Nonlocal Vibration, Buckling and Bending of 1D Layered Quasicrystal Nanobeams

YUAN Qingdan; GUO Junhong

doi:10.21656/1000-0887.440260

Volume 45 Issue 2

Feb. 2024

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YUAN Qingdan, GUO Junhong. Nonlocal Vibration, Buckling and Bending of 1D Layered Quasicrystal Nanobeams[J]. Applied Mathematics and Mechanics, 2024, 45(2): 208-219. doi: 10.21656/1000-0887.440260

Citation:

YUAN Qingdan, GUO Junhong. Nonlocal Vibration, Buckling and Bending of 1D Layered Quasicrystal Nanobeams[J]. Applied Mathematics and Mechanics, 2024, 45(2): 208-219. doi: 10.21656/1000-0887.440260

Citation:

YUAN Qingdan, GUO Junhong. Nonlocal Vibration, Buckling and Bending of 1D Layered Quasicrystal Nanobeams[J]. Applied Mathematics and Mechanics, 2024, 45(2): 208-219. doi: 10.21656/1000-0887.440260

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Nonlocal Vibration, Buckling and Bending of 1D Layered Quasicrystal Nanobeams

doi: 10.21656/1000-0887.440260

YUAN Qingdan^1
,,
GUO Junhong^{1, 2
,
,}

1.
Department of Mechanics, College of Science, Inner Mongolia University of Technology, Hohhot 010051, P.R.China
2.
School of Aeronautics, Inner Mongolia University of Technology, Hohhot 010051, P.R.China

Received Date: 2023-08-28
Rev Recd Date: 2023-10-20
Publish Date: 2024-02-01

Abstract

Abstract

Based on the nonlocal theory, a 1D layered nano-quasicrystal (QC) simply supported beam model was established to investigate the free vibration, buckling behavior, and bending deformation of nano-QC beams. The pseudo-Stroh formula was used to derive the governing equations for the nanobeam. Using the transfer matrix method, exact solutions of the natural frequency, the critical buckling load, the generalized displacement and the generalized stress for bending problems of layered nano-QC beams was obtained under simply supported boundary conditions. The effects of the height-span ratio, the layer thickness ratio, the stacking sequence, and the nonlocal effect on the natural frequency, the critical buckling load and the bending deformation of layered nano-QC simply supported beams were analyzed. The results show that, the natural frequency and the critical buckling load decrease with increasing nonlocal parameter. The bigger the outer-layer quasicrystal elastic constant is, the higher the natural frequency and the buckling critical load will be. The stacking sequence has a significant effect on the mechanical behavior of nano-QC beams. The obtained exact solution provides a reference for various numerical methods and experimental results of nanoscale beam structures.
- nano-quasicrystal,
- simply supported beam,
- free vibration,
- buckling,
- bending,
- nonlocal effect

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References(34)

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