Mustafa Mehmet Fatih KARAHAN, Beyza BOSTANCI

Gergin Elastik Tele Bağlı Kütlenin Doğrusal Olmayan Salınımının Yaklaşık Çözümleri

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

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.

Keywords:

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

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