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Research Papers

Modeling and Analysis of Multilayered Elastic Beam Using Spectral Finite Element Method

[+] Author and Article Information
Ahmet Unal, Q. H. Zuo

Department of Mechanical
and Aerospace Engineering,
The University of Alabama in Huntsville,
Huntsville, AL 35899

Gang Wang

Department of Mechanical
and Aerospace Engineering,
The University of Alabama in Huntsville,
Huntsville, AL 35899
e-mail: gang.wang@uah.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 30, 2015; final manuscript received March 30, 2016; published online May 25, 2016. Assoc. Editor: Nader Jalili.

J. Vib. Acoust 138(4), 041013 (May 25, 2016) (12 pages) Paper No: VIB-15-1103; doi: 10.1115/1.4033355 History: Received March 30, 2015; Revised March 30, 2016

Multilayered elastic structures are widely used in engineering applications. In this paper, a spectral finite element model (SFEM) is developed to predict the dynamic behavior of a multilayered beam structure. First, a higher-order multilayered beam model is derived. Each layer is modeled as a Timoshenko beam, in which both shear deformation and rotational inertia are considered. By allowing different rotation in each layer, the overall sectional warping effect is included as well. A set of fully coupled governing equations presented in a compact form and associated boundary conditions are obtained by the application of Hamilton's principle. Second, a semi-analytical solution of these equations is determined and used in formulating the SFEM. The SFEM predictions are validated against the nastran results and other results in literature. Compared to the conventional FEM (CFEM), a very small number of elements are required in the SFEM for comparable accuracy, which substantially reduce the computing time, especially for simulations of high-frequency wave propagations. Finally, the SFEM is used to predict the lamb wave responses in multilayered beams. Wave propagation characteristics in both undamaged and damaged cases are well captured. In summary, the SFEM can accurately and efficiently predict the behavior of multilayered beams and serve as a framework to conduct wave propagation prediction and damage diagnostic analysis in structural health monitoring (SHM) applications.

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Figures

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Fig. 1

Composite beam theories [1,3]

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Fig. 3

Spectral finite element of a multilayered beam: (a) nodal displacement components and (b) nodal force components

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Fig. 5

FRF of a two-layered beam

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Fig. 6

FRF of a two-layered beam: 8000–10,000 Hz

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Fig. 7

Three-layered beam

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Fig. 8

FRF of a three-layered beam

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Fig. 9

Two-layer beam configuration

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Fig. 10

Waveform of a unit tip force at 50 kHz sine burst

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Fig. 11

Undamaged two-layered beam wave response

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Fig. 12

Damaged two-layered beam wave response: 50% notch damage on the top layer

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Fig. 13

Five-layered beam

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Fig. 14

Undamaged five-layered beam wave response

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Fig. 15

Damaged five-layered beam wave response

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