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Research Papers

Free Vibration of a Multilayered One-Dimensional Quasi-Crystal Plate

[+] Author and Article Information
Natalie Waksmanski

Department of Civil Engineering,
University of Akron,
Akron, OH 44325-3905
e-mail: npw5@zips.uakron.edu

Ernian Pan

Fellow ASME
Department of Civil Engineering,
University of Akron,
Akron, OH 44325-3905
e-mail: pan2@uakron.edu

Lian-Zhi Yang

College of Science, College of Engineering,
China Agricultural University,
Beijing 100083, China
e-mail: ylz_xiaozhu@126.com

Yang Gao

College of Science,
China Agricultural University,
Beijing 100083, China
e-mail: gaoyangg@gmail.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 January 24, 2014; final manuscript received March 25, 2014; published online June 2, 2014. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 136(4), 041019 (Jun 02, 2014) (8 pages) Paper No: VIB-14-1026; doi: 10.1115/1.4027632 History: Received January 24, 2014; Revised March 25, 2014

An exact closed-form solution of free vibration of a simply supported and multilayered one-dimensional (1D) quasi-crystal (QC) plate is derived using the pseudo-Stroh formulation and propagator matrix method. Natural frequencies and mode shapes are presented for a homogenous QC plate, a homogenous crystal plate, and two sandwich plates made of crystals and QCs. The natural frequencies and the corresponding mode shapes of the plates show the influence of stacking sequence on multilayered plates and the different roles phonon and phason modes play in dynamic analysis of QCs. This work could be employed to further expand the applications of QCs especially if used as composite materials.

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Figures

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Fig. 1

N-layered QC plate

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Fig. 2

First mode shape for (a) crystal homogenous plate with normalized natural frequency Ω = 1.19, (b) QC homogenous plate with Ω = 1.28, (c) sandwich plate C/QC/C with Ω = 1.09, and (d) sandwich plate QC/C/QC with Ω = 1.35

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Fig. 3

Second mode shape for (a) crystal homogenous plate with normalized natural frequency Ω = 2.30, (b) QC homogenous plate with Ω = 2.73, (c) sandwich plate C/QC/C with Ω = 2.33, and (d) sandwich plate QC/C/QC with Ω = 2.75

Grahic Jump Location
Fig. 4

Third mode shape for (a) crystal homogenous plate with normalized natural frequency Ω = 3.83, (b) QC homogenous plate with Ω = 4.22, (c) sandwich plate C/QC/C with Ω = 3.76, and (d) sandwich plate QC/C/QC with Ω = 4.26

Grahic Jump Location
Fig. 5

Fourth mode shape for (a) crystal homogenous plate with normalized natural frequency Ω = 5.81, (b) QC homogenous plate with Ω = 6.35, (c) sandwich plate C/QC/C with Ω = 5.51, and (d) sandwich plate QC/C/QC with Ω = 6.42

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