second and third floor. The base excitation of the structural model is characterized by a broad band random process with constant spectral density in a frequency range between 3 and 30 Hz. In the numerical study, the digital recorded acceleration of the base excites the mechanical model of the investigated structures. Numerical outcomes assuming fictitious unlimited elastic material behaviour of the shear frame are set in contrast to results from experiments and computational simulations where the measured non‐linear force displacement relation of the elastic–plastic floor is approximated by a piecewise linear curve. The effect of elastic–plastic materials on the dynamic interaction between primary and secondary structure is shown and the difference to unlimited elastic material behaviour is worked out in detail. Copyright © 2001 John Wiley & Sons, Ltd.     

Winkler弹性地基板梁的自由振动分析

中短型轨道板的几何构型介于梁、板之间,属于宽梁结构。从Mindlin板理论出发,退化得到适用于宽梁的Mindlin板梁控制方程;引入Winkler地基刚度系数,推导得到位移和转角的模态函数表达式。考虑两端简支的边界条件,得到弹性地基板梁的自由振动特征方程。通过无量纲数值算例求解出弹性地基板梁的自振频率,并与Timoshenko梁理论和Mindlin板理论进行对比。研究高跨比、泊松比和弹性地基刚度等参数对结构自振特性的影响,总结出弹性地基板梁方程的特点及适用范围,即宽度效应显著且泊松比较大的宽梁结构。     

The scattering of SH waves by a finite crack with a superposition-based diffraction technique

The problem of diffraction of cylindrical and plane horizontally polarized shear waves (SH waves) by a finite crack embedded in a plane bidimensional elastic full-space is revisited. Particularly, we construct an approximate solution by the addition of independent diffracted terms. In our method the derivation of the fundamental case of a semi-infinite crack obtained as a degenerate case of a generalized wedge is first considered. This result is then used as a building block to compute the diffraction of the main incident waves. The interaction between the opposite edges of the crack is later considered in terms of a series, one term at a time until a desired tolerance is reached. Moreover, we propose a procedure to determine the number of required interactions as a function of frequency. The solution derived with the superposition technique is shown to be effective at low and high frequencies and as shown by comparisons with a direct boundary element method software, highly accurate solutions are obtained after retaining just a few terms of the infinite series.     

一种Timoshenko裂纹梁的静力挠度分析方法

建立了一种Timoshenko裂纹梁的分析模型并且获得了闭合形式的挠度解析解。首先,在一致梁的理论框架下,通过引入δ函数模拟裂纹导致的局部柔度,建立用广义函数表示的Timoshenko裂纹梁的微分控制方程,进而得到挠度的闭合形式的解答;其次,根据线弹性断裂力学理论,利用转角及挠度突变与局部柔度系数的关系,建立Timoshenko裂纹梁的模型参数与裂纹深度的显式表示;最后,通过对裂纹深度与挠度、转角和曲率间关系的分析,总结了结构响应的损伤敏感性及其特征,并且通过与引入裂纹奇异单元的有限元结果进行比较,验证了本文所建分析模型及求解方法的正确性。研究结果表明,本文所建立的Timoshenko裂纹梁的分析模型,具有较高的计算精度和效率,在结构模型修正和损伤识别中具有良好的应用前景。     

半无限地下介质中与垂直张性裂缝相关联的应力场和地面形变

本文笔者把垂直并贯穿达地表面之张性裂缝作为格里菲思（Griffith）裂隙来考虑,从而研讨了在已给裂缝变形情况下的半无限地下介质中的应力场和地面形变.推导出了估计这些应力和变形的一系列公式.考查了地表面的变形和与裂缝的存在相伴随的应力降.关于裂缝的张开,假设按线性规律从裂缝的顶部到底部逐渐减小至零,而裂缝顶部开裂的宽度与裂缝深度比较,则认为相对地较小.     

基于各向异性岩石物理的缝隙流体因子AVAZ反演

裂缝型储层表现出较强的各向异性特征.缝隙中充填不同流体时,裂缝储层的地震响应特征也不相同.本文从各向异性岩石物理模型出发,引入可有效识别缝隙流体的指示因子,并研究缝隙充填流体类型、饱和度以及缝隙纵横比与流体因子的相互关系,进而分析不同流体充填时介质的地震响应特征,并基于AVAZ反演方法估测缝隙流体指示因子.首先对缝隙流体因子的敏感性进行了分析,讨论当缝隙充填不同流体时,缝隙流体因子值的变化特征,同时研究了不同流体类型充填时裂缝储层反射系数随方位角和入射角的变化特征.某工区测井数据和复杂裂缝模型应用表明,基于各向异性岩石物理的缝隙流体因子AVAZ反演方法合理、可靠,且具有良好的抗噪性,即当对合成地震记录添加信噪比不小于1/2的随机噪声时,利用AVAZ反演方法估测所得流体因子值与真实值仍然吻合较好.     

