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1.
Two linear-hysteretic-damping models that provide energy dissipation independent of the deformation frequency, are studied in this paper: a hysteretic Kelvin element and a hysteretic Maxwell element. Both models use the Hilbert transform and yield integro–differential equations for the equations of motion of structures when real-valued signals are utilized in the formulation. It is shown that the use of analytic (complex-valued) signals allows the transformation of these integro–differential equations into differential equations with analytic input signals and complex-valued coefficients. These differential equations show both stable and unstable poles. A technique for the solution of these differential equations is presented; it consists of a conventional modal decomposition of the state-space equations and the integration of the differential equations forward in time for the modal co-ordinates associated with stable poles, and backwards in time for the modal co-ordinates associated with unstable poles. Some numerical examples are presented to illustrate the characteristics of the models and the proposed analysis technique. 相似文献
2.
A modal procedure for non-linear analysis of multistorey structures with high-damping base-isolation systems was proposed. Two different isolation devices were considered in the analysis: an high-damping laminated rubber bearing and a lead-rubber bearing. Starting from deformational properties verified by tests, the isolation systems were characterized using three different analytical models (an Elastic Viscous, a Bilinear Hysteretic and a Wen's Model) with parameters depending from maximum lateral strain. After non-linear modelling of isolation and lateral-force-resisting systems, the effects of material non-linearities were considered as pseudo-forces applied to the equivalent linear system (Pseudo-Force Method) and the formally linearized equations of motion were uncoupled by the transformation defined by the complex mode shapes. The modal responses were finally obtained with an extension of Nigam–Jennings technique to non-linear and non-classically damped systems, in conjunction with an iterative technique searching for non-linear contributions satisfying equations of motion and constitutive laws. Since the properties of the isolated structure usually change with maximun lateral strain of isolation bearings, the integration of a new set of governing equations was required for each design-displacement value. The procedure proposed was described in detail and then applied for the determination of modal and total seismic responses in some real cases. At first, a very good agreement between non-linear responses obtained with the proposed mode superposition and with a direct integration method was observed. Then a comparison of results obtained with the three different analytical models of the isolation bearings was carried out. At last, the exact modal response obtained with analytical models depending from the design displacement of the isolation bearings was compared with two different approximated solutions, evaluated using mode shapes and isolation properties, respectively, calculated under simplified hypothesis.© 1998 John Wiley & Sons, Ltd. 相似文献
3.
The discrete nature of the numerical methods utilized in 1D site response analysis and calculation of the response spectra (e.g., frequency domain, Duhamel integral, and Newmark β methods) introduces time-step dependence in the resulting solution. Using an input ground motion with too large of a time-step leads to under-prediction of high-frequency characteristics of the system response due to limitations in the numerical solution of single and multiple degree of freedom systems. In order to reduce potential errors, using a sampling rate at least ten times greater than the maximum considered frequency is recommended. The preferred alternative is selection of input ground motions with a sufficiently small time step to avoid introducing numerical errors. However, where such motions are not available, then the time step of the ground motion can be reduced through interpolation. This paper demonstrates that the use of Fourier transform zero-padded interpolation is the preferred approach to obtain a ground motion with an adequate time step for the calculation of the elastic acceleration response spectra, and to analyze site response using either frequency or time domain methods. 相似文献
4.
L. ESKOLA 《Geophysical Prospecting》1979,27(3):616-627
A numerical method is proposed for solving the problem of steady current flow. The electrodynamic model is replaced by the equivalent stationary charge distribution obtained by Poisson's analysis, in which the surface integral equation for field intensity is reduced to a set of simultaneous linear algebraic equations by means of the method of sub-areas. The solution of the set allows the calculation of an approximation for the charge density distribution on the discontinuity surfaces of conductivity. The method is valid for complex conductivities, whereby the apparent phase shift of IP can be calculated from the complex potential or field intensity. The phase shift anomaly calculated as an application is very similar to the corresponding frequency effect anomaly. The method allows the calculation of the mise-à-la-masse effect as a solution to a potential problem, in which the primary current electrode is located within the body to be surveyed. 相似文献
5.
We present a concept of the hybrid finite volume–integral equation technique for solving Maxwell's equation in a quasi-static form. The divergence correction was incorporated to improve the convergence and stability of the governing linear system equations which pose a challenge on the discretization of the curl–curl Helmholtz equation. A staggered finite volume approach is applied for discretizing the system of equations on a structured mesh and solved in a secondary field technique. The bi-conjugate gradient stabilizer was utilized with block incomplete lower-upper factorization preconditioner to solve the system of equation. To obtain the electric and magnetic fields at the receivers, we use the integral Green tensor scheme. We verify the strength of our hybrid technique with benchmark models relative to other numerical algorithms. Importantly, from the tested models, our scheme was in close agreement with the semi-analytical solution. It also revealed that the use of a quasi-analytical boundary condition helps to minimize the runtime for the linear system equation. Furthermore, the integral Green tensor approach to compute at the receivers demonstrates better accuracy compared with the conventional interpolation method. This adopted technique can be applied efficiently to the inversion procedure. 相似文献
6.
