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Journals / Gümüşhane Üniversitesi Fen Bilimleri Dergisi / 2019 / Cilt: 9 - Sayı: 2

Approximate Solutions of Nonlinear Oscillation of a Mass Attached to a Stretched Elastic Wire

Gergin Elastik Tele Bağlı Kütlenin Doğrusal Olmayan Salınımının Yaklaşık Çözümleri

Mustafa Mehmet Fatih KARAHAN
Beyza BOSTANCI
Pages
207–214
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

MSLP method gives better results for strong nonlinearities.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Nonlinear Oscillation of a Mass Attached to a Stretched Elastic Wire is considered.
📊
Key Findings & Data:Equation of motion of the system is obtained.
💡
Conclusion & Impact:MSLP method gives better results for strong nonlinearities.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Çok Ölcekli Lindstedt Poincare Metodu · Çok Ölcekli Metot · Kuvvetli Doğrusal Olmayan Sistemler

Abstract

Nonlinear Oscillation of a Mass Attached to a Stretched Elastic Wire is considered. Equation of motion of the system is obtained. The classical multiple scales method (MS) and multiple scales Lindstedt Poincare (MSLP) method are applied to the equation of motion. Approximate analytical solutions of the equation of motion are obtained using the stated methods. Obtained solutions are compared with numerical solution of the equation of motion. MSLP method gives better results for strong nonlinearities.

Özet

Gergin elastik bir tele bağlı kütlenin doğrusal olmayan titreşim hareketi ele alınmıştır. Sistemin hareket denklemi oluşturulmuştur. Hareket denklemine çok ölçekli metot (ÇÖM) ve çok ölçekli Lindstedt Poincare (ÇÖLP) metodu uygulanmıştır. Belirtilen metotlar kullanılarak hareket denkleminin yaklaşık analitik çözümleri bulunmuştur. Belirtilen çözümler hareket denkleminin sayısal çözümü ile karşılaştırılmıştır. Kuvvetli doğrusal olmayan sistemlerde ÇÖLP metodu iyi sonuçlar vermiştir.

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Cite This Article

KARAHAN, M. M. F., BOSTANCI, B. (2022). Approximate Solutions of Nonlinear Oscillation of a Mass Attached to a Stretched Elastic Wire. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, Cilt: 9 - Sayı: 2, 207–214. https://ajindex.com/articles/527056

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References (12)

  1. Durmaz, S., Demirbağ, S. A., Kaya, M. O., 2011. Approximate solutions for nonlinear oscillation of a mass attached to a stretched elastic wire, Computers and Mathematics with Applications, 61, 578-585.
  2. Hu, H., 2004a. A classical perturbation technique which is valid for large parameters, Journal of Sound and Vibration, 269, 409-412.
  3. Hu, H., 2004b. A classical perturbation technique that works even when the linear part of restoring force is zero, Journal of Sound and Vibration, 271, 1175-1179.
  4. Hu, H., ve Xiong, Z. G., 2004. Comparison of two Lindstedt-Poincare type perturbation methods, Journal of Sound and Vibration, 278, 437-444.
  5. Jamshidi, N. ve Ganji, D. D., 2010. Application of energy balance method and variational iteration method to an oscillation of a mass attached to a stretched elastic wire, Current Applied Physics, 10, 484-486.
  6. Karahan, M. M. F., Pakdemirli, M., 2017a. Free and Forced Vibrations of the Strongly Nonlinear Cubic-Quintic Duffing Oscillators, Zeitschrift für Naturforschung A, 72(1), 59-69.
  7. Karahan, M. M. F., Pakdemirli, M., 2017b. Vibration Analysis of a Beam on a Nonlinear Elastic Foundation, Structural Engineering and Mechanics, 62(2), 171-178.
  8. Karahan, M. M. F., 2017. Approximate Solutions for the Nonlinear Third-Order Ordinary Differential Equations, Zeitschrift für Naturforschung A, 72(6), 547-557.
  9. Nayfeh, A. H., 1981. Introduction to Perturbation Techniques, John Wiley and Sons, New York, 532p. Pakdemirli, M., Karahan, M. M. F. Karahan ve Boyacı H., 2009. A new perturbation algorithm with better convergence properties: Multiple Scales Lindstedt Poincare method, Mathematical and Computational Applications, 14, 31-44.
  10. Pakdemirli M. ve Karahan, M. M. F., 2010. A New Perturbation Solution for Systems with Strong Quadratic and Cubic Nonlinearities, Mathematical Methods in the Applied Sciences, 33, 704-712.
  11. Pakdemirli, M., Karahan, M. M. F. Karahan ve Boyacı H., 2011. Forced Vibrations of Strongly Nonlinear Systems with Multiple Scales Lindstedt Poincare Method, Mathematical and Computational Applications, 16, 879-889.
  12. Sun, W. P., Wu, B. S. Ve Lim, C. W., 2007. Approximate analytical solutions for oscillation of a mass attached to a stretched elastic wire, Journal of Sound and Vibration, 300, 1042-1047.