Numerical and Analytical Solution for Nonlinear Free Vibration of Tapered Beams

Authors

Zain Abu Shaeer Abu Shaeer, Assistant Professor, Department of Basic Science, Higher Institute of Engineering and Technology, ‎Kafrelsheikh
Ramy I. Shahin, Assistant ProfessorDepartment of Civil Engineering, Higher Institute of Engineering and Technology, Kafrelsheikh, Egypt
Galal I. El-Baghdady, Department of Mathematics & Engineering Physics, Faculty of Engineering, Mansoura University, EgyptFollow
Saad A. Yehia, Department of Civil Engineering, Higher Institute of Engineering and Technology, Kafrelsheikh, Egypt

Subject Area

Mathematics and Engineering Physics

Article Type

Original Study

Abstract

This study introduces a computational approach that combines numerical and semi-analytical methods to solve tapered beams' nonlinear free vibration equation. The study employs a numerical approach that relies on the cubic B-spline collocation method and an approximation technique known as the Homotopy perturbation method to approximate the solution to the equation governing nonlinear large-amplitude free vibrations of tapered beams. The effect of vibration amplitude on the frequency of nonlinear vibrations is investigated. The next step is to look at different ways to get close to exact solutions across the whole range of oscillation amplitude. This will show how useful and easy the cubic B-spline collocation method is. According to this study, the mentioned approaches are characterized as efficient, simple, and highly accurate, leading to the prediction that the proposed method will find extensive application in engineering problems.

Keywords

Nonlinear vibration, Homotopy Perturbation Method, Tapered beams, Cubic B-Spline collocation method.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Shaeer, Zain Abu Shaeer Abu; Shahin, Ramy I.; El-Baghdady, Galal I.; and Yehia, Saad A. (2024) "Numerical and Analytical Solution for Nonlinear Free Vibration of Tapered Beams," Mansoura Engineering Journal: Vol. 49 : Iss. 3 , Article 6.
Available at: https://doi.org/10.58491/2735-4202.3179