Free-Vibration Analysis for Truncated Uflyand–Mindlin Plate Models: An Alternative Theoretical Formulation
Abstract
:1. Introduction
2. Mathematical Model
2.1. Pioneering and Modern Plate Studies
2.2. Direct Method
2.3. Variational Formulation
2.4. Original Uflyand–Mindlin Theory (Model I)
2.5. Uflyand–Mindlin Plate Model Based on Slope Inertia (Model II)
2.6. Truncated Uflyand–Mindlin Plate Model (Model III)
2.7. Transformation of Governing Differential Equations
3. Numerical Comparison and Discussion
3.1. Theoretical Formulation of a Rectangular Plate with Four Edges That Are Simply Supported
3.2. Numerical Example for a Rectangular Plate with Four Edges That Are Simply Supported
- -
- When the aspect ratio increases, the natural frequencies decrease;
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- When the thickness ratio increases, the free frequencies increase.
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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= 0.01 | = 0.1 | = 0.2 | |
---|---|---|---|
1 | 19.732 | 19.077 | 17.429 |
49.304 | 45.492 | 37.773 | |
78.845 | 69.715 | 54.089 | |
98.522 | 84.838 | 63.529 | |
128.011 | 106.207 | 76.167 | |
167.282 | 132.613 | 90.953 | |
177.091 | 138.889 | 94.363 | |
196.698 | 151.092 | 100.901 | |
245.657 | 179.788 | 115.879 | |
255.439 | 185.249 | 118.678 | |
2 | 12.326 | 11.373 | 9.443 |
19.711 | 17.429 | 13.522 | |
32.003 | 26.552 | 19.042 | |
41.820 | 33.153 | 22.738 | |
49.175 | 37.773 | 25.225 | |
61.414 | 44.947 | 28.969 | |
71.191 | 50.285 | 31.687 | |
78.514 | 54.089 | 33.596 | |
90.703 | 60.098 | 36.575 | |
98.006 | 63.529 | 38.261 |
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De Rosa, M.A.; Elishakoff, I.; Lippiello, M. Free-Vibration Analysis for Truncated Uflyand–Mindlin Plate Models: An Alternative Theoretical Formulation. Vibration 2024, 7, 264-280. https://doi.org/10.3390/vibration7010014
De Rosa MA, Elishakoff I, Lippiello M. Free-Vibration Analysis for Truncated Uflyand–Mindlin Plate Models: An Alternative Theoretical Formulation. Vibration. 2024; 7(1):264-280. https://doi.org/10.3390/vibration7010014
Chicago/Turabian StyleDe Rosa, Maria Anna, Isaac Elishakoff, and Maria Lippiello. 2024. "Free-Vibration Analysis for Truncated Uflyand–Mindlin Plate Models: An Alternative Theoretical Formulation" Vibration 7, no. 1: 264-280. https://doi.org/10.3390/vibration7010014