Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

doi:10.1007/s10483-021-2743-6

Applied Mathematics and Mechanics (English Edition) ›› 2021, Vol. 42 ›› Issue (8): 1077-1094.doi: https://doi.org/10.1007/s10483-021-2743-6

• 论文 • 下一篇

Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

Tuoya SUN¹, Junhong GUO^1,2, E. PAN³

1. Department of Mechanics, Inner Mongolia University of Technology, Hohhot 010051, China;
2. School of Aeronautics, Inner Mongolia University of Technology, Hohhot 010051, China;
3. College of Engineering, Cleveland State University, Cleveland, Ohio 44115, U.S.A.

收稿日期:2021-02-21 修回日期:2021-04-13 出版日期:2021-08-01 发布日期:2021-07-28
通讯作者: Junhong GUO, E-mail:jhguo@imut.edu.cn
基金资助:
the National Natural Science Foundation of China (Nos. 12072166 and 11862021), the Program for Science and Technology of Inner Mongolia Autonomous Region of China (No. 2021GG0254), and the Natural Science Foundation of Inner Mongolia Autonomous Region of China (No. 2020MS01006)

Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

Tuoya SUN¹, Junhong GUO^1,2, E. PAN³

1. Department of Mechanics, Inner Mongolia University of Technology, Hohhot 010051, China;
2. School of Aeronautics, Inner Mongolia University of Technology, Hohhot 010051, China;
3. College of Engineering, Cleveland State University, Cleveland, Ohio 44115, U.S.A.

Received:2021-02-21 Revised:2021-04-13 Online:2021-08-01 Published:2021-07-28
Contact: Junhong GUO, E-mail:jhguo@imut.edu.cn
Supported by:
the National Natural Science Foundation of China (Nos. 12072166 and 11862021), the Program for Science and Technology of Inner Mongolia Autonomous Region of China (No. 2021GG0254), and the Natural Science Foundation of Inner Mongolia Autonomous Region of China (No. 2020MS01006)

摘要/Abstract

摘要： A mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional (3D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories. Numerical examples are provided to display the effects of the quasiperiodic direction, length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence, and medium elasticity on the vibration frequency and critical buckling load of the 2D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate. This feature is useful since the frequency and critical buckling load of the 2D decagonal QCs as coating materials of plate structures can now be tuned as one desire.

关键词: two-dimensional (2D) quasicrystal (QC), nanoplate, vibration, buckling, elastic medium, exact solution

Abstract: A mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional (3D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories. Numerical examples are provided to display the effects of the quasiperiodic direction, length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence, and medium elasticity on the vibration frequency and critical buckling load of the 2D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate. This feature is useful since the frequency and critical buckling load of the 2D decagonal QCs as coating materials of plate structures can now be tuned as one desire.

Key words: two-dimensional (2D) quasicrystal (QC), nanoplate, vibration, buckling, elastic medium, exact solution

中图分类号:

Tuoya SUN, Junhong GUO, E. PAN. Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(8): 1077-1094.

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Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

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