Mechanical Analysis of Functionally Graded Multilayered Two-Dimensional Decagonal Piezoelectric Quasicrystal Laminates with Imperfect Interfaces
Abstract
:1. Introduction
2. Description and Formulation of the Problem
2.1. Basic Equations
2.2. State Equations of a Homogeneous QC Laminate Layer
3. General Solutions for a 2D QC Laminate
4. Imperfect Conductive Interface Analysis
5. Numerical Examples
6. Conclusions
- As the degree of imperfect connection at the interface increases, some physical quantities become discontinuous at the interface, such as displacements.
- As the functional gradient factor changes, each physical quantity only changes its numerical magnitude while keeping its variation trend.
- An increase in the interface compliance would reduce the overall stiffness of the laminates while an increase in functional gradient factor would enhance the stiffness. The free vibration frequency will gradually increase as the interface compliance decreases and the functional gradient factor increases.
- The variation trends of the field quantities under different loading frequencies are similar to that of the eigenmode shape at the natural frequency, which is near the loading frequency.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix A.1. The State Equations in the Partial Differential Form Are
Appendix A.2. The State Equations for the Dynamic Problem
Appendix A.3. The Exported Components and the Coefficients in Equations (A1) and (A2)
Appendix A.4. The State Equations in the Partial Differential Form
Appendix A.5. The State Equations under SSSS Boundary Conditions with Opposite Edge Discretization
Appendix A.6. The State Equations under CCCC Boundary Conditions with Opposite Edge Discretization
Appendix A.7. The Coefficients in Equations (A5) and (A6)
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C11 | C12 | C13 | C33 | C44 | K1 | K2 | K4 | |
QC1 | 234.33 | 57.41 | 66.63 | 232.22 | 70.19 | 122 | 24 | 12 |
QC2 | 166 | 77 | 78 | 162 | 43 | 0 | 0 | 0 |
e15 | e31 | e33 | ρ | R1 | ||||
QC1 | 5.8 | −2.2 | 9.3 | 22.4 | 22.4 | 25.2 | 4186 | 8.846 |
QC2 | 11.6 | −4.4 | 18.6 | 11.2 | 11.2 | 12.6 | 5800 | 0 |
δ* = 0 | δ* = 2.5 | δ* = 5 | δ* = 7.5 | δ* = 10 | |
---|---|---|---|---|---|
η = −0.5 | 1.3510 | 0.8549 | 0.7392 | 0.6865 | 0.6560 |
η = −0.25 | 1.3563 | 0.8564 | 0.7408 | 0.6883 | 0.6580 |
η = 0 | 1.3616 | 0.8580 | 0.7425 | 0.6902 | 0.6599 |
η = 0.25 | 1.3670 | 0.8596 | 0.7442 | 0.6920 | 0.6619 |
η = 0.5 | 1.3723 | 0.8612 | 0.7460 | 0.6940 | 0.6639 |
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Wang, Y.; Liu, C.; Zhang, L.; Pan, E.; Gao, Y. Mechanical Analysis of Functionally Graded Multilayered Two-Dimensional Decagonal Piezoelectric Quasicrystal Laminates with Imperfect Interfaces. Crystals 2024, 14, 170. https://doi.org/10.3390/cryst14020170
Wang Y, Liu C, Zhang L, Pan E, Gao Y. Mechanical Analysis of Functionally Graded Multilayered Two-Dimensional Decagonal Piezoelectric Quasicrystal Laminates with Imperfect Interfaces. Crystals. 2024; 14(2):170. https://doi.org/10.3390/cryst14020170
Chicago/Turabian StyleWang, Yuxuan, Chao Liu, Liangliang Zhang, Ernian Pan, and Yang Gao. 2024. "Mechanical Analysis of Functionally Graded Multilayered Two-Dimensional Decagonal Piezoelectric Quasicrystal Laminates with Imperfect Interfaces" Crystals 14, no. 2: 170. https://doi.org/10.3390/cryst14020170
APA StyleWang, Y., Liu, C., Zhang, L., Pan, E., & Gao, Y. (2024). Mechanical Analysis of Functionally Graded Multilayered Two-Dimensional Decagonal Piezoelectric Quasicrystal Laminates with Imperfect Interfaces. Crystals, 14(2), 170. https://doi.org/10.3390/cryst14020170