A time domain boundary element in a cylindrical coordinate system is developed for the analysis of wave propagation in a half space. The integral formulation is based on Graffi's dynamic reciprocal theorem and Stokes' fundamental solutions. The field quantities (displacements and tractions) are expressed as products of Fourier series in the tangential direction and linear polynomials in the other spatial directions. Gaussian integration is used to integrate the non-singular parts of the integral equations, whereas the integration of the singular components, which are either of order 1/r or 1/r2, is handled by special numerical schemes. In the time marching aspect, the field quantities are assumed to vary linearly in the temporal direction as well. Examples for wave propagation due to various forms of surface excitations are reported to demonstrate the accuracy of the method. 相似文献
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An array of 24 strong-motion accelerometers produced records for the New-Lian River Bridge, a five-span continuous bridge, during 25 February 1995 earthquake (weak motion) and 25 June 1995 earthquake (strong motion). This paper describes the application of linear discrete-time system identification methodology to the array of strong-motion measurements, in order to assess seismic response characteristics of the bridge. The structural system identification will concentrate not only on the global identification but also on the local structural system identification. Results of this application show that: (1) weak and strong ground excitation will induce significant differences on the dynamic response of the bridge; (2) linear models provide an excellent fit to the measured motions of the bridge from the records of these two seismic events; (3) the rigid-body rocking of the bridge pier during strong shaking is significant and cannot be ignored during identification; (4) the transverse motion at mid-span of the bridge is controlled by the quasi-static response from the boundary system and this phenomenon is quite significant during strong ground excitation. Also, systematic estimates of modal damping ratio and equivalent assessments of pier stiffness developed in the bridge during earthquake are discussed. © 1997 by John Wiley & Sons, Ltd. 相似文献
9.
本文主要研究如何通过合理设计来提高高层钢结构的整体抗震能力。首先,给出了高层钢结构的非线性计算模型;其次,建立了高层钢结构在强地震动作用下的倒塌失效模式的极限状态判别准则;然后,通过模态pushover分析,研究了高层钢结构在水平地震作用下的损伤规律;最后,重点研究了高层钢结构的整体抗震能力的提高方法,提出了均匀损伤的设计方法,该方法通过消除结构的薄弱层,来达到提高高层钢结构的整体抗震能力的目的。通过对两栋20层的高层钢框架结构进行极限时程分析和极限pushover分析,验证了文中提出的均匀损伤的设计方法的可行性。本文的工作可为高层钢结构的抗地震倒塌设计提供参考依据。 相似文献
10.
A dynamic analysis of elastic–viscoplastic systems, incorporating the modal co-ordinate transformation technique, is presented. The formulation results in uncoupled incremental equations of motion with respect to the modal co-ordinates. The elastic–viscoplastic model adopted allows the analysis not to involve yielding regions and loading/unloading processes. An implicit Runge–Kutta scheme together with the Newton–Raphson method are used to solve the non-linear constitutive equations. Stability and accuracy of the numerical solution are improved by utilizing a local time step sub-incrementing procedure. Applications of the analyses to multi-storey shear buildings show that good results can be obtained for the maximum displacement response by including only a few lower modes in the computation, but the prediction of the ductility factor response tends to underestimate the peak values when too few modes are used. In addition, stable and valid results can be obtained even with a sizable time step increment. 相似文献
11.
A simplified multisupport response spectrum method is presented.The structural response is a sum of two components of a structure with a first natural period less than 2 s.The first component is the pseudostatic response caused by the inconsistent motions of the structural supports,and the second is the structural dynamic response to ground motion accelerations.This method is formally consistent with the classical response spectrum method,and the effects of multisupport excitation are considered for any modal response spectrum or modal superposition.If the seismic inputs at each support are the same,the support displacements caused by the pseudostatic response become rigid body displacements.The response spectrum in the case of multisupport excitations then reduces to that for uniform excitations.In other words,this multisupport response spectrum method is a modification and extension of the existing response spectrum method under uniform excitation.Moreover,most of the coherency coefficients in this formulation are simplified by approximating the ground motion excitation as white noise.The results indicate that this simplification can reduce the calculation time while maintaining accuracy.Furthermore,the internal forces obtained by the multisupport response spectrum method are compared with those produced by the traditional response spectrum method in two case studies of existing long-span structures.Because the effects of inconsistent support displacements are not considered in the traditional response spectrum method,the values of internal forces near the supports are underestimated.These regions are important potential failure points and deserve special attention in the seismic design of reticulated structures. 相似文献
12.
