Gergin Elastik Tele Bağlı Kütlenin Doğrusal Olmayan Salınımının Yaklaşık Çözümleri

Yıl 2019, , 207 - 214, 15.04.2019

M. M. Fatih Karahan , Beyza Bostancı

https://doi.org/10.17714/gumusfenbil.410731

Cited By: 1

Öz

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.

Anahtar Kelimeler

Çok Ölcekli Lindstedt Poincare Metodu, Çok Ölcekli Metot, Kuvvetli Doğrusal Olmayan Sistemler, Perturbasyon Metotları, Sayısal Çözümler

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

Öz

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.

Anahtar Kelimeler

Multiple Scales Lindstedt Poincare Technique, Method of Multiple Scales, Strong Nonlinearities, Perturbation Methods, Numerical Solution

Kaynakça

• 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.