Prediction of the Transient Local Energy by Energy Finite Element Analysis
Abstract
:1. Introduction
2. Energy Flow Model
2.1. Energy Density Governing Equation
2.2. Analytical Solution of the Transient Equation
2.3. Energy Transmission Coefficients for Beams
3. Validation and Discussion
3.1. Numerical Simulations and Verifications
3.2. A Single Beam under the Unloading Condition
3.3. Coupled Beams under Unloading Condition
3.4. Coupled Beams under the Loading Conditions
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix B
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Wang, H.; Yu, K.; Zhao, R. Prediction of the Transient Local Energy by Energy Finite Element Analysis. Mathematics 2023, 11, 4590. https://doi.org/10.3390/math11224590
Wang H, Yu K, Zhao R. Prediction of the Transient Local Energy by Energy Finite Element Analysis. Mathematics. 2023; 11(22):4590. https://doi.org/10.3390/math11224590
Chicago/Turabian StyleWang, Huaizhi, Kaiping Yu, and Rui Zhao. 2023. "Prediction of the Transient Local Energy by Energy Finite Element Analysis" Mathematics 11, no. 22: 4590. https://doi.org/10.3390/math11224590
APA StyleWang, H., Yu, K., & Zhao, R. (2023). Prediction of the Transient Local Energy by Energy Finite Element Analysis. Mathematics, 11(22), 4590. https://doi.org/10.3390/math11224590