Free and forced vibration of layered one-dimensional quasicrystal nanoplates with modified couple-stress effect
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ly 2020 Vol. 63 No. 7: 274621 https://doi.org/10.1007/s11433-020-1547-3
Free and forced vibration of layered one-dimensional quasicrystal nanoplates with modified couple-stress effect 1*†
1†
1,2
JunHong Guo , Miao Zhang , WeiQiu Chen , and XiaoYan Zhang 1
1
Department of Mechanics, Inner Mongolia University of Technology, Hohhot 010051, China; 2 Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China Received February 2, 2020; accepted March 15, 2020; published online April 20, 2020
Citation:
J. H. Guo, M. Zhang, W. Q. Chen, and X. Y. Zhang, Free and forced vibration of layered one-dimensional quasicrystal nanoplates with modified couple-stress effect, Sci. China-Phys. Mech. Astron. 63, 274621 (2020), https://doi.org/10.1007/s11433-020-1547-3
To the editor, A new type of solid, called quasicrystal (QC) was discovered after Shechtman et al. [1] accidently got in 1982 a five-fold symmetry diffraction image of rapidly cooled Al-Mn alloys. In contrast with crystals with periodic atomic arrangement, QCs have perfect long-range order (like mirror symmetry) but no periodic translational symmetry. Due to their intrinsic brittleness at room temperature, QCs cannot be used directly as structural materials. However, QCs as thin films and coatings of metals in industry are applied to surface modified materials and the reinforcing phase in structural materials. At present, it is difficult to prepare bulk QCs in experiments. Some nano-QCs have been successfully produced with a better mechanical property than the conventional crystalline alloys. The newly prepared nano-QC alloys have been used as some heat-resisting parts in automobiles. Recently, a multilayered nano-QC structure was formed by depositing ductile vanadium layers with Al-Cu-Fe-based QC-alloy layers [2]. The modified couple-stress theory involving only one material length scale l [3] has been validated by the experimental observations and molecular dynamics simulation [4]. As indicated in ref. [5], although both the modified couplestress theory and Eringen’s nonlocal elasticity theory could
*Corresponding author (email: [email protected]) †These authors contributed equally to this work.
accurately predict the static behavior, the former agrees much better than the latter with the experimentally observed dynamic responses of polysilicon micro-beams. In this consideration, we here focus on the three-dimensional free and forced vibration responses of a layered one-dimensional QC nanoplate with the modified couple-stress effect. The four edges of the plate are simply supported, which allows a double Fourier series solution. Details about problem description and computational process could be found in the Materials and Methods Section of Supporting Information. Based on the modified couple-stress theory, the final governing equation for the vibration problem can be derived as: s 2C 2 + s C1 + C 0
(
)
+0.25Gl 2 s 4 D4 + s 3 D 3 + s 2 D 2 + s D1 + D 0 a = 0,
(1)
T
where a=[a1, a2, a3, a4] , and matrices Ci (i=0, 1, 2) and Di (i=0, 1,
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