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Analyzing nonlinear oscillations with He's frequency-amplitude method and numerical comparison in jet engine
M Abul Kawser1, Md Abdul Alim2, Nazmul Sharif2
1Department of Mathematics, Islamic University, Kushtia, Bangladesh.
Heliyon
|January 31, 2024
Summary
This study solves jet engine vibration equations using He's frequency-amplitude Method (HFAM). The method provides accurate, general solutions for nonlinear vibration systems, verified numerically.
Area of Science:
- Mechanical Engineering
- Aerospace Engineering
- Applied Mathematics
Background:
- Jet engine vibrations are critical in aerospace and other industries.
- Solving nonlinear vibration equations accurately is essential for system design and safety.
- Existing methods may be complex or lack generality.
Purpose of the Study:
- To solve the jet engine vibration equation using a novel method.
- To derive general periodic solutions for the system.
- To validate the accuracy and effectiveness of the proposed method.
Main Methods:
- Application of He's frequency-amplitude Method (HFAM) to the jet engine vibration equation.
- Derivation of general periodic solutions considering damping and driving forces.
- Numerical verification using the fourth-order Runge-Kutta method.
Main Results:
- Successful derivation of general periodic solutions for jet engine vibrations.
- Demonstration of HFAM's effectiveness and simplicity for nonlinear equations.
- Excellent agreement between HFAM solutions and numerical results.
Conclusions:
- HFAM is a powerful and straightforward tool for solving complex nonlinear vibration problems.
- The derived solutions offer high accuracy and general applicability.
- This work validates HFAM for critical engineering applications like jet engines.
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