A hybrid approach for the time domain analysis of linear stochastic structures

Wu, Feng; Zhong, Wanxie

doi:10.1016/j.cma.2013.06.006

Cited by 13 publications

(4 citation statements)

References 33 publications

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“…More information about the SPFEM can be found in works of Liu et al (1986), Wu and Zhong (2013). Suppose that the model of the random static system produced by the finite element method can be written as…”

Section: The Stochastic Perturbation Finite Element Methodsmentioning

confidence: 99%

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A Modified Computational Scheme for the Stochastic Perturbation Finite Element Method

2015

Lat. Am. j. solids struct.

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A modified computational scheme of the stochastic perturbation finite element method (SPFEM) is developed for structures with low-level uncertainties. The proposed scheme can provide secondorder estimates of the mean and variance without differentiating the system matrices with respect to the random variables. When the proposed scheme is used, it involves finite analyses of deterministic systems. In the case of one random variable with a symmetric probability density function, the proposed computational scheme can even provide a result with fifth-order accuracy. Compared with the traditional computational scheme of SPFEM, the proposed scheme is more convenient for numerical implementation. Four numerical examples demonstrate that the proposed scheme can be used in linear or nonlinear structures with correlated or uncorrelated random variables.

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Section: The Stochastic Perturbation Finite Element Methodsmentioning

confidence: 99%

“…To demonstrate this point, a brief introduction about the perturbation estimate of the eigenvalue is given. More information can be found in the work of Wu and Zhong (2013). If the eigenproblem considered here is defined by …”

Section: The Plane Steel Framementioning

confidence: 99%

A Modified Computational Scheme for the Stochastic Perturbation Finite Element Method

2015

Lat. Am. j. solids struct.

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“…The basis of the latter approach is on the rational series expansion and the stochastic perturbation technique. By means of the second-order perturbation technique, modal analysis, and the number-theoretical method, Wu and Zhong 12 developed a hybrid method to scrutinize the dynamic response of a structure. Guerine et al.…”

Section: Introductionmentioning

confidence: 99%

Non-probabilistic interval process method for analyzing two-stage straight bevel gear system with uncertain time-varying parameters

Lafi

Djemal

Tounsi

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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A two-stage straight bevel gear system is a gear system that can be used in various applications. The straight bevel gear is known for its complex tooth geometry. Due to the variation of the number of pairs of teeth in contact, the mesh stiffness function can be considered as a time-varying function. However, the mesh stiffness for the straight bevel gear is sensitive to measurement and modeling errors. Thus, at each time step, its value can not assigned to deterministic one. Generally, the uncertain parameters are assumed to be time-independent. In this paper, the interval process method has been used to represent the time-varying uncertain parameters, whose bounds are determined through the potential energy method. The lumped parameter model of two-stage straight bevel gear has been proposed. We have considered that the masses of the straight bevel gear system components and bearing stiffnesses along with time-varying mesh stiffnesses are uncertain parameters which can be represented by the interval process model. The Chebyshev polynomial expansion has been used to approximate the response of the two-stage straight bevel gear system with respect to the interval variables. The lower and higher bounds of the eigenvalues of the system have been determined. The bounds of dynamic displacements of the straight bevel gear system have been computed and compared with those computed by the Monte Carlo method.

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“…3 The transverse vibration response of high-speed elevator car system and analysis of parameter sensitivity In this section, the transverse vibration dynamic response of the car system is discussed by using the random perturbation method [9][10][11][12]. Since this system has ma, j a , 3 and l 4 a total of 12 random parameters, the mass matrix M, damping matrix C , and stiffness matrix K in the differential equations of motion also have randomness, and the following transformation is needed:…”

Section: High-speed Elevator Car System Dynamics Modelmentioning

confidence: 99%

Analysis of Transverse Vibration Acceleration of a High-Speed Elevator with Random Parameters under Random Excitation

Zhang

Yang

2017

Period. Polytech. Mech. Eng.

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A hybrid approach for the time domain analysis of linear stochastic structures

Cited by 13 publications

References 33 publications

A Modified Computational Scheme for the Stochastic Perturbation Finite Element Method

A Modified Computational Scheme for the Stochastic Perturbation Finite Element Method

Non-probabilistic interval process method for analyzing two-stage straight bevel gear system with uncertain time-varying parameters

Analysis of Transverse Vibration Acceleration of a High-Speed Elevator with Random Parameters under Random Excitation

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