On the accuracy of direct integration methods for structural dynamics

Abstract

This paper presents a method of eigen analysis to evaluate the accuracy of the time integration method in the structural dynamic analysis of both transient and steady state responses. Accuracy measure for transient response is evaluated by period elongation and amplitude decay after a complete cycle of response of an undamped system. The proposed method is a unique measure, independent of the initial conditions. Accuracy measure for steady state response is evaluated by the amplitude decay and phase angle of a frequency response. The accuracy measure proposed by this method can be applied to all ranges of ?t/T. The significance of the large range ?t/T is discussed. The proposed method is used to evaluate the accuracy of three commonly used time integration methods: the Wilson method, the Newmark method and the Houbolt method.     

On the accuracy of some domain-by-domain algorithms for parallel processing of transient structural dynamics

Two domain-by-domain algorithms, suitable for coarse-grained parallel processing analysis of the transient structural dynamics equation, are investigated for accuracy. The application under specific consideration is the analysis of three-dimensional framed structures subjected to time-varying loading. The domain-by-domain approaches attempt to include the advantageous aspects of both conditionally stable explicit algorithms, which require no simultaneous solution of equations and employ simple communication, and unconditionally stable implicit algorithms, which permit large time steps. The alternating group explicit algorithm is developed for finite element analysis, and its accuracy is investigated for a linear formulation. The group implicit algorithm is extended to non-linear finite element analysis, and its accuracy is investigated for the frame dynamics application. Both algorithms are shown to provide inadequate accuracy for practical time step sizes.     

Explicit solutions in the stochastic dynamics of structural systems

The paper presents a procedure to derive in explicit form the stationary response of a linear structure subjected to Gaussian white noise stochastic excitation. Namely, the analytical relationship between the second order statistical moments of the response and the structural parameters (element stiffness and modal damping ratio) is furnished. The method is based on the solution of complex eigenvalue problems, one for each variable structural parameter, possessing a number of eigenvalues different from zero much smaller than the problem dimension. If a single structural quantity is treated as a parameter then the exact explicit solution is found. When more parameters are present, the explicit solution is approximate and the introduction of cross terms is suggested to obtain more accurate predictions.The aforementioned explicit solution is exploited herein in the field of uncertain structures. The structural parameters are modeled as random variables and a Monte Carlo procedure is adopted to get the conditional, given the structural parameters, probability density function of the second order moments of the response. The efficiency and the accuracy of the proposed procedure are evidenced by numerical applications.     

On the application of the pontryagin''s maximum principle for identification of the radiogenic heat distribution in the Earth''s interior

Pontryagin's maximum principle is used for the mathematical modeling of the radiogenic heat production in the Earth's interior. Following the usual procedure we find that the optimal model is described by an exponential function. The logarithmic decrement of this exponential function is related with the slope of observed linear surface heat flow and heat generation curve and further the nature of this relationship depends upon the interpretations of the reduced heat flow.     

Stochastic design sensitivity in structural dynamics

A method to analyse stochastic design sensitivity for problems of structural dynamics is presented. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element context. An alternative form of the constraint functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The terminal problem of the adjoint system is solved using equivalent homogeneous equations exicited by initial velocities. The numerical procedures are shown to be much more efficient when based on the fold superposition technique: the generalized co-ordinates are normalized and the correlated random variables are transformed to uncorrelated variables, whereas the secularities are eliminated by the fast Fourier transform of complex valued sequences. Numerical algorithms have been worked out and proved to be accurate and efficient; they can be readily adapted to fit into the existing finite element codes whose element derivative matrices can be explicitly generated. A number of numerical results for the deterministic and stochastic sensitivity analysis of beams and shells illustrates the paper.     

Fundamentals of system identification in structural dynamics

Methods of identification for structural dynamic systems are reviewed in this report. Emphasis is placed on methods relevant to the identification of linear and nonlinear behavior of structures subjected to such environmental loads as ground motion due to earthquakes, wind-generated pressure and wind-induced ocean wave forces. The methods considered are the least square, instrumental variable, maximum likelihood and a method utilizing the extended Kalman filter. In order to verify the validity of these methods, numerical simulation studies are carried out utilizing mathematical models of a suspension bridge, offshore tower and building structure. On the basis of such simulation studies, the efficiency of these methods are investigated under several conditions of observational noise.     

