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Research Papers

Multiple Dynamic Response Patterns of Flexible Multibody Systems With Random Uncertain Parameters

[+] Author and Article Information
Zhe Wang

MOE Key Laboratory of Dynamics and
Control of Flight Vehicle,
School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: cwangzhe@126.com

Qiang Tian

MOE Key Laboratory of Dynamics and
Control of Flight Vehicle,
School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: tianqiang_hust@aliyun.com

Haiyan Hu

MOE Key Laboratory of Dynamics and
Control of Flight Vehicle,
School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: haiyan_hu@bit.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 24, 2018; final manuscript received September 15, 2018; published online January 7, 2019. Assoc. Editor: Yan Wang.

J. Comput. Nonlinear Dynam 14(2), 021008 (Jan 07, 2019) (15 pages) Paper No: CND-18-1231; doi: 10.1115/1.4041580 History: Received May 24, 2018; Revised September 15, 2018

The mechanisms with uncertain parameters may exhibit multiple dynamic response patterns. As a single surrogate model can hardly describe all the dynamic response patterns of mechanism dynamics, a new computation methodology is proposed to study multiple dynamic response patterns of a flexible multibody system with uncertain random parameters. The flexible multibody system of concern is modeled by using a unified mesh of the absolute nodal coordinate formulation (ANCF). The polynomial chaos (PC) expansion with collocation methods is used to generate the surrogate model for the flexible multibody system with random parameters. Several subsurrogate models are used to describe multiple dynamic response patterns of the system dynamics. By the motivation of the data mining, the Dirichlet process mixture model (DPMM) is used to determine the dynamic response patterns and project the collocation points into different patterns. The uncertain differential algebraic equations (DAEs) for the flexible multibody system are directly transformed into the uncertain nonlinear algebraic equations by using the generalized-alpha algorithm. Then, the PC expansion is further used to transform the uncertain nonlinear algebraic equations into several sets of nonlinear algebraic equations with deterministic collocation points. Finally, two numerical examples are presented to validate the proposed methodology. The first confirms the effectiveness of the proposed methodology, and the second one shows the effectiveness of the proposed computation methodology in multiple dynamic response patterns study of a complicated spatial flexible multibody system with uncertain random parameters.

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Figures

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Fig. 1

The computation procedures for the PC expansion algorithm with the collocation samplings

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Fig. 2

The Gibbs sampling algorithm for the DPMM

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Fig. 3

The computation flow of the proposed computation methodology

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Fig. 4

Schematic view of a flexible mechanism

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Fig. 5

The time history of rotational angle of the driven arm B1 for the flexible mechanism

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Fig. 6

The Y-displacements of point P computed from 3000 samplings of MCS: (a) The Y-displacements of point P and (b) The zoomed view of Fig. 6(a)

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Fig. 7

The configuration of the flexible mechanism when t = 0.7 s

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Fig. 8

The configurations of the flexible mechanism when t = 0.9 s: (a) the configuration I and (b) the configuration II

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Fig. 9

The mean values and variances of the Y-displacements of point P computed by using the traditional PC method: (a) mean values of the Y-displacement of point P and (b) variances of the Y-displacement of point P

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Fig. 10

The interval bounds of Y-displacements of point P computed by using the traditional PC method

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Fig. 11

The mean values and variances of the Y-displacements of point P computed by using the proposed computation methodology: (a) mean values of the Y-displacement of point P and (b)variances of the Y-displacement of point P

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Fig. 12

The interval bounds of Y-displacements of point P computed by the proposed computation methodology

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Fig. 13

The configurations of a more flexible mechanism when t = 0.9 s: (a) The configuration I and (b) The configuration II

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Fig. 14

The Y-displacements of point P computed from 3000 samplings of MCS

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Fig. 15

The mean values and variances of the Y-displacements of point P computed by using the proposed computation methodology: (a) mean values of the Y-displacement of point P and (b) variances of the Y-displacement of point P

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Fig. 16

The interval bounds of Y-displacements of point P computed by using the proposed computation methodology

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Fig. 17

The Y-displacements of point P computed from 3000 samplings of MCS

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Fig. 18

The mean values and variances of the Y-displacements of point P computed by using the proposed computation methodology: (a) mean values of the Y-displacement of point P and (b) variances of the Y-displacement of point P

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Fig. 19

The interval bounds of Y-displacements of point P computed by using the proposed computation methodology

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Fig. 20

Schematic view of a flexible 3-RRS robot

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Fig. 21

The rotational angles of the driven arms of the flexible 3-RRS robot

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Fig. 22

The Z-displacements of workspace center O from 1500 samplings of MCS: (a) the Z-displacements of workspace center O and (b)the zoomed view of Fig. 20(a)

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Fig. 23

The configuration of the flexible 3-RRS robot when t = 1.2 s

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Fig. 24

The configurations of the flexible 3-RRS robot when t = 1.5 s: (a) the configuration I and (b) the configuration II

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Fig. 25

The mean values and variances of Z-displacement of the workspace center computed by using the traditional PC method: (a) mean values of the Z-displacement of the workspace center and (b) variances of the Z-displacement of the workspace center

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Fig. 26

The interval bounds of Z-displacements of the workspace center computed by using the traditional PC method

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Fig. 27

The mean values and variances of Z-displacements of the workspace center by the proposed computation methodology: (a) mean values of the Z-displacement of the workspace center and (b) variances of the Z-displacement of the workspace center

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Fig. 28

The interval bounds of Z-displacements of the workspace center computed by using the proposed computation methodology

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