On the dynamic stochastic response of FE models

Schenk, Christian A.; Pradlwarter, H. J.; Schuëller, G.I.

doi:10.1016/j.probengmech.2003.11.013

Cited by 17 publications

(8 citation statements)

References 10 publications

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“…The question of nonstationary Gaussian equivalent linearization (GEL) has been also addressed interestingly by the team of Schuëller in [46,54,55], who proposed a method based on the Karhunen-Loéve (K-L) expansion of the excitation. Accordingly, the K-L expansion of the modal state space vector of the structure is substituted into the linearized equation of motion.…”

Section: Has Beenmentioning

confidence: 99%

Perturbation methods in evolutionary spectral analysis for linear dynamics and equivalent statistical linearization

Canor

Caracoglia

Denoël

2016

Probabilistic Engineering Mechanics

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a b s t r a c tThe analysis of large-scale structures subject to transient random loads, coherent in space and time, is a classic problem encountered in earthquake and wind engineering. The simulation-based framework is usually seen as the most convenient approach for both linear and nonlinear dynamics. However, the generation of statistically consistent samples of an excitation field remains a heavy computational task. In light of this, perturbation techniques are applied to develop and improve evolutionary spectral analysis.Advantageously performed in a standard modal basis, this evolutionary spectral analysis for linear structures requires the computation of the modal impulse response matrix. However, this matrix has no general closed-form expression in the presence of modal coupling. We propose therefore to model it by an asymptotic approximation, obtained by the inverse Fourier transform of an asymptotic expansion of the modal transfer matrix of the structure. This latter expansion considers the modal coupling as a perturbation of a main decoupled system. This strategy leads to an expansion known in a closed-form. Finally, the semi-group property allows the use of an efficient recurrence relation to approximate the modal evolutionary transfer matrix, i.e. the evolutionary extension of the transfer matrix.The asymptotic expansion-based method and the recurrence relation are then applied to nonlinear transient dynamics by using Gaussian equivalent linearization. This extension is formalized by a multiple timescales approach, allowing to consider a linearized structure, namely a time variant system, as piecewise linear time invariant depending on a statistical timescale. The proposed developments are finally illustrated on realistic civil engineering applications.

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Section: Has Beenmentioning

confidence: 99%

Perturbation methods in evolutionary spectral analysis for linear dynamics and equivalent statistical linearization

Canor

Caracoglia

Denoël

2016

Probabilistic Engineering Mechanics

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“…The previous characterization for the evolution of the set of variables y(t) allows to model different types of nonlinearities including hysteresis and degradation [18][19][20][21]. The previous formulation is particularly well suited for cases where most of the components of the structural system remain linear and only a small part behaves in a nonlinear manner [22]. The external force vector f(t) is modeled as a non-stationary stochastic process.…”

Section: Mathematical Modelmentioning

confidence: 99%

Reliability sensitivity analysis of stochastic finite element models

Jensen

Mayorga

Papadimitriou

2015

Computer Methods in Applied Mechanics and Engineering

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This contribution presents a scheme for integrating a model reduction technique into a simulation-based method for reliability sensitivity analysis of a class of medium/large nonlinear finite element models under stochastic excitation. The solution of this type of problems requires a large number of finite element model re-analyses to be performed over the space of system parameters. A component mode synthesis technique is implemented to carry out the sensitivity analysis in a reduced space of generalized coordinates. The reliability sensitivity analysis is performed by an approach based on a simple post-processing of an advanced sampling-based reliability analysis. The feasibility and effectiveness of the proposed scheme is demonstrated on a bridge finite element model under stochastic ground excitation.

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“…The eigenvalues λ j decrease rather quickly with the increasing of j [9], and this characteristic is used in this paper to reduce the computation workload by truncatioñ…”

Section: Modeling Of Stochastic Loadingmentioning

confidence: 99%

“…Schenk and H.J. Pradlwarter [7][8][9] developed a method to deal with dynamic stochastic response of FE models under non-stationary random excitation, non-zero mean, non-white, non-stationary Gaussian distributed excitation is represented by the well known K-L expansion. For the case where the stochastic loading is described by a finite set of deterministic K-L vectors, which in fact is considered in this paper, and to deal with double random vibration analysis.…”

Section: Introductionmentioning

confidence: 99%

Random structural dynamic response analysis under random excitation

Liao¹,

Xu²,

Bing-yan³

2014

Period. Polytech. Civil Eng.

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Liao JunCollege of Mechanical and Electrical Engineering, Central South University, Changsha, 410001, China e-mail: liaojun@csu.edu.cn Xu DafuAerospace System Engineering Shanghai, Shanghai, 201108, China Jiang BingyanSchool of Aeronautics and Astronautics, Central South University, Changsha, 410001, China IntroductionIn practical engineering problems, not only the external excitations such as wind loading, seismic waves etc., demonstrate uncertainty, but also the structural parameters exhibit uncertainty. The uncertainty of structural parameters may have a strong influence on structural reliability. [1, 2], therefore it is more reasonable to consider the variability of structural physical parameters in dynamic response analysis of structures.The double random vibration analysis, i.e. the random vibration analysis of stochastic parameter structures subjected to random excitation, attracts much interest in researchers. In current literatures there are mainly three ways to tackle this problem. The first is Monte Carlo simulation method [1]. This method is robust and powerful in this aspect of structural analysis, but it is very time-consuming. The second is stochastic finite element method. Although the random eigen value problem, static analysis problem and structural stability problem, etc. can be solved efficiently with this method [2], the stochastic finite method is haunted by the notorious secular term in random dynamic response analysis of structures. The third is orthogonal series expansion method [3][4][5][6] in which the structural response is expanded as a set of orthogonal series and the corresponding numerical characteristics are given as analytical solution. Li [6] developed an order expanded system method by applying sequential orthogonal expansion to deal with double random vibration analysis. Some numerical examples indicate that orthogonal series expansion method avoids the secular term of perturbation methods and does not have to assume the variability of structural parameters to be small. However, the method is still very timeconsuming for large degree of freedom FE model. C.A. Schenk and H.J. Pradlwarter [7][8][9] developed a method to deal with dynamic stochastic response of FE models under non-stationary random excitation, non-zero mean, non-white, non-stationary Gaussian distributed excitation is represented by the well known K-L expansion. For the case where the stochastic loading is described by a finite set of deterministic K-L vectors, which in fact is considered in this paper, and to deal with double random vibration analysis. Then, the classic vibration analysis method can apply to the order-expanded equation, and the probabilistic in-

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On the dynamic stochastic response of FE models

Cited by 17 publications

References 10 publications

Perturbation methods in evolutionary spectral analysis for linear dynamics and equivalent statistical linearization

Perturbation methods in evolutionary spectral analysis for linear dynamics and equivalent statistical linearization

Reliability sensitivity analysis of stochastic finite element models

Random structural dynamic response analysis under random excitation

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