Solution of random structural system subject to nonstationary excitation: transforming the equation with random coefficients to one with deterministic coefficients and random initial conditions

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.     

Dynamic response analysis of a multiple-beam structure subjected to a moving load

In this study, the dynamic response of an elastically connected multi-beam structure subjected to a moving load with elastic boundary conditions is investigated. The boundary conditions and properties of each beam vary, and the difficulty of solving the motion equation is reduced by using a Fourier series plus three special transformations. By examining a high-speed railway (HSR) with mixed boundary conditions, the rationality for the newly proposed method is verified, the difference in simulated multiple-beam models with different beam numbers is explored, and the influence of material parameters and load speed on the dynamic response of multiple-beam structures is examined. Results suggest that the number of beams in the model should be as close to the actual beam number as possible. Models with an appropriate beam number can be used to describe in detail the dynamic response of the structure. Neglecting the track-structure can overestimate the resonant speed of a high-speed railway, simply-supported beam bridge. The effective interval of foundation stiffness (EIFS) can provide a reference for future engineering designs.

     

基于Duffing振子混沌系统的地震速度分析方法

强随机噪声干扰是导致地震勘探资料低信噪比的主要原因,如何在强随机噪声干扰下获取有效的信息是值得关注的问题.Duffing振子混沌系统是一个非线性的动力学系统,其对强随机噪声具有免疫能力,而对特定的周期性信号具有敏感性.本文提出一种基于Duffing振子混沌系统的速度分析方法.对CMP道集按照时距曲线关系进行移动窗口截取,将所截取的信号构建为待测信号加入Duffing振子混沌系统,通过相图网格分割方法(GPM)判断系统状态的改变,从而在强随机噪声背景下获得高分辨率的速度谱.理论模型和实际资料的处理结果表明,与传统的水平叠加速度分析方法相比,本方法能够在强随机噪声背景下获得更准确的速度分析结果.     

基于模态分析和神经网络的裂缝损伤识别

提出了裂缝损伤诊断的神经网络方法,探讨了用模态技术和神经网络对混凝土结构裂缝损伤进行识别与定位的方法。文中以一简支矩形截面梁为研究对象,通过完好结构和损伤结构的有限元分析,获取两者的损伤标识量,输入BP神经网络训练。以损伤位置和裂缝高度作为输出参数,对其进行单处损伤定位的研究。数值仿真结果表明,采用神经网络方法可以对裂缝做出较好的诊断。     

小剪跨比格构式混凝土墙体抗震性能试验

文章旨在研究不同剪跨比的格构式混凝土墙体抗震性能.将生产车间预制成EPS保温模块拼接成墙体模板,在横向和纵向孔洞中分别布置钢筋,然后在孔内浇筑自密实混凝土,形成“EPS新型节能”格构式混凝土墙体,然后对6个参数不同的试件进行低周反复水平荷载作用的试验.结果,墙体破坏形态为:首先墙体相邻格构柱间的连梁出现环状裂缝和“X”...     

Spatially coupled vibrations of a suspension bridge under random highway traffic

The problem of spatial dynamic response of a suspension bridge to the passage of trains of concentrated forces with random values is considered. The arrival of forces at the bridge is assumed to constitute a Poisson process of events. Such an excitation process is an appropriate model of vehicular traffic loads acting on the bridge. The bridge is idealized by a single-span thin-walled beam underslung to two cables. The response of the bridge in the space-time domain is described by a coupled system of non-linear, integro-differential equations. The dynamic influence functions of vertical and horizontal deflections at each cross-section point are obtained for the linear case. Cumulants and probability density functions of response are determined. Numerical methods have been used to develop a computer-oriented algorithm aimed at the numerical solution of the problem. As examples, numerical results for a particular bridge with some practical load cases are presented and illustrated by graphs.     

移动荷载对桥梁动力响应的影响研究——以开裂预应力混凝土简支梁为例

混凝土桥梁在工作过程中会产生裂缝,为分析移动荷载对开裂混凝土桥梁结构刚度的影响,对开裂梁动力响应进行分析。建立简支T梁桥有限元模型,并将移动荷载施加至有限元模型中。根据简支T梁桥破坏横向分布位置和强度的不同,研究不同工况下各梁荷载横向分布及不同移动速度对裂缝扩展宽度的影响。结果表明,数值模拟结果能较好地验证计算模型的准确性;在较大的移动荷载作用下,混凝土开裂,导致结构刚度减小、位移增大;随着移动荷载和速度的增加,开裂时间增加,结构刚度降低,持续时间增加,位移增大,使结构响应呈现明显非线性。     

