Bending and vibration of two-dimensional decagonal quasicrystal nanoplates via modified couple-stress theory

• Published in: Applied mathematics and mechanics 2022-03, Vol.43 (3), p.371-388
• Main Authors: Zhang, Miao, Guo, Junhong, Li, Yansong
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Bending; Boundary conditions; Classical Mechanics; Deformation; Displacement; Eigenvalues; Equations of motion; Exact solutions; Fluid- and Aerodynamics; Free boundaries; Free vibration; Harmonic response; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Matrix methods; Partial Differential Equations; Phonons; Quasicrystals; Resonant frequencies; Stacking sequence (composite materials); Traction; Vibration analysis; Vibration response
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-022-2818-6

Based on the modified couple-stress theory, the three-dimensional (3D) bending deformation and vibration responses of simply-supported and multilayered two-dimensional (2D) decagonal quasicrystal (QC) nanoplates are investigated. The surface loading is assumed to be applied on the top surface in the bending analysis, the traction-free boundary conditions on both the top and bottom surfaces of the nanoplates are used in the free vibration analysis, and a harmonic concentrated point loading is applied on the top surfaces of the nanoplates in the harmonic response analysis. The general solutions of the extended displacement and traction vectors for the homogeneous QC nanoplates are derived by solving the eigenvalue problem reduced from the final governing equations of motion with the modified couple-stress effect. By utilizing the propagator matrix method, the analytical solutions of the displacements of the phonon and phason fields for bending deformation, the natural frequency of free vibration, and the displacements of the phonon and phason fields for the harmonic responses are obtained. Numerical examples are illustrated to show the effects of the quasiperiodic direction, the material length scale parameter, and the the stacking sequence of the nanoplates on the bending deformation and vibration responses of two sandwich nanoplates made of QC and crystal materials.