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Research Papers

Vibration Frequencies and Modes of a Z-Shaped Beam With Variable Folding Angles

[+] Author and Article Information
W. Zhang

Beijing Key Laboratory on Nonlinear Vibrations
and Strength of Mechanical Structures,
College of Mechanical Engineering,
Beijing University of Technology,
Beijing 100124, China
e-mail: sandyzhang0@yahoo.com

W. H. Hu

Beijing Key Laboratory on Nonlinear Vibrations
and Strength of Mechanical Structures,
College of Mechanical Engineering,
Beijing University of Technology,
Beijing 100124, China;
Tianjin Key Laboratory of the Design and
Intelligent Control of the Advanced
Mechatronical System,
Tianjin University of Technology,
Tianjin 300384, China

D. X. Cao, M. H. Yao

Beijing Key Laboratory on Nonlinear Vibrations
and Strength of Mechanical Structures,
College of Mechanical Engineering,
Beijing University of Technology,
Beijing 100124, China

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 17, 2015; final manuscript received March 1, 2016; published online May 18, 2016. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 138(4), 041004 (May 18, 2016) (7 pages) Paper No: VIB-15-1059; doi: 10.1115/1.4033196 History: Received February 17, 2015; Revised March 01, 2016

In this paper, we investigate the vibration characteristics of a Z-shaped beam with variable folding angles which is used to model a folding wing of a morphing aircraft under the condition of a fixed structure. The governing equations of motions for the Z-shaped beam are formulated. For a specific set of material and geometrical parameters, the first three in-plane and the first two out-of-plane linear frequencies of the Z-shaped beam are theoretically calculated, and validated by the experiments and numerical simulations. Additionally, the theoretical mode shapes at a fixed folding angle are compared to the experimental results and the finite element simulations. The theoretical results agree well with numerical simulations and experiments. The results obtained in this paper are helpful for designing and controlling Z-shaped beam structures, and can also be used as a basis to study the nonlinear dynamics of these structures.

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Figures

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Fig. 1

The model of the Z-shaped beam is depicted: (a) the schematic diagram of a Z-wing and (b) the Z-shaped beam

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Fig. 2

The displacements of the element for the beam are given: (a) an infinitesimal length of the beam and (b) angular changes of a cross section

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Fig. 3

The experimental setup is given: (a) the excitation in the Y-direction and (b) the excitation in the Z-direction

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Fig. 4

The comparison of the analytical, experimental, and numerical linear frequencies is obtained

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Fig. 5

The first in-plane mode shapes of the Z-shaped beam with a 60 deg folding angle are obtained: (a) the theoretical mode shape, (b) the numerical mode shape, and (c) the experimental mode shape

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Fig. 6

The second in-plane mode shapes of the Z-shaped beam with a 60 deg folding angle are obtained: (a) the theoretical mode shape, (b) the numerical mode shape, and (c) the experimental mode shape

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Fig. 7

The third in-plane mode shapes of the Z-shaped beam with a 60 deg folding angle are obtained: (a) the theoretical mode shape, (b) the numerical mode shape, and (c) the experimental mode shape

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Fig. 8

The first out-of-plane order mode shapes of the Z-shaped beam with a 60 deg folding angle are obtained: (a) the theoretical mode shape, (b) the numerical mode shape, and (c) the experimental mode shape

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Fig. 9

The second out-of-plane mode shapes of the Z-shaped beam with a 60 deg folding angle are obtained: (a) the theoretical mode shape, (b) the numerical mode shape, and (c) the experimental mode shape

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