Dynamic response of a tunnel buried in a saturated poroelastic soil layer to a moving point load

The dynamic response of a tunnel buried in a two-dimensional poroelastic soil layer subjected to a moving point load was investigated theoretically. The tunnel was simplified as an infinite long Euler–Bernoulli beam, which was placed parallel to the traction-free ground surface. The saturated layer was governed by Biot’s theory. Combined with the specified boundary conditions along the beam and saturated poroelastic layer, the coupled equations of the system were solved analytically in the frequency–wavenumber domain based on Fourier transform. The time domain responses were obtained by the fast inverse Fourier transform. The critical velocity of the considered structure was determined from the dispersion curves. The different dynamic characteristics of the elastic soil medium and the saturated poroelastic medium subjected to the underground moving load were investigated. It is concluded that, for coarse materials or fine materials subjected to the high-velocity loading, models ignoring the coupling effects between the pore fluid and the soil skeleton may cause errors. The shear modulus and the permeability coefficients of the saturated soil as well as the load moving velocity had significant influence on the displacement and pore pressure responses.     

A multifractal model of crack coalescence in rocks

Geometric characteristics of fractal sets of cracks are investigated from the standpoint of their coalescence. A 1D computer model, in which a realistic character of forms of crack sets is achieved through the inducing of sets with the use of the multiplicative cascade procedure, is considered. The investigation is aimed at the determination of conditions of coalescence of cracks organized as a superposition of fractal subsets of a unified set of cracks. The process of crack coalescence is investigated for three different values of the coalescence criterion. The geometric characteristics of the sets of cracks that are necessary for the transition of the crack coalescence process into an avalanche-like stage are estimated.     

Magma reservoir systems inferred from tilt patterns

Inflation patterns based on water-tube tiltmeter and levelling observation show different features for Krafla Volcano in Iceland and Kilauea Volcano in Hawaii. Monotonous sawtooth shape inflation is observed at Krafla, while inflation curves at Kileauea are more or less complicated. The difference was attributed to differences in the system of magma reservoir for the two volcanoes. By using the electrical equivalent of a magma reservoir and volcanic conduit as a capacitor and a resistor, an electrical oseillator was considered to be a possible model for a magma reservoir system. In the case of Krafla, the magma reservoir system is replaced with one electric oscillator called «Single system» or «Icelandic type» system. The complicated inflation pattern of Kilauea was interpreted as the assembly of a main magma reservoir and the group of surrounding small reservoirs. The equivalent electric analogue is the composite parallel and serial connection of a single oscillator which generates irregular output voltage during a charging process. The proposed magma reservoir system of Kilauea is called «Multi-coupled system» or «Hawaiian type system» which also help in interpreting the wondering of the uplift center and tidal phenomena of the Halemaumau lava lake.     

Dynamic response of multistoreyed brick buildings

The paper presents the seismic response analysis of a typical multistoreyed brick building. A number of variables representing the physical properties of the structural system, namely, number of storeys from one to four, wall thickness in various storeys from one to one and a half brick thick and damping from 5 per cent to 15 per cent of critical value are considered. A shear beam type multi-degree-of-freedom oscillator is taken to represent these buildings mathematically in which the masses of the floors and walls are assumed as lumped at the floor levels and the floors are assumed as rigid diaphragms. Koyna and El Centro earthquake accelerograms, representing two seismicity levels, are used for computing dynamic response of the buildings. Overturning and torsional effects have been included in the determination of timewise net stresses in the building elements and their seismic capabilities have been examined. From this study the critical sections for providing reinforcing have been identified and the minimum amount of necessary steel has been estimated.     

Reflection and refraction at an imperfectly bonded interface between poroelastic solid and cracked elastic solid

Porous solid is in contact with a cracked elastic solid at a plane interface between them. For the presence of vertically aligned microcracks, the elastic solid behaves transversely isotropic to wave propagation. The coefficients of elastic anisotropy depend on the crack density and crack porosity in the medium. A loose bonding is considered between the two solids so that a limiting case could be the welded contact. At the plane interface, the imperfection in welded bonding is represented by tangential slipping and, hence, results in the dissipation of a part of strain energy. Three types of waves propagate in an isotropic fluid-saturated porous medium, which are considered for incidence at the interface. Incidence of a wave results in three reflected waves and two refracted waves. Partition of incident energy among the reflected and refracted waves is studied for each incidence, varying from normal to grazing directions. Numerical example calculates the energy shares of reflected and refracted waves at the plane interface between water-saturated sandstone and basalt. These energy shares are computed and analyzed for different values of crack parameters as well as loose bonding parameter.