VoIP原理及其在无线局域网中的QoS保障

VoIP技术现正成为一项构建语音网络的重要技术。本文介绍了VoIP的基本原理,以及VoIP在无线局域网中的应用,分析了无线VoIP业务质量中的问题及解决方法。通过某VoIP无线局域网实例说明了WLAN VoIP的结构和配置,并结合VoIP话音质量评价标准,从无线VoIP传送话音所存在的问题出发,着重探讨了解决这些问题的方法。     

浅析包装中色彩运用的文化原则

从某种程度上讲,包装是对产品的一种定位和阐释。心理学有关研究表明,人的视觉器官,在观察物体时,最初的20秒内色彩感觉占80%,而形体感觉占20%:两分钟后色彩占60%,形体占40%;5分钟后各占一半,并且这种状态将继续保持。可见,包装给人的印象多么迅速、深刻、持久。国外学者曾有过一项研究,发现由广告媒体招徕的顾客中,有33%的人在销售现场会选择包装吸引人的品牌,包装重要性不言而喻。可以说,包装的素材、形式和色彩等因素综合在一起,将产品引伸至一个深层的文化氛围。     

Mass identification from lambdamatrices in structural dynamics

Summary The discretization of vibration problems in structural dynamics by means of fundamental solutions results in a nonlinear representation by so-called lambdamatrices.Here the dynamic stiffness matrix with transcendental elements is replaced by a linear eigenvalue formulation with static stiffness and a mass matrix. The mass results from interpolating the lambdamatrix either in a Taylor-like or in a Lagrange-like manner.For the present the essential steps of this procedure are demonstrated for vibrations of beams.     

工程结构整体可靠性分析研究进展

结构整体可靠度评估一直以来是结构可靠度领域研究的热点与难点。该文将结构整体可靠度分类,并给出其对应功能函数的统一描述;结合提出的有效维度两步分析法和共轭无迹变换法,发展了改进统计矩点估计法;结合最大熵原理和改进统计矩点估计法,提出了适用于两类结构整体可靠度的统一分析方法;通过2个数值算例对该文方法进行了验证。算例分析结果表明：同一精度水平下,该文方法的计算效率较传统的三变量降维近似统计矩点估计法高2.3倍~2.6倍;该文方法具有高的精度水平,其最大相对误差低于2%,适用于结构整体可靠度评估。     

Random matrix eigenvalue problems in structural dynamics

Natural frequencies and mode shapes play a fundamental role in the dynamic characteristics of linear structural systems. Considering that the system parameters are known only probabilistically, we obtain the moments and the probability density functions of the eigenvalues of discrete linear stochastic dynamic systems. Current methods to deal with such problems are dominated by mean‐centred perturbation‐based methods. Here two new approaches are proposed. The first approach is based on a perturbation expansion of the eigenvalues about an optimal point which is ‘best’ in some sense. The second approach is based on an asymptotic approximation of multidimensional integrals. A closed‐form expression is derived for a general rth‐order moment of the eigenvalues. Two approaches are presented to obtain the probability density functions of the eigenvalues. The first is based on the maximum entropy method and the second is based on a chi‐square distribution. Both approaches result in simple closed‐form expressions which can be easily calculated. The proposed methods are applied to two problems and the analytical results are compared with Monte Carlo simulations. It is expected that the ‘small randomness’ assumption usually employed in mean‐centred‐perturbation‐based methods can be relaxed considerably using these methods. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimal experimental design in stochastic structural dynamics

This paper provides a methodology for optimal prediction of the response of randomly vibrating structures using information from a limited number of measurements. The objective is to optimize the locations of sensors for the purpose of making the most accurate predictions of the response at unmeasured locations in structural systems. The kriging method is used to find the response predictions and the corresponding mean-square errors at unmeasured locations. The mean-square errors in the predictions depend on the locations of sensors and the correlation characteristics of the response evaluated from the model of dynamics and the characteristics of the excitation. The response predictions depend also on the information contained in measurements. The optimal sensor locations are selected to minimize the total mean-square error of the response predictions at unmeasured points. This leads to a complicated non-convex optimization problem in which multiple local and global optima may exist. A hybrid optimization method based on evolution strategies is used to determine a global minimum. The optimal experimental design method presented in the paper is illustrated by designing the optimal sensor locations for an elastic beam and a plate subjected to a class of random stationary loads.     

On some unconditionally stable,higher order methods for the numerical solution of the structural dynamics equations

Third- and fourth-order accurate Nørsett rational approximations to the exponential and associated semi-implicit Runge–Kutta methods are used for the construction of efficient, accurate and unconditionally stable schemes for the direct numerical integration of the linear, nonhomogeneous, second-order equations of structural dynamics.     

Entropy propagation analysis in stochastic structural dynamics: application to a beam with uncertain cross sectional area

This paper investigates the impact of different probabilistic models of uncertain parameters on the response of a dynamical structure. The probabilistic models of the uncertain parameters are constructed using the maximum entropy principle, where different information is considered, such as bounds, mean value, etc. Nested probabilistic models are constructed with increasing information; as the information given increases, the level of entropy of the input model decreases. The response of the linear dynamical model is given in the frequency domain, and the propagation of the input uncertainty throughout the computational model is analyzed in terms of Shannon’s entropy. Low and high frequencies are analyzed because uncertainties propagate differently depending on the frequency band. A beam discretized by means of the finite element method with random cross sectional area (random field) is the application analyzed.     

Generalization of Onsager's principle and its application

A principle is introduced to the thermodynamics of irreversible processes which generalizes the well-known Onsager principle. On the basis of this principle, an equation of heat conduction is derived with a finite velocity of heat propagation, and a system of equations of coupled thermoelasticity is set up.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 4, pp. 736–741, October, 1973.