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Research Papers

A Practical Estimation of Frequency Response Functions for System Decoupling Indirectly Using a Variable Cross Section Rod

[+] Author and Article Information
Jun Wang

Jiangsu Key Laboratory of Advanced Food
Manufacturing Equipment and Technology,
Jiangnan University,
Wuxi 214122, China;
Key Laboratory of Advanced Manufacture
Technology for Automobile Parts,
Chongqing University of Technology,
Wuxi 214122, China
e-mail: wangj_1982@jiangnan.edu.cn

Tian-Ya Meng

Jiangsu Key Laboratory of Advanced Food
Manufacturing Equipment and Technology,
Department of Packaging Engineering,
Jiangnan University,
Wuxi 214122, China
e-mail: mengtianya9@163.com

Ming-Yu Li

Jiangsu Key Laboratory of Advanced Food
Manufacturing Equipment and Technology,
Department of Packaging Engineering,
Jiangnan University,
Wuxi 214122, China
e-mail: 943554074@qq.com

Teik C. Lim

Office of The Provost,
University of Texas at Arlington,
701 South Nedderman Drive,
Davis Hall, Suite 321,
Arlington, TX 76019-0118
e-mail: teik.lim@uta.edu

Wen-Xuan Kuang

Jiangsu Key Laboratory of Advanced Food
Manufacturing Equipment and Technology,
Department of Packaging Engineering,
Jiangnan University,
Wuxi 214122, China;
Ningbo Institute of Technology,
Zhejiang University,
Ningbo 315100, China
e-mail: 877988934@qq.com

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 19, 2017; final manuscript received March 22, 2018; published online May 7, 2018. Assoc. Editor: Julian Rimoli.

J. Vib. Acoust 140(5), 051019 (May 07, 2018) (11 pages) Paper No: VIB-17-1269; doi: 10.1115/1.4039868 History: Received June 19, 2017; Revised March 22, 2018

It is of high importance to be able to decouple a system to obtain the dynamic characteristics of its substructures; however, the necessary frequency response functions (FRFs) of the coupling interface are usually challenging to measure due to the limited accessible space and complex geometries. In this paper, a measurement technique in the decoupling process of a coupled system is proposed in order to obtain the FRFs at coupling interface. Specifically, a variable cross section rod is adopted to transmit the dynamic behavior of coupling interface. The proposed technique has three advantages: (a) the thick end with large cross section can provide enough area for applying excitation force like using impact hammer and/or setting up sensors; (b) the slender end with small cross section can break through the spatial limitation more easily; and (c) the convenience that no additional experimental setup is required but just using an available variable cross section rod. Vibrational equation of the variable cross section probe method is derived and then combined with the existing decoupling theories. Finally, the proposed probe method and the new decoupling theory combining probe theory are validated through numerical simulations (FEM) and laboratory experiments, respectively. The results show its great practicability in decoupling process especially in low frequency range.

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References

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Figures

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Fig. 1

Two-component rigidly coupled system

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Fig. 2

Free body diagram of a bar with variable cross section

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Fig. 3

Finite element models for study of probe theory: (a) a plate under free boundary condition (element type: solid 186 size: 10 mm nodes: 8641 elements: 4070), (b) a plate with FRF probe under free boundary condition when α = 0.5 (element type: solid 186 size: 10 mm nodes: 13,496 elements: 2013), (c) a plate under fixed boundary condition (element type: solid 186 size: 10 mm nodes: 8641 elements: 4070), and (d) a plate with FRF probe under fixed boundary condition when α = 0.5 (element type: solid 186 size: 10 mm nodes: 13,496 elements: 2013)

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Fig. 4

Frequency response functions of prediction by probe method: (a) FRFs when α = 0.5 under free boundary condition, (b) FRFs when α = 0.7 under free boundary condition, (c) FRFs when α = 0.5 under fixed boundary condition, and (d) FRFs when α = 0.7 under fixed boundary condition

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Fig. 5

Finite element models for application of probe method to decoupling theory: (a) substructure A (element type: solid 186 size: 5 mm nodes: 1292 elements: 629), (b) substructure B (element type: solid 186 size: 15 mm nodes: 7574 elements: 3515), (c) coupled system (element type: solid 186 size: 15 mm nodes: 7804 elements: 3463), and (d) coupled system with a probe (element type: solid 186 size: 15 mm nodes: 7928 elements: 3524)

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Fig. 6

Modal shapes of variable cross section rod: (a) the seventh vibration mode, (b) the eighth vibration mode, (c) the ninth vibration mode, and (d) the tenth vibration mode

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Fig. 7

FRFs results for validation of FRF probe method from FEM

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Fig. 8

Validation results for application of probe technique in decoupling method from FEM

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Fig. 9

Experimental models: (a) substructure A, (b) rigidly coupled system, and (c) rigidly coupled system with a variable cross section probe

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Fig. 10

FRFs for validation of FRF probe method from experiments

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Fig. 11

Experimental validation results for application of probe technique in decoupling method

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