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Research Papers

Nonlocal Analytical Solutions for Multilayered One-Dimensional Quasicrystal Nanoplates

[+] Author and Article Information
Natalie Waksmanski

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

Ernian Pan

Fellow ASME
Department of Civil Engineering,
The University of Akron,
Akron, OH 44325
e-mail: pan2@uakron.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 August 8, 2016; final manuscript received September 28, 2016; published online February 3, 2017. Assoc. Editor: Matthew Brake.

J. Vib. Acoust 139(2), 021006 (Feb 03, 2017) (16 pages) Paper No: VIB-16-1391; doi: 10.1115/1.4035106 History: Received August 08, 2016; Revised September 28, 2016

An exact closed-form solution for the three-dimensional static deformation and free vibrational response of a simply supported and multilayered quasicrystal (QC) nanoplate with the nonlocal effect is derived. Numerical examples are presented for a homogeneous crystal nanoplate, homogenous QC nanoplate, and sandwich nanoplates with various stacking sequences. Induced by traction boundary conditions, extended displacements and stresses reveal the important role that the nonlocal parameter plays in the structural analysis of nanoquasicrystals (nano-QCs). The natural frequencies and the corresponding mode shapes of the nanoplates further show the influence of stacking sequence and phonon–phason coupling effect. This exact solution is useful for it provides benchmark results to assess the accuracy of finite element nano-QC models and can assist engineers in tuning their quasicrystal nanoplate design.

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References

Figures

Grahic Jump Location
Fig. 1

Schematic configuration of a QC nanoplate with J layers

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Fig. 2

Variation of phonon stress σ33 along the thickness direction in homogeneous crystal nanoplate made of BaTiO3 with different nonlocal parameters l. Results in the homogeneous QC nanoplate made of Al–Ni–Co, sandwich C/Q/C nanoplate, and sandwich Q/C/Q nanoplate overlap the phonon stress σ33.

Grahic Jump Location
Fig. 3

Through-thickness variation of the normalized phonon (a) displacement u1, (b) displacement u3, (c) normal stress σ11, and (d) shear stress σ13 in the homogeneous crystal nanoplate with different nonlocal parameters l

Grahic Jump Location
Fig. 4

Through-thickness variation of the normalized (a) phonon displacement u1, (b) phonon displacement u3, (c) phonon normal stress σ11, (d) phonon shear stress σ13, (e) phason displacement w3, and (f) phason stress H33 in the homogeneous QC nanoplate with different nonlocal parameters l

Grahic Jump Location
Fig. 5

Through-thickness variation of the normalized (a) phonon displacement u1, (b) phonon displacement u3, (c) phonon normal stress σ11, (d) phonon shear stress σ13, (e) phason displacement w3, and (f) phason stress H33 in the sandwich C/Q/C nanoplate with different nonlocal parameters l

Grahic Jump Location
Fig. 6

Through-thickness variation of the normalized (a) phonon displacement u1, (b) phonon displacement u3, (c) phonon normal stress σ11, (d) phonon shear stress σ13, (e) phason displacement w3, and (f) phason stress H33 in the sandwich Q/C/Q nanoplate with different nonlocal parameters l

Grahic Jump Location
Fig. 7

Nonlocal effect on the (a) phonon displacement u1 and (b) phonon displacement u3 along the thickness direction of the homogeneous crystal nanoplate on the first modal frequency

Grahic Jump Location
Fig. 8

Nonlocal effect on the (a) phonon displacement u3 and (b) phason displacement w3 along the thickness direction of the homogeneous QC nanoplate on the first modal frequency

Grahic Jump Location
Fig. 9

Nonlocal effect on the (a) phonon displacement u1, (b) phonon displacement u3, and (c) phason displacement w3 along the thickness direction of the C/Q/C sandwich nanoplate on the first modal frequency

Grahic Jump Location
Fig. 10

Nonlocal effect on the (a) phonon displacement u1, (b) phonon displacement u3, and (c) phason displacement w3 along the thickness direction of the Q/C/Q sandwich nanoplate on the first modal frequency

Grahic Jump Location
Fig. 11

Nonlocal effect on the (a) phonon displacement u1 and (b) phonon displacement u3 along the thickness direction of the homogenous crystal nanoplate on the third modal frequency

Grahic Jump Location
Fig. 12

Nonlocal effect on the (a) phonon displacement u1 and (b) phason displacement w3 along the thickness direction of the homogenous QC on the third modal frequency

Grahic Jump Location
Fig. 13

Nonlocal effect on the (a) phonon displacement u1, (b) phonon displacement u3, and (c) phason displacement w3 along the thickness direction of the C/Q/C sandwich nanoplate on the third modal frequency

Grahic Jump Location
Fig. 14

Nonlocal effect on the (a) phonon displacement u1, (b) phonon displacement u3, and (c) phason displacement w3 along the thickness direction of the C/Q/C sandwich nanoplate on the third modal frequency

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