共查询到20条相似文献，搜索用时 504 毫秒
1.
Real and complex Ritz vector bases for dynamic analysis of large linear systems with non-proportional damping are presented and compared. Both vector bases are generated utilizing load dependent vector algorithms that employ recurrence equations analogous to the Lanczos algorithm. The choice of static response to fixed spatial loading distribution, as a starting vector in recurrence equations, is motivated by the static correction concept. Different phases of dynamic response analysis are compared with respect to computational efficiency and accuracy. It is concluded that the real vector basis approach is approximately eight times more efficient than the complex vector basis approach. The complex vector basis has some advantages with respect to accuracy, if the excitation is of piecewise linear form, since the exact solution can be utilized. In addition, it is demonstrated that both Ritz vector bases, real and complex, possess superior accuracy over the adequate eigenvector bases. 相似文献
2.
This paper considers a solution method for viscously damped linear structural systems which are subjected to transient loading. The equations of motion of such systems are written in a first-order form. A solution subspace is generated using the damped dynamic matrix and the static deflection from the first-order form of the equations of motion. Two convenient bases, Lanczos vectors and Ritz vectors, are constructed from this subspace. An approximate solution is then obtained by superposition of the Lanczos vectors or the Ritz vectors. In contrast to the traditional mode superposition method using complex eigenvectors, the Lanczos vectors or the Ritz vectors are less expensive to generate than the complex eigenvectors, yet yield comparable accuracy. In addition, there is no need for a static correction since the static deflection is already contained in our solution subspace. Numerical examples are presented to show the potential of using the Ritz vectors to compute responses of damped dynamic systems. 相似文献
3.
A generation procedure of Ritz vectors to control the inclusion of static effect and the number of vectors in mode superposition dynamic analysis is presented. The original algorithm of the Ritz vectors15 is modified to improve stability in the generation procedure and to include the use of static residual. To reject unimportant Ritz vectors, cut-off criteria, which are based on the participation of mass distribution and spatial load distribution, are proposed. Numerical examples are presented to illustrate the effectiveness of the derived Ritz vectors over the eigenvectors and the performance of the cutoff criteria in the mode superposition dynamic analysis. 相似文献
4.
The solution of the eigenvalue problem for large structures is often the most costly phase of a dynamic response analysis. In this paper, the need for the exact solution of this large eigenvalue problem is eliminated. A new algorithm, based on error minimization, is presented for the generation of a sequence of Ritz vectors. These orthogonal vectors are used to reduce the size of the system. Only Ritz vectors with a large participation factor are used in the subsequent mode superposition analysis. In all examples studied, the superposition of Ritz vectors yields more accurate results, with fewer vectors, than if the exact eigenvectors are used. The proposed method not only reduces computer time requirements significantly but provides an error estimation for the dynamic analysis. The approach automatically includes the advantages of the proven numerical techniques of static condensation, Guyan reduction and static correction due to higher mode truncation. 相似文献
5.
The accuracy of a numerical method is demonstrated for the dynamic analysis of large complex finite element systems in which the spatial distribution of the loading is constant. The method is based on the use of a special class of Ritz vectors which were previously proposed and can be generated with minimum numerical effort. The purpose of this paper is to extend the use of these vectors to the solution of wave propagation and foundation response problems. The method is applied to one-, twoand three-dimensional problems in order to illustrate the efficiency and accuracy of the technique. Unless it is necessary to evaluate the very high-frequency behaviour of a structural system, it is shown that a small number of Ritz vectors will produce excellent results. Therefore, they can be very effective in the solution of three-dimensional soil-structure systems subjected to earthquake loading. 相似文献
6.
Real-time simulations are used to a significant extent in many engineering fields. However, if nonlinearities are included, the real-time requirement significantly limits the size and complexity of numerical models. The present work constitutes the second of two papers where a general basis method to simulate kinematic nonlinear structures more efficiently is introduced. The advantage of the basis formulation is that it enables the number of basis vectors to be increased without increasing the number of unknown basis co-ordinates. This allows for larger numerical kinematically nonlinear models to run in real time. The basis is organized from a Taylor series that includes the system mode shapes and their complete first-order modal derivatives derived in Part I. The Taylor series predicts fixed linear relations between the modal co-ordinates of the system mode shapes and the modal derivatives, respectively. Thus, the full solution is known solely by determining the modal co-ordinates of the mode shapes, which significantly minimizes the computational costs. Furthermore, it is illustrated that the stability of the Taylor basis formulation is dependent on the mode shape frequencies only, allowing the applied time steps to be significantly larger than in standard nonlinear basis analysis. An example illustrates a case where the computational time can be decreased by one order of magnitude using a Taylor basis formulation compared with a standard basis formulation including identical basis vectors. 相似文献
7.
