Inverse Eigenvalue Theory-Based Rigid Multibody Modeling Method of Complex Flexible Structures in Large-Scale Mechanical Systems
Increasing attention is paid to modeling flexibility of individual components in the multibody simulation of large-scale mechanical systems. Nevertheless, the high model order of common methods such as FEA restricts efficient explorations, especially in dynamic design and iterative optimization. In...
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2020/8329395 |
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doaj-11dc4ec9a99e4b24ae221204c81a93672020-11-25T02:10:48ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/83293958329395Inverse Eigenvalue Theory-Based Rigid Multibody Modeling Method of Complex Flexible Structures in Large-Scale Mechanical SystemsJiulin Wu0Lizhan Zeng1Bin Han2Xin Luo3Xuedong Chen4Wei Jiang5State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, ChinaState Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, ChinaState Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, ChinaState Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, ChinaState Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, ChinaState Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, ChinaIncreasing attention is paid to modeling flexibility of individual components in the multibody simulation of large-scale mechanical systems. Nevertheless, the high model order of common methods such as FEA restricts efficient explorations, especially in dynamic design and iterative optimization. In this paper, a rigid multibody modeling strategy (RMMS) with low DOFs and explicit physical meaning is proposed, which directly discretizes a continuous structure into a number of rigid finite elements (RFEs) connected by spring-damping elements (SDEs). In the RMMS, a new identification method from the perspective of the inverse vibration problem is particularly put forward to resolve the parameters of SDEs, which is crucial to the implementation of RMMS in complex flexible structures. With decoupling and linearization, this nonlinear problem is transformed into solving the incompatible linear equations in Rn2 vector space based on vectorization operator and Kronecker product, and optimal parameters are obtained by calculating the Moore–Penrose generalized inverse. Finally, the comparison of the experimental results with the simulated ones by the RMMS strongly validates the feasibility and correctness of the RMMS in predicting the dynamic behaviors while with few DOFs and explicit physical meaning; the application in a lithography system exhibits the applicability of the RMMS for dynamic modeling of large-scale mechanical systems.http://dx.doi.org/10.1155/2020/8329395 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Jiulin Wu Lizhan Zeng Bin Han Xin Luo Xuedong Chen Wei Jiang |
spellingShingle |
Jiulin Wu Lizhan Zeng Bin Han Xin Luo Xuedong Chen Wei Jiang Inverse Eigenvalue Theory-Based Rigid Multibody Modeling Method of Complex Flexible Structures in Large-Scale Mechanical Systems Mathematical Problems in Engineering |
author_facet |
Jiulin Wu Lizhan Zeng Bin Han Xin Luo Xuedong Chen Wei Jiang |
author_sort |
Jiulin Wu |
title |
Inverse Eigenvalue Theory-Based Rigid Multibody Modeling Method of Complex Flexible Structures in Large-Scale Mechanical Systems |
title_short |
Inverse Eigenvalue Theory-Based Rigid Multibody Modeling Method of Complex Flexible Structures in Large-Scale Mechanical Systems |
title_full |
Inverse Eigenvalue Theory-Based Rigid Multibody Modeling Method of Complex Flexible Structures in Large-Scale Mechanical Systems |
title_fullStr |
Inverse Eigenvalue Theory-Based Rigid Multibody Modeling Method of Complex Flexible Structures in Large-Scale Mechanical Systems |
title_full_unstemmed |
Inverse Eigenvalue Theory-Based Rigid Multibody Modeling Method of Complex Flexible Structures in Large-Scale Mechanical Systems |
title_sort |
inverse eigenvalue theory-based rigid multibody modeling method of complex flexible structures in large-scale mechanical systems |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2020-01-01 |
description |
Increasing attention is paid to modeling flexibility of individual components in the multibody simulation of large-scale mechanical systems. Nevertheless, the high model order of common methods such as FEA restricts efficient explorations, especially in dynamic design and iterative optimization. In this paper, a rigid multibody modeling strategy (RMMS) with low DOFs and explicit physical meaning is proposed, which directly discretizes a continuous structure into a number of rigid finite elements (RFEs) connected by spring-damping elements (SDEs). In the RMMS, a new identification method from the perspective of the inverse vibration problem is particularly put forward to resolve the parameters of SDEs, which is crucial to the implementation of RMMS in complex flexible structures. With decoupling and linearization, this nonlinear problem is transformed into solving the incompatible linear equations in Rn2 vector space based on vectorization operator and Kronecker product, and optimal parameters are obtained by calculating the Moore–Penrose generalized inverse. Finally, the comparison of the experimental results with the simulated ones by the RMMS strongly validates the feasibility and correctness of the RMMS in predicting the dynamic behaviors while with few DOFs and explicit physical meaning; the application in a lithography system exhibits the applicability of the RMMS for dynamic modeling of large-scale mechanical systems. |
url |
http://dx.doi.org/10.1155/2020/8329395 |
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