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1 .IntroductionNowadays tremendous efforts have been devotedtothe analysis of randomseismic responses .Forexample ,American PetroleumInstitute (API) has declared that the analysis of randomseismic re-sponsesis a useful tool for safety inspection. Owing to the complexity of platformand randomness ofload,it is difficult to carry out the randomresponse analysis of a jacket platform. The conventionalrandomvibration methods ,such as square root of the sumof squares (SRSS) and complete quadratic… 相似文献
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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
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Jiahao Lin Guizhen Song Yong Sun F. W. Williams 《Soil Dynamics and Earthquake Engineering》1995,14(4)
In this paper, a direct Ritz method is presented for analysing the responses of non-uniform shear beams subjected to the action of an evolutionary random seismic excitation. Because of the use of a pseudo ground acceleration, time-dependent random responses can conveniently be calculated by solving a set of deterministic equations of motion. These responses include power spectral densities, variances and higher spectral moments of any required responses of the beam. A non-uniform beam example was solved and the time-dependent variances and second spectral moments of both the beam-top displacement and the beam-base shear force are given to show the simplicity and effectiveness of the method, which can also easily be applied to other continuous elastic structures. 相似文献
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A step‐by‐step approximate procedure taking into consideration high‐frequency modes, usually neglected in the modal analysis of both classically and non‐classically damped structures, is presented. This procedure can be considered as an extension of traditional modal correction methods, like the mode‐acceleration method and the dynamic correction method, which are very effective for structural systems subjected to forcing functions described by analytical laws. The proposed procedure, herein called improved dynamic correction method, requires two steps. In the first step, the number of differential equations of motion are reduced and consequently solved by using the first few undamped mode‐shapes. In the second step, the errors due to modal truncation are reduced by correcting the dynamic response and solving a new set of differential equations, formally similar to the original differential equations of motion. The difference between the two groups of differential equations lies in the forcing vector, which is evaluated in such a way as to correct the effects of modal truncation on applied loads. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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In this paper, the vibratory characteristics of a rectangular plate in contact with water on one side are studied. The elastic plate is considered to be a part of a vertical rectangular rigid wall in contact with water, the edges of which are elastically restrained and parallel to those of the rigid wall. The location and size of the plate on the rigid wall may vary arbitrarily. The water with a free surface is in a rectangular domain infinite in the length direction. The effects of free surface waves, compressibility of the water and the hydrostatic water pressure are neglected in the analysis. An analytical‐Ritz method is developed to analyse the interaction of the plate–water system. First of all, by using the method of separation of variables and the method of Fourier series expansion, the exact expression of the motion of water is derived in the form of integral equations including the dynamic deformation of the plate. Then the Rayleigh–Ritz approach is used to derive the eigenfrequency equation of the system via the variational principle of energy. By selecting beam vibrating functions as the admissible functions of the plate, the added virtual mass incremental (AVMI) matrices for plate vibration are obtained. The convergency studies are carried out. The effects of some parameters such as the depth and width of water, the support stiffnesses, location and aspect ratio of the plate and the plate–water size and density ratios on the eigenfrequencies of the plate–water system are investigated. Several numerical examples are given. The validity of AVMI factor approach is also confirmed by comparing the AVMI factor solutions with the analytical‐Ritz solutions. The results show that the approach presented here can also be used as excellent approximate solutions for rectangular plates in contact with water of infinite width and/or infinite depth. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
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The title problem is solved in the case where uniform applied loading is present at the plate outer boundary. Two independent solutions are obtained: the optimized Rayleigh–Ritz method and the finite element algorithmic procedure. Good engineering agreement is shown to exist. The proposed analytical procedure is convenient from a designer's viewpoint. Admittedly exact analytical solutions can be found in terms of Bessel functions, the procedure being rather complex from an engineering viewpoint. 相似文献
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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
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A. Oya J. Navarro-Moreno J. C. Ruiz-Molina 《Stochastic Environmental Research and Risk Assessment (SERRA)》2007,21(4):317-326
An approach to the simulation of spatial random fields is proposed. The target random field is specified by its covariance
function which need not be homogeneous or Gaussian. The technique provided is based on an approximate Karhunen–Loève expansion
of spatial random fields which can be readily realized. Such an approximate representation is obtained from a correction to
the Rayleigh–Ritz method based on the dual Riesz basis theory. The resulting numerical projection procedure improves Rayleigh–Ritz
algorithm in the approximation of second-order random fields. Simulations are developed to illustrate the convergence and
accuracy of the method presented.
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| J. C. Ruiz-MolinaEmail: |
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In this paper, an analytical method is proposed to determine the dynamic response of 3‐D rectangular liquid storage tanks with four flexible walls, subjected to horizontal seismic ground motion. Fluid–structure interaction effects on the dynamic responses of partially filled fluid containers, incorporating wall flexibility, are accounted for in evaluating impulsive pressure. The velocity potential in which boundary conditions are satisfied is solved by the method of separation of variables using the principle of superposition. The impulsive pressure distribution is then computed. Solutions based on 3‐D modeling of the rectangular containers are obtained by applying the Rayleigh–Ritz method using the vibration modes of flexible plates with suitable boundary conditions. Trigonometrical functions that satisfy boundary conditions of the storage tank such that the flexibility of the wall is thoroughly considered are used to define the admissible vibration modes. The analysis is then performed in the time domain. Moreover, an analytical procedure is developed for deriving a simple formula that evaluates convective pressure and surface displacements in a similar rigid tank. The variation of dynamic response characteristics with respect to different tank parameters is investigated. A mechanical model, which takes into account the deformability of the tank wall, is developed. The parameters of such a model can be obtained from developed charts, and the maximum seismic loading can be predicted by means of a response spectrum characterizing the design earthquake. Accordingly, a simplified but sufficiently accurate design procedure is developed to improve code formulas for the seismic design of liquid storage tanks. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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沥青混凝土心墙作为堆石坝的防渗结构,其受力安全备受工程领域的关注,对其进行快速简便地受力变形分析具有重要意义。利用薄板小挠度弯曲理论以及里兹法求解了置于Winkler弹性地基上三边固支一边自由矩形薄板在水压力作用下的挠曲变形函数,推导了矩形薄板的变形、内力和应力计算公式;建立了矩形薄板与实际沥青混凝土心墙之间的一一映射关系,将矩形薄板的变形、内力和应力映射到实际河谷断面心墙上,从而建立了沥青混凝土心墙简化解析受力分析模型。借助有限元方法对模型的可靠性进行了验证,最后将该模型应用于工程实例。研究结果表明,此模型有助于快速预估沥青混凝土心墙受力变形,同时研究思路也拓展了沥青混凝土心墙受力变形的计算方法。 相似文献
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