A New Method for Free Vibration Analysis of Triangular Isotropic and Orthotropic Plates of Isosceles Type Using an Accurate Series Solution
Abstract
:1. Introduction
2. Theory Formulation
2.1. Governing Differential Equation and Boundary Value Problem
2.2. Construction of General Solution
2.3. Infinite System of Linear Algebraic Equations
3. Numerical Results and Discussion
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
References
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N = 18 | |||||||
---|---|---|---|---|---|---|---|
Diaplacement and rotation W, ϕ | l (See Column 1 of the Table) | ||||||
0 | 1 | 2 | 3 | 4 | 5 | Prescribed B.C (exact) | |
1.00001 | 0.99999 | 1.00001 | 0.99995 | 0.99953 | 1.00092 | 1 | |
1.00000 | 1.00000 | 1.00000 | 0.99995 | 1.00002 | 1.00092 | 1 | |
0.00000 | −0.00002 | 0.00005 | 0.00030 | 0.00081 | 0.00913 | 0 | |
N = 24 | |||||||
Diaplacement and rotation W, ϕ | l (See Column 1 of the Table) | ||||||
0 | 1 | 2 | 3 | 4 | 5 | Prescribed B.C (exact) | |
1.00002 | 1.00000 | 0.99997 | 0.99992 | 1.00005 | 1.00021 | 1 | |
1.00000 | 1.00000 | 1.00000 | 1.00001 | 1.00002 | 1.00021 | 1 | |
0.00000 | −0.00002 | 0.00002 | 0.00030 | 0.00089 | 0.00891 | 0 |
θ | |||
---|---|---|---|
Ref. [1] | 13.646 | 8.626 | 6.841 |
Present | 13.686 | 8.618 | 6.839 |
Method | Non-Dimensional Natural Frequency () | ||||
---|---|---|---|---|---|
Present | 8.6177 | 11.9063 | 11.9061 | 14.8814 | 15.3748 |
Ref [12] | 8.6178 | 11.9075 | 11.9128 | 14.9210 | 15.4150 |
Ref [13] | 8.6166 | 11.9039 | 11.9039 | 14.9137 | 15.4068 |
θ | Non-Dimensional Natural Frequency () | |||||||
---|---|---|---|---|---|---|---|---|
12.6923 | 15.6017 | 18.6982 | 19.1273 | 19.5364 | 22.3531 | 25.3006 | 25.6629 | |
7.6432 | 10.3031 | 10.7894 | 12.8591 | 13.6279 | 13.8966 | 15.4193 | 16.2192 | |
5.8533 | 7.7661 | 8.3775 | 9.6595 | 10.3058 | 10.9457 | 11.5676 | 12.1677 |
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Papkov, S.; Banerjee, J.R. A New Method for Free Vibration Analysis of Triangular Isotropic and Orthotropic Plates of Isosceles Type Using an Accurate Series Solution. Mathematics 2023, 11, 649. https://doi.org/10.3390/math11030649
Papkov S, Banerjee JR. A New Method for Free Vibration Analysis of Triangular Isotropic and Orthotropic Plates of Isosceles Type Using an Accurate Series Solution. Mathematics. 2023; 11(3):649. https://doi.org/10.3390/math11030649
Chicago/Turabian StylePapkov, Stanislav, and Jnan Ranjan Banerjee. 2023. "A New Method for Free Vibration Analysis of Triangular Isotropic and Orthotropic Plates of Isosceles Type Using an Accurate Series Solution" Mathematics 11, no. 3: 649. https://doi.org/10.3390/math11030649
APA StylePapkov, S., & Banerjee, J. R. (2023). A New Method for Free Vibration Analysis of Triangular Isotropic and Orthotropic Plates of Isosceles Type Using an Accurate Series Solution. Mathematics, 11(3), 649. https://doi.org/10.3390/math11030649