The simple Lanczos method presented in a recent paper by the writers, with application to single vector loads, is extended to include a more general dynamic loading represented as a linear combination of k vectors (load patterns). The result is a set of orthogonal vectors that is used to transform the equations of motion to a banded form, the half-bandwidth of which becomes k + 1. When k is small relative to the number of equations, this approach provides for a very efficient time-stepping solution. 相似文献
8.
Vibration tests were conducted on a 1/24-scale model of the North Fork Dam, a double-curvature arch dam, to determine natural frequencies, mode shapes and hydrodynamic pressures. The mode shapes and natural frequencies were determined from tests using two vibrators mounted on the crest of the dam. Hydrodynamic pressures at the dam/reservoir interface were determined from tests in which the vibrator was attached to the downstream foundation of the dam. The hydrodynamic pressures calculated using Westergaard's theory and a theory for arch dams developed by Perumalswami and Kar accurately predicted the measured pressure at frequencies below the first mode frequency of the dam. The differences in the two theories were insignificant. The Structural Analysis Program (SAP), a linear three-dimensional (3-D) finite element code, was used to compute mode shapes and frequencies for the dam with its base fixed and with a foundation. Numerical solution schemes used in the finite element analysis consisted of a Ritz analysis and a subspace iteration method. Calculations were conducted for both full and empty reservoir conditions. The accuracy of the Ritz analysis improved considerably as more nodes in flexible regions of the dam were loaded. However, the lowest eigenvalues were computed using the subspace iteration method. For the full reservoir, the natural frequencies decreased by 20-30 per cent when the foundation was included in the finite element model. The difference was less when the reservoir was empty. The calculations using the subspace iteration scheme and including the foundation agreed closely with experimental mode shapes and corresponding natural frequencies. 相似文献
9.
Analysis in the frequency domain using discrete Fourier transforms is an efficient means of calculating the dynamic response of linear systems. In fact, for systems with frequency dependent parameters and also in those cases where the complex frequency response functions are more easily determined, frequency domain analysis may be the only effective means of determining the dynamic response. The use of discrete transforms along with finite summation requires that the forcing function and the impulse function be converted into periodic forms. This modification may introduce unacceptable errors in the results of analysis, unless appropriate steps are taken to avoid or minimize the effect of aliasing or overlapping. For single-degree-of-freedom systems, procedures that will eliminate the effect of aliasing have already been developed. However, problems related to frequency domain analysis still exist for multi-degree-of-freedom systems with non-proportional damping, in analysis through substructuring and in those cases where a continuum solution is involved. A new procedure which addresses these problems and is applicable to both single- and multi-degree-of-freedom system as well as to analysis through substructuring is presented here. 相似文献
10.
地铁循环荷载作用下饱和软黏土的动力特性研究对于揭示软黏土在地铁荷载下的孔压、强度以及变形模式具有重要意义,可以为控制地铁长期沉降、降低运营风险提供理论依据。试验加载形式的不同会带来不同的动力特性表征,需选取最能反映地铁列车真实性质的荷载形式。本文在列车荷载作用下研究土动力特性,采用室内动三轴试验的方法,对比分析不同形式下动力荷载作用效果。试验研究表明:偏压正弦波可以作为简化波形研究列车荷载,它不仅可以确保加载过程中地基土只有压应力,而且能较好地模拟列车循环荷载。 相似文献
11.
Load‐dependent Ritz (LDR) vectors are used in conjunction with the multiple‐support response spectrum (MSRS) combination rule for analysis of structures subjected to spatially varying earthquake ground motions. The LDR vector approach for MSRS analysis is motivated by the fact that LDR vectors in general are more accurate and computationally simpler than eigenvectors in mode superposition analysis, and because many researchers and engineers are using LDR vectors in linear structural dynamic analysis. Mode truncation rules for the original MSRS method are modified to apply to LDR vectors. Two methods for selecting LDR vectors for multicomponent MSRS analysis are introduced. Idealized models of two real bridges with differing structural characteristics are used to investigate the accuracy and efficiency of the two LDR‐MSRS methods in comparison with results obtained by the original MSRS method as well as an extended version that accounts for the static contribution of truncated modes. The results show that the LDR‐MSRS method is generally more accurate than the original MSRS method and at least as accurate as the extended MSRS method. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
12.
