An Investigation of Fractional Bagley–Torvik Equation
Abstract
:1. Introduction
2. Preliminaries
3. General Form of the Bagley–Torvik Equation and Its Solution
4. Results and Discussion
4.1. Case-I: When Driving Force on the Plate Is Constant
4.2. Case-II: When Driving Force on the Plate Is a Quadratic Function of Time
4.3. Case-III: When Driving Force on the Plate Is a Periodic Function of Time
5. Modelling of Experimental One-Degree-of-Freedom Mechanical Oscillator
6. Conclusions and Future Work
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
FC | Fractional calculus |
FDE | Fractional differential equation |
BTE | Bagley–Torvik equation |
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Model | ||||||
---|---|---|---|---|---|---|
A | 0 | 2 | 196.359 | 1.73345 | 0.436005 | 0.328796 |
B | 0.9999946 | 1.99999 | 196.394 | 1.73192 | 0.436556 | 0.328778 |
C | 0.5 | 2 | 224.652 | 092534 | 0.500898 | 0.361783 |
D | 0.9 | 2 | 3761.75 | 25.1388 | 8.53502 | 0.420043 |
E | 0 | 1.95 | 167.157 | 0.74288 | 0.370936 | 0.361385 |
F | 0 | 1.85 | 120.003 | 0.60625 | 0.265951 | 0.51812 |
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Zafar, A.A.; Kudra, G.; Awrejcewicz, J. An Investigation of Fractional Bagley–Torvik Equation. Entropy 2020, 22, 28. https://doi.org/10.3390/e22010028
Zafar AA, Kudra G, Awrejcewicz J. An Investigation of Fractional Bagley–Torvik Equation. Entropy. 2020; 22(1):28. https://doi.org/10.3390/e22010028
Chicago/Turabian StyleZafar, Azhar Ali, Grzegorz Kudra, and Jan Awrejcewicz. 2020. "An Investigation of Fractional Bagley–Torvik Equation" Entropy 22, no. 1: 28. https://doi.org/10.3390/e22010028
APA StyleZafar, A. A., Kudra, G., & Awrejcewicz, J. (2020). An Investigation of Fractional Bagley–Torvik Equation. Entropy, 22(1), 28. https://doi.org/10.3390/e22010028