An analysis is made of the coupled lateral-torsional response of a partially symmetric single-storey building model to horizontal translatory earthquake excitation. Interest centres on the evaluation of realistic estimates for two equivalent static actions (a shear and a torque) which account for the worst dynamic consequences of torsional unbalance. The results substantiate the findings of previous investigations which have given rise to the belief that strong modal coupling and severely coupled lateral and torsional responses are possible even in nominally symmetric buildings. The response of the model is assumed to be linearly elastic and viscously damped. In a preliminary analysis the equations of motion are solved using the modal analysis technique and the conditions necessary for full modal coupling are ascertained. Then by employing the design spectrum concept, together with suitably conservative procedures for combining the modal maxima, dimensionless forms of the equivalent static actions are evaluated as functions of two independent parameters. The final results are furnished by modified square root of the sum of the squares (SRSS) combination functions which take account of the spacing between the translational and torsional frequencies. Examples at the end of the paper illustrate the practical significance of the work. 相似文献
13.
为提高变截面梁地震动力求解的计算效率,提出了基于离散时间传递矩阵法的时程分析方法。首先,从欧拉梁的偏微分振动方程出发,基于逐步时间积分法的线性化方法并结合张量变换原理,建立了变截面梁的动力时程计算方法;其次,考虑地震动激励的非一致输入效应,采用数值迭代求解的方式建立了变截面梁地震动力时程分析的离散时间传递矩阵算法;最后,编制了数值仿真计算程序,并结合具体算例进行了算法的有效性和高效性验证。算例结果表明:在采用相同计算模型的前提下,离散时间传递矩阵法不仅能够在计算精度方面与有限元法保持一致,同时还拥有更高的计算效率。 相似文献
14.
A three‐dimensional (3D) electrical resistivity modelling code is developed to interpret surface and subsurface data. Based on the integral equation, it calculates the charge density caused by conductivity gradients at each interface of the mesh, allowing the estimation of the potential everywhere without the need to interpolate between nodes. Modelling generates a huge matrix, made up of Green's functions, which is stored by using the method of pyramidal compression. The potential is compared with the analytical and the numerical solutions obtained by finite‐difference codes for two models: the two‐layer case and the vertical contact case. The integral method is more accurate around the source point and at the limits of the domain for the potential calculation using a pole‐pole array. A technique is proposed to calculate the sensitivity (Jacobian) and Hessian matrices in 3D. The sensitivity is based on the derivative with respect to the block conductivity of the potential computed using the integral equation; it is only necessary to compute the electrical field at the source location. A direct extension of this technique allows the determination of the second derivatives. The technique is compared with the analytical solutions and with the calculation of the sensitivity according to the method using the inner product of the current densities calculated at the source and receiver points. Results are very accurate when the Green's function that includes the source image is used. The calculation of the three components of the electric field on the interfaces of the mesh is carried out simultaneously and quickly, using matrix compression. 相似文献
15.
The Cagniard-de Hoop method is ideally suited to the analysis of wave propagation problems in stratified media. The method applies to the integral transform representation of the solution in the transform variables (s, p) dual of the time and transverse distance. The objective of the method is to make the p-integral take the form of a forward Laplace transform, so that the cascade of the two integrals can be identified as a forward and inverse transform, thereby making the actual integration unnecessary. That is, the exponent (–sw(p)) is set equal to –sτ, with τ varying from some (real) finite time to infinity. As usually presented, the p-integral is deformed onto a contour on which the exponent is real and decreases to –∞ as p tends to infinity. We have found that it is often easier to introduce a complex variable τ for the exponent and carry out the deformation of contour in the complex τ-domain. In the τ-domain the deformation amounts to ‘closing down’ the contour of integration around the real axis while taking due account of singularities off this axis. Typically, the method is applied to an integral that represents one body wave plus other types of waves. In this approach, the saddle point of w(p) that produces the body wave plays a crucial role because it is always a branch point of the integrand in the τ-domain integral. Furthermore, the paths of steepest ascent from the saddle point are always the tails of the Cagniard path along which w(p) →∞. That is, the image of the pair of steepest ascent paths in the p-domain is a double covering of a segment of the Re τ-axis in the τ-domain. The deformed contour in the p-domain will be the only pair of steepest ascent paths unless the original integrand had other singularities in the p-domain between the imaginary axis and this pair of contours. This motivates the definition of a primary p-domain, i.e. the domain between the imaginary axis and the steepest descent paths, and its image in the τ-domain, the primary τ-domain. In terms of these regions, singularities in the primary p-domain have images in the primary τ-domain and the deformation of contour on to the real axis in the τ-domain must include contributions from these singularities. This approach to the Cagniard-de Hoop method represents a return from de Hoop's modification to Cagniard's original method, but with simplifications that make the original method more tractable and straightforward. This approach is also reminiscent of van der Waerden's approach to the method of steepest descents, which starts exactly the same way. Indeed, after the deformation of contour in the τ-domain, the user has the choice of applying asymptotic analysis to the resulting ‘loop’ integrals (Watson's lemma) or continuing to obtain the exact, although usually implicit, time-domain solution by completing the Cagniard-de Hoop analysis. In developing the method we examine the transformation from a frequency-domain representation of the solution (ω) to a Laplace representation (s). Many users start from the frequency-domain representation of solutions of wave propagation problems. In this case issues arising from the movement of singularities under the transformation from ω to s must be considered. We discuss this extension in the context of the Sommerfeld half-plane problem. 相似文献
16.
