A hybrid numerical method for vibration analysis of linear multibody systems with flexible components

Hanjing Lu; Xiaoting Rui; Yuanyuan Ding; Yu Chang; Yiheng Chen; Jianguo Ding; Xuping Zhang

doi:10.1016/j.apm.2021.09.015

A hybrid numerical method for vibration analysis of linear multibody systems with flexible components

Hanjing Lu, Xiaoting Rui^*, Yuanyuan Ding, Yu Chang, Yiheng Chen, Jianguo Ding, Xuping Zhang

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

18 Citationer (Scopus)

Abstract

This paper presents a novel hybrid numerical method combining the transfer matrix method for multibody systems with the finite element method and the Craig-Bampton reduction method. In the proposed method, the multibody system is divided into two types of subsystems, depending on the shape and stiffness of each component. All the subsystems are independently analysed by the transfer matrix method for multibody systems or the finite element method and the Craig-Bampton reduction method. The whole system is recombined by deriving the relation equations of the connection points amongst subsystems. Then, the overall transfer equation and the eigenvalue equation of the whole system are obtained. Verifications on a simple system and rigid-flexible manipulator system show that the natural frequencies and modal shapes agree well with the finite element method. The dynamic model of the ultra-precision fly-cutting machine tool concerning the linearly elastic deformation of the fly-cutting head is established by the proposed method and validated by the experimental modal test. According to the comparison of computational speed with the finite element method, the proposed method has advantages in easy programming, low matrix order, low computational effort, and high applicability to the linear time-invariant mechanical system with flexible components.

Originalsprog	Engelsk
Tidsskrift	Applied Mathematical Modelling
Vol/bind	101
Sider (fra-til)	748-771
Antal sider	24
ISSN	0307-904X
DOI	https://doi.org/10.1016/j.apm.2021.09.015
Status	Udgivet - jan. 2022

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title = "A hybrid numerical method for vibration analysis of linear multibody systems with flexible components",

abstract = "This paper presents a novel hybrid numerical method combining the transfer matrix method for multibody systems with the finite element method and the Craig-Bampton reduction method. In the proposed method, the multibody system is divided into two types of subsystems, depending on the shape and stiffness of each component. All the subsystems are independently analysed by the transfer matrix method for multibody systems or the finite element method and the Craig-Bampton reduction method. The whole system is recombined by deriving the relation equations of the connection points amongst subsystems. Then, the overall transfer equation and the eigenvalue equation of the whole system are obtained. Verifications on a simple system and rigid-flexible manipulator system show that the natural frequencies and modal shapes agree well with the finite element method. The dynamic model of the ultra-precision fly-cutting machine tool concerning the linearly elastic deformation of the fly-cutting head is established by the proposed method and validated by the experimental modal test. According to the comparison of computational speed with the finite element method, the proposed method has advantages in easy programming, low matrix order, low computational effort, and high applicability to the linear time-invariant mechanical system with flexible components.",

keywords = "Craig-Bampton reduction method, Finite element method, Multibody systems, Transfer matrix method for multibody systems, Ultra-precision fly-cutting machine tool",

author = "Hanjing Lu and Xiaoting Rui and Yuanyuan Ding and Yu Chang and Yiheng Chen and Jianguo Ding and Xuping Zhang",

year = "2022",

month = jan,

doi = "10.1016/j.apm.2021.09.015",

language = "English",

volume = "101",

pages = "748--771",

journal = "Applied Mathematical Modelling",

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T1 - A hybrid numerical method for vibration analysis of linear multibody systems with flexible components

AU - Lu, Hanjing

AU - Rui, Xiaoting

AU - Ding, Yuanyuan

AU - Chang, Yu

AU - Chen, Yiheng

AU - Ding, Jianguo

AU - Zhang, Xuping

PY - 2022/1

Y1 - 2022/1

N2 - This paper presents a novel hybrid numerical method combining the transfer matrix method for multibody systems with the finite element method and the Craig-Bampton reduction method. In the proposed method, the multibody system is divided into two types of subsystems, depending on the shape and stiffness of each component. All the subsystems are independently analysed by the transfer matrix method for multibody systems or the finite element method and the Craig-Bampton reduction method. The whole system is recombined by deriving the relation equations of the connection points amongst subsystems. Then, the overall transfer equation and the eigenvalue equation of the whole system are obtained. Verifications on a simple system and rigid-flexible manipulator system show that the natural frequencies and modal shapes agree well with the finite element method. The dynamic model of the ultra-precision fly-cutting machine tool concerning the linearly elastic deformation of the fly-cutting head is established by the proposed method and validated by the experimental modal test. According to the comparison of computational speed with the finite element method, the proposed method has advantages in easy programming, low matrix order, low computational effort, and high applicability to the linear time-invariant mechanical system with flexible components.

AB - This paper presents a novel hybrid numerical method combining the transfer matrix method for multibody systems with the finite element method and the Craig-Bampton reduction method. In the proposed method, the multibody system is divided into two types of subsystems, depending on the shape and stiffness of each component. All the subsystems are independently analysed by the transfer matrix method for multibody systems or the finite element method and the Craig-Bampton reduction method. The whole system is recombined by deriving the relation equations of the connection points amongst subsystems. Then, the overall transfer equation and the eigenvalue equation of the whole system are obtained. Verifications on a simple system and rigid-flexible manipulator system show that the natural frequencies and modal shapes agree well with the finite element method. The dynamic model of the ultra-precision fly-cutting machine tool concerning the linearly elastic deformation of the fly-cutting head is established by the proposed method and validated by the experimental modal test. According to the comparison of computational speed with the finite element method, the proposed method has advantages in easy programming, low matrix order, low computational effort, and high applicability to the linear time-invariant mechanical system with flexible components.

KW - Craig-Bampton reduction method

KW - Finite element method

KW - Multibody systems

KW - Transfer matrix method for multibody systems

KW - Ultra-precision fly-cutting machine tool

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U2 - 10.1016/j.apm.2021.09.015

DO - 10.1016/j.apm.2021.09.015

M3 - Journal article

AN - SCOPUS:85116634520

SN - 0307-904X

VL - 101

SP - 748

EP - 771

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

ER -

A hybrid numerical method for vibration analysis of linear multibody systems with flexible components

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