Mode superposition is a widely used method for solving the dynamic equilibrium equation in structural dynamic analysis. However, the accuracy of this method may be reduced when the dynamic equilibrium equations are set up using displacement excitation. A new method for developing solutions for dynamic equilibrium equations based on displacement excitation is introduced. The dynamic equilibrium equation is decomposed into two parts, namely displacement excitation and velocity excitation, and precise integration and mode superposition methods are combined to solve the equation. Ritz vectors are then used to calculate the static response of the truncated modes of the structure, and a method for determining the number of participating modes is obtained. Using multi-degree-of-freedom systems as two computational examples, the differences in the structural responses obtained from the displacement excitation and acceleration excitation are compared and analyzed. It is shown that the new solution method generates consistent accuracy between the displacement excitation and acceleration excitation. 相似文献
13.
It is pointed out that the number of modes which should be included in a mode superposition dynamic response analysis depends on both the frequency content and the distribution of the loading. If the loading frequency is low the effect of the higher modes can be approximated by a static analysis. A technique is described for calculating this static contribution from the higher modes; the total response is then represented by the sum of the lower mode dynamic response and the higher mode static effects. The effectiveness of the procedure is demonstrated by a numerical example. 相似文献
14.
Spectral analysis of systems with non-classical damping using classical mode superposition technique
A spectral method for random vibration analysis of a structural system with non-proportional damping is presented using classical (undamped) mode superposition technique. The method obtains the frequency response function of the system by solving the dynamic equilibrium equations in generalized co-ordinates through an iterative process. The iterative solution is written in closed form and the proof for convergence of the iterative process is given. Numerical examples show the convergence characteristics of the process and an excellent accuracy of the obtained results. The method turns out to be computationally more efficient than the conventional methods of spectral analysis using damped mode shapes and frequencies. 相似文献
15.
An approximate method for linear analysis of asymmetric‐plan, multistorey buildings is specialized for a single‐storey, base‐isolated structure. To find the mode shapes of the torsionally coupled system, the Rayleigh–Ritz procedure is applied using the torsionally uncoupled modes as Ritz vectors. This approach reduces to analysis of two single‐storey systems, each with vibration properties and eccentricities (labelled ‘effective eccentricities’) similar to corresponding properties of the isolation system or the fixed‐base structure. With certain assumptions, the vibration properties of the coupled system can be expressed explicitly in terms of these single‐storey system properties. Three different methods are developed: the first is a direct application of the Rayleigh–Ritz procedure; the second and third use simplifications for the effective eccentricities, assuming a relatively stiff superstructure. The accuracy of these proposed methods and the rigid structure method in determining responses are assessed for a range of system parameters including eccentricity and structure flexibility. For a subset of systems with equal isolation and structural eccentricities, two of the methods are exact and the third is sufficiently accurate; all three are preferred to the rigid structure method. For systems with zero isolation eccentricity, however, all approximate methods considered are inconsistent and should be applied with caution, only to systems with small structural eccentricities or stiff structures. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
16.
A general procedure for analysis of the response of concrete gravity dams, including the dynamic effects of impounded water and flexible foundation rock, to the transverse (horizontal) and vertical components of earthquake ground motion is presented. The problem is reduced to one in two dimensions, considering the transverse vibration of a monolith of the dam. The system is analysed under the assumption of linear behaviour for the concrete, foundation rock and water. The complete system is considered as composed of three substructures—the dam, represented as a finite element system, the fluid domain, as a continuum of infinite length in the upstream direction, and the foundation rock region as a viscoelastic half-plane. The structural displacements of the dam are expressed as a linear combination of Ritz vectors, chosen as normal modes of an associated undamped dam-rock system. The effectiveness of this analytical formulation lies in its being able to produce excellent results by considering only a few Ritz vectors. The generalized displacements due to earthquake motion are computed by synthesizing their complex frequency responses using Fast Fourier Transform procedures. The stress responses are calculated from the displacements. An example analysis is presented to illustrate results obtained from this analytical procedure. Computation times for several analyses are presented to illustrate the effectiveness of the procedure. 相似文献
17.
