Karışık Dalgalarda Nonlineer