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Gergin Elastik Tele Bağlı Kütlenin Doğrusal Olmayan Salınımının Yaklaşık Çözümleri

Year 2019, , 207 - 214, 15.04.2019
https://doi.org/10.17714/gumusfenbil.410731

Abstract

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.

References

  • 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.
  • Hu, H., 2004a. A classical perturbation technique which is valid for large parameters, Journal of Sound and Vibration, 269, 409-412.
  • 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.
  • Hu, H., ve Xiong, Z. G., 2004. Comparison of two Lindstedt-Poincare type perturbation methods, Journal of Sound and Vibration, 278, 437-444.
  • 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.
  • 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.
  • 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.
  • Karahan, M. M. F., 2017. Approximate Solutions for the Nonlinear Third-Order Ordinary Differential Equations, Zeitschrift für Naturforschung A, 72(6), 547-557.
  • 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.
  • 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.
  • 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.
  • 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.

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

Year 2019, , 207 - 214, 15.04.2019
https://doi.org/10.17714/gumusfenbil.410731

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.

References

  • 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.
  • Hu, H., 2004a. A classical perturbation technique which is valid for large parameters, Journal of Sound and Vibration, 269, 409-412.
  • 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.
  • Hu, H., ve Xiong, Z. G., 2004. Comparison of two Lindstedt-Poincare type perturbation methods, Journal of Sound and Vibration, 278, 437-444.
  • 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.
  • 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.
  • 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.
  • Karahan, M. M. F., 2017. Approximate Solutions for the Nonlinear Third-Order Ordinary Differential Equations, Zeitschrift für Naturforschung A, 72(6), 547-557.
  • 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.
  • 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.
  • 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.
  • 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.
There are 13 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

M. M. Fatih Karahan

Beyza Bostancı This is me

Publication Date April 15, 2019
Submission Date March 29, 2018
Acceptance Date August 7, 2018
Published in Issue Year 2019

Cite

APA Karahan, M. M. F., & Bostancı, B. (2019). Gergin Elastik Tele Bağlı Kütlenin Doğrusal Olmayan Salınımının Yaklaşık Çözümleri. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 9(2), 207-214. https://doi.org/10.17714/gumusfenbil.410731