For super high-rise buildings,the vibration period of the basic mode is several seconds,and it is very close to the period of the fluctuating wind.The damping of super high-rise buildings is low,so super high-rise buildings are very sensitive to fluctuating wind.The wind load is one of the key loads in the design of super high-rise buildings.It is known that only the basic mode is needed in the wind-response analysis of tall buildings.However,for super high-rise buildings,especially for the acceleration response,because of the frequency amplification of the high modes,the high modes and the mode coupling may need to be considered.Three typical super high-rise projects with the SMPSS in wind tunnel tests and the random vibration theory method were used to analyze the effect of high modes on the wind-induced response.The conclusions can be drawn as follows.First,for the displacement response,the basic mode is dominant,and the high modes can be neglected.Second,for the acceleration response,the high modes and the mode coupling should be considered.Lastly,the strain energy of modes can only give the vibration energy distribution of the high-rise building,and it cannot describe the local wind-induced vibration of high-rise buildings,especially for the top acceleration response. 相似文献
18.
Experimental study on the influence of seismic subsidence of loess under bidirectional loading modes
《地震研究进展（英文）》2021,1(4):100064
Water content, dry density, void ratio, depth of soil layer, and seismic loading may all exert influence on the seismic subsidence of loess. Many scholars have carried out seismic subsidence tests of loess to simulate the stress on soil using unidirectional (axial) vibration instead of bidirectional vibration. We conduct seismic subsidence tests of loess using two different dynamic stress loading methods, unidirectional and bidirectional dynamic stress. In addition, the effects of different dynamic stress loading modes on the development of seismic subsidence of loess are compared for a case-study in northwestern China. The results show that (1) the increasing ratio of radial stress to axial stress has exerted significant influence on the seismic subsidence coefficient of loess under the loading mode of bidirectional dynamic stress (2) there is a critical ratio of radial stress to axial stress for seismic subsidence of loess, ranging from 0.6 to 0.8; when the ratio of radial load to axial load is greater than the critical value, the effect of bidirectional load on the development of seismic subsidence is more remarkable (3) when the ratio of radial load to axial load is smaller, the seismic subsidence of loess calculated by the existing unidirectional stress loading method is safe for engineering projects. However, if the value exceeds the safety ratio range it is dangerous to conduct safety evaluations using the seismic loess subsidence. The prediction value of seismic subsidence at engineering sites directly affects the later foundation treatment and the safety of the overlying structures. The seismic subsidence calculation and evaluation method in this study may provide a scientific basis for safety evaluations of loess sites in northwestern China. 相似文献
19.
An investigation on the ground motion parameters and seismic response of underground structures 
下载免费PDF全文
下载免费PDF全文 Peak ground acceleration (PGA), frequency content and time duration are three fundamental parameters of seismic loading. This study focuses on the seismic load frequency and its effect on the underground structures. Eight accelerograms regarding different occurred earthquakes that are scaled to an identical PGA and variation of ground motion parameters with ratio of peak ground velocity (PGV) to PGA, as a parameter related to the load frequency, are considered. Then, concrete lining response of a circular tunnel under various seismic conditions is evaluated analytically. In the next, seismic response of underground structure is assessed numerically using two different time histories. Finally, effects of incident load frequency and frequency ratio on the dynamic damping of geotechnical materials are discussed. Result of analyses show that specific energy of seismic loading with identical PGA is related to the seismic load frequency. Furthermore, incident load frequency and natural frequency of a system have influence on the wave attenuation and dynamic damping of the system. 相似文献
20.
The first known solution of the title problem is presented. The Ritz method is used, with algebraic polynomials forming the set of trial functions. The condition that all three components of displacement be zero at the four corners is straightforwardly enforced. Numerical studies show that the convergence is relatively slow, requiring more terms than for shells which are completely free. The class of problems studied includes independent, constant curvature in each of the directions parallel to the edges, yielding vibration modes which fall into one of four symmetry classes, with symmetry or antisymmetry of the displacements existing with respect to each of the two symmetry axes of the problem. Detailed results are given for the frequencies and mode shapes of the first two modes of each symmetry class for shells having square planform and circular cylindrical, spherical and hyperbolic paraboloidal curvatures. Accuracy of the results is partially established by comparison with other previously published, accurate results for the corner supported flat square plate. 相似文献