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.
Highlights
Quasicrystals (QCs)[1] are novel phases of matter which possess quasiperiodic atomic arrangements and rotational symmetries, including five-fold, eight-fold, and ten-fold symmetry c The Author(s) 2021Tuoya SUN, Junhong GUO, and E
If the 2D decagonal QC nanoplate is embedded in an elastic medium, the traction boundary conditions are given by t1(H) = (0, 0, q3H, 0, 0)T, t1(0) = (0, 0, q30, 0, 0)T, (25)
We analyze the nonlocal vibration and buckling of 2D decagonal QC homogeneous nanoplates and two sandwich nanoplates made of 2D decagonal Al-Ni-Co QC and BaTiO3 crystal with the elastic medium for mode (m, n) = (1, 1)
Summary
Quasicrystals (QCs)[1] are novel phases of matter which possess quasiperiodic atomic arrangements and rotational symmetries, including five-fold, eight-fold, and ten-fold symmetry. By using double-well potentials, Chen et al.[8] obtained the decagonal and dodecagonal QCs through MD simulation Owing to their unique structures, QCs possess many unusual properties such as high hardness, high oxidation resistance, low frictional coefficient, low surface energy, low thermal conductivity, high wear resistance, elevated corrosion resistance, reduced wetting, and superplasticity above 700 ◦C, which make them attractive for technological applications such as superconductivity, photonics, coatings, and reinforced composites[9,10,11]. Guo et al.[31] considered the nonlocal buckling of composite nanoplates with coated 1D QCs in an elastic medium. The present study focuses on the vibration and buckling of 2D decagonal QC layered nanoplates on top of or embedded in an elastic medium based on the nonlocal theory.
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