Dynamic computation of flexible multibody system with uncertain material properties

Wu, Jinglai; Luo, Zhen; Zhang, Nong; Zhang, Yunqing

doi:10.1007/s11071-016-2757-6

Cited by 19 publications

(6 citation statements)

References 47 publications

(47 reference statements)

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“…As a result, the nth-order PC expansion of function f(Ε), Ε ∈ R k+m , is expressed as the following equation where , and the number of coefficients is s=(n+1) k+m . The coefficients can still be computed by the multi-dimensional Gaussian integral formula or by the least square method [44], and the interpolation points will be the tensor product of the roots of univariate orthogonal polynomials with order n+1 in k+m dimensional space, expressed as It should be noted that the number of interpolation points equals to the number of coefficients in PC expansion, i.e. (n+1) k+m , which increases exponentially with the increase of dimension.…”

Section: Polynomial Chaos Expansion Methodsmentioning

confidence: 99%

“…It can be used to handle the random variables with relatively larger uncertainty. The PC expansion method has been widely used, such as in fluid mechanics [41], vehicle dynamics [42,43], multibody dynamic systems [44][45][46], structure dynamics [47], optimization problems [48], and hybrid uncertainties [27,49]. One weakness for the PC expansion is the dimensional curse problem, so that it may not be suitable for the high dimensional problems.…”

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confidence: 99%

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Uncertain dynamic analysis for rigid-flexible mechanisms with random geometry and material properties

Luo

Zhang

et al. 2017

Mechanical Systems and Signal Processing

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As one of the most important systems in mechanical engineering, almost all the multibody dynamic mechanical systems (or mechanisms) involve various uncertain factors, which may influence the performance of a system especially for the high-speed dynamic systems. For instance, the geometry size of a component in the mechanism has a tolerance to facilitate manufacturing process; the fabrication of different kinds of raw material may lead to the inhomogeneous distribution of the material, which will further lead to the variation of material properties, such as the Young's modulus, Poisson's ratio, and material density. To improve the computational accuracy of dynamic analysis of the mechanism, it is necessary to investigate their dynamic responses by considering these unavoidable uncertain factors. The dynamic study of the mechanisms under deterministic conditions has been developed from traditional rigid multibody systems to flexible multibody systems and rigid-flexible multibody systems. The modelling of rigid multibody systems has been well studied [1], and some commercial software has also been widely used. On the other hand, the study of flexible multibody systems and rigid-flexible multibody systems has been attracting more and more attention over the past two decades. When the flexible components are involved in multibody systems, the deformation of these flexible components has to be considered. Since flexible components in multibody systems often experience large rotation and deformation, the traditional finite element methods based on the small rotation and deformation may give an improper solution [2]. However, the Absolute Nodal Coordinate Formulation (ANCF) [3] shows good capability for solving flexible multibody problems with large rotation and deformation. ANCF defines elemental coordinates as the absolute displacements and global slopes, which forces the mass matrix of the system equations to remain constant and the centrifugal and Coriolis forces identically equal to zero [4,5]. As a non-incremental finite Uncertain dynamic analysis for rigid-flexible mechanisms with random geometry and material properties Jinglai Wu a, ⁎

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Section: Polynomial Chaos Expansion Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

Uncertain dynamic analysis for rigid-flexible mechanisms with random geometry and material properties

Luo

Zhang

et al. 2017

Mechanical Systems and Signal Processing

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“…Ryan et al proposed a novel automation process of multibody dynamics under uncertainty using polynomial chaos expansion and variational work [11]. Further, a generalized PCE was developed [8] and presented a widespread application in multibody systems, such as manipulator dynamics [12], vehicle dynamics [13], and flexible multibody systems [14].…”

Section: Introductionmentioning

confidence: 99%

Interval Uncertainty Quantification for the Dynamics of Multibody Systems Combing Bivariate Chebyshev Polynomials with Local Mean Decomposition

Jiang

Bai

2022

Mathematics

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Interval quantification for multibody systems can provide an accurate dynamic prediction and a robust reliability design. In order to achieve a robust numerical model, multiple interval uncertain parameters should be considered in the uncertainty propagation of multibody systems. The response bounds obtained by the bivariate Chebyshev method (BCM) present an intensive deterioration with the increase of time history in the interval dynamic analysis. To circumvent this problem, a novel method that combines the bivariate Chebyshev polynomial and local mean decomposition (BC-LMD) is proposed in this paper. First, the multicomponent response of the system was decomposed into the sum of several mono-component responses and a residual response, and the corresponding amplitude and phase of the mono-component were obtained. Then, the bivariate function decomposition was performed on the multi-dimensional amplitude, phase, and residual to transform a high-dimensional problem into several one-dimensional and two-dimensional problems. Subsequently, a low order Chebyshev polynomial can be used to construct surrogate models for the multi-dimensional amplitude, phase, and residual responses. Then, the entire coupling surrogate model of the system can be established, and the response bounds of the system can be enveloped. Illustrative examples of a slider-crank mechanism and a double pendulum are presented to demonstrate the effectiveness of the proposed method. The numerical results indicate that, compared to the BCM, BC-LMD can present a tight envelope in the long time-dependent dynamic analysis under multiple interval parameters.

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“…al. [5,6] proposed a Polynomial-Chaos-Chebyshev Interval method for vehicle dynamics involving hybrid uncertainty parameters and a flexible multibody system with uncertain material properties was considered as well.…”

Section: Introductionmentioning

confidence: 99%

Application and Comparison of Uncertainty Quantification Methods for Railway Vehicle Dynamics with Random Mechanical Parameters

Zhang

Bigoni

2019

mech

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This paper aims to investigate uncertainties in railway vehicle suspension components and the implement of uncertainty quantification methods in railway vehicle dynamics. The sampling-based method represented by Latin Hypercube Sampling (LHS) and generalized polynomial chaos approaches including the stochastic Galerkin and Collocation methods (SGM and SCM) are employed to analyze the propagation of uncertainties from the parameters input in a vehicle-track mathematical model to the results of running dynamics. In order to illustrate the performance qualities of SGM, SCM and LHS, a stochastic wheel model with uncertainties of the stiffness and damping is firstly formulated to study the vertical displacement of wheel. Numerical results show that SCM, which can be easily implemented by means of the existing deterministic model, has explicit advantages over SGM and LHS in terms of the efficiency and accuracy. Furthermore, a simplified stochastic bogie model with three random suspension parameters is also established by means of SCM and LHS to analyze the critical speed, which is affected obviously by the parametric uncertainties. Finally, a stochastic vertical vehicle-track coupled model with parametric uncertainties is built comprehensively on the basis of SCM, by which the impact behavior of wheel-rail interaction under a rail defect is investigated and the dynamic response of vehicles under the track irregularity is explored in terms of the Sperling index. It concludes that the uncertainties of parameters have a significant influence on P2 force and Sperling index from the view of the running quality.

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Dynamic computation of flexible multibody system with uncertain material properties

Cited by 19 publications

References 47 publications

Uncertain dynamic analysis for rigid-flexible mechanisms with random geometry and material properties

Uncertain dynamic analysis for rigid-flexible mechanisms with random geometry and material properties

Interval Uncertainty Quantification for the Dynamics of Multibody Systems Combing Bivariate Chebyshev Polynomials with Local Mean Decomposition

Application and Comparison of Uncertainty Quantification Methods for Railway Vehicle Dynamics with Random Mechanical Parameters

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