The use of predictive models for the understanding and management of sediment and contaminant transport generally requires knowledge of particle size and settling velocity. Particle size is often obtained by direct measurements, and the settling velocities are usually predicted using the Stokes' law (or a modification thereof) for single‐grained spherical particles. Such measurements and estimates are not satisfactory measures for cohesive sediments, which exist as agglomerated particles called flocs and whose behaviour is significantly different from that of the single‐grained particles. Direct measurement of settling velocity and size using optical methods in settling columns has also been employed to improve these predictions; however, the subjectivity in determining which particles are in focus results in unreliable size data. An out‐of‐focus particle will generally possess a larger size than in reality. This paper evaluates a laser‐assisted particle sizing/settling velocity determination technique's ability to eliminate the subjectivity and improve particle‐sizing accuracy during settling column experiments. Although the diffraction of light by the translucent standard beads (used for evaluating the technique's accuracy for determining particle size) posed a problem, the results suggest that this technique has potential for assisting researchers to obtain the most accurate settling particle size data possible. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
17.
In this paper, the Cesàro mean technique is applied to regularize the divergent problem which occurs in ground motion deconvolution analysis in geotechnical engineering. To deal with this ill-posed problem, we use the corner of the L-curve as the compromise point to determine the optimal order of Cesàro mean so that the high frequency content can be suppressed instead of engineering judgement using the concept of a cutoff frequency. The fractional order of Cesàro mean has been derived and used to fulfill this purpose. From the examples shown, it is found that the wave form including maximum acceleration can be accurately predicted and that both the high frequency content and divergent results can be avoided by using the proposed regularization technique. 相似文献
18.
Peter Furness 《Geophysical Prospecting》1996,44(1):27-40
Modelling the theoretical response of several important geophysical systems involves the solution of Poisson's equation with homogeneous Neumann boundary conditions (i.e. a zero normal gradient) imposed over either open or closed surfaces. A simple integral equation solution to this problem is derived from first principles. It is applicable to both types of surface and in this respect represents an improvement on existing integral equation techniques. However, the present surface integral equation displays a strong singularity of order 1/R3 which requires an appropriate interpretation for its implementation. A comparison of some numerical results with analytical data taken from the literature demonstrates that the proposed integral equation technique is suitably robust, accurate and efficient for practical application in geophysical interpretation. 相似文献
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本文提出一种空间波数混合域磁异常场三维数值模拟方法.该方法利用磁位三维空间域积分为卷积的特点,沿水平方向进行二维傅里叶变换,把空间域磁位满足的三维积分问题转化为不同波数之间相互独立的垂向一维积分问题.保留垂向为空间域,优势之一在于便于浅层单元剖分可适当加密,随着深度增加,单元剖分适当稀疏,可以准确模拟任意复杂地形和磁性体的磁异常,兼顾了计算精度与计算效率;优势之二在于一维积分垂向可离散为多个单元积分之和,每个单元采用二次形函数表征磁化强度,可得出单元积分的解析表达式,计算精度高、效率高.该方法充分利用一维形函数积分的高效和高精度、快速傅里叶变换的高效性及算法高度并行性,实现了磁异常场高效、高精度的数值模拟.设计棱柱体模型,将模型解析解与空间波数混合域法的数值解对比,结果表明该方法计算精度高、效率高.设计了组合棱柱体复杂模型,对比分析了标准FFT扩边法与Gauss-FFT法的计算精度与计算效率,总结了标准FFT的扩边系数选取策略.针对任意复杂地形条件下的磁异常模拟问题,本文提出一种适用于起伏地形条件下的磁异常场快速计算方法,并对其有效性进行了验证. 相似文献