Influence of Spiral Stiffeners’ Symmetric and Asymmetric Angles on Nonlinear Vibration Responses of Multilayer FG Cylindrical Shells
Abstract
:1. Introduction
2. Basic Formulations
2.1. MFG Cylindrical Shells Reinforced by FGSSs
2.2. Governing Equation
- MFG cylindrical shells:
- FG spiral stiffeners:
2.3. Semi-Analytical Solutions
2.4. Addressing the Nonlinear Equation with the MMSs
3. Numerical Results
3.1. Validation of the Current Results
3.2. Results of NVs for MFG Cylindrical Shells Reinforced by FGSS
4. Conclusions
- The velocity of MFG cylindrical shells reinforced by FGSSs is lower in the modes () with stiffener angles and , in the modes () with stiffener angles and or , and in the modes () with stiffener angles and or or , compared to other configurations.
- The phase plane of the vibration of the MFG cylindrical shells, reinforced by FGSSs with modes () and stiffener angles and , tends towards a limit cycle quickly. Consequently, the NVs of the system are stabilized rapidly.
- By increasing the temperatures, the disorder on the maximum deflection versus velocity curve of the MFG cylindrical shells reinforced by FGSSs with the modes () and the modes () increases. Conversely, the vibration amplitude of the system with the modes () decreases slightly.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix B
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Present | Zhang et al. [30] | Song et al. [31] | Yang et al. [32] | ||||
---|---|---|---|---|---|---|---|
Discrepancy | Discrepancy | Discrepancy | |||||
0.0151266 | 0.0161065 | 6.10 | 0.0161299 | 6.20 | 0.0151185 | 0.05 | |
0.1097431 | 0.1098113 | 0.06 | 0.1097653 | 0.02 | 0.1096523 | 0.08 | |
0.0161008 | 0.0161011 | 0.002 | 0.0161011 | 0.002 | 0.0161003 | 0.003 | |
0.0050421 | 0.0050418 | 0.006 | 0.0050424 | 0.006 | 0.0050423 | 0.004 |
Material | Properties | |||||
---|---|---|---|---|---|---|
(Ceramic) | 3.48 × 1011 | 0 | −3.07 × 10−4 | 2.16 × 10−7 | −8.95 × 10−11 | |
2370 | 0 | 0 | 0 | 0 | ||
5.87 × 10−6 | 0 | 9.10 × 10−4 | 0 | 0 | ||
13.723 | 0 | 0 | 0 | 0 | ||
(Metal) | 2.01 × 1011 | 0 | 3.08 × 10−4 | −6.53 × 10−7 | 0 | |
8166 | 0 | 0 | 0 | 0 | ||
1.23 × 10−5 | 0 | 8.09 × 10−4 | 0 | 0 | ||
15.379 | 0 | 0 | 0 | 0 |
R (m) | |||||||||
---|---|---|---|---|---|---|---|---|---|
0.3 | 0.01 | 2.5 | 40 | 1 |
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Foroutan, K.; Torabi, F. Influence of Spiral Stiffeners’ Symmetric and Asymmetric Angles on Nonlinear Vibration Responses of Multilayer FG Cylindrical Shells. Symmetry 2024, 16, 1318. https://doi.org/10.3390/sym16101318
Foroutan K, Torabi F. Influence of Spiral Stiffeners’ Symmetric and Asymmetric Angles on Nonlinear Vibration Responses of Multilayer FG Cylindrical Shells. Symmetry. 2024; 16(10):1318. https://doi.org/10.3390/sym16101318
Chicago/Turabian StyleForoutan, Kamran, and Farshid Torabi. 2024. "Influence of Spiral Stiffeners’ Symmetric and Asymmetric Angles on Nonlinear Vibration Responses of Multilayer FG Cylindrical Shells" Symmetry 16, no. 10: 1318. https://doi.org/10.3390/sym16101318
APA StyleForoutan, K., & Torabi, F. (2024). Influence of Spiral Stiffeners’ Symmetric and Asymmetric Angles on Nonlinear Vibration Responses of Multilayer FG Cylindrical Shells. Symmetry, 16(10), 1318. https://doi.org/10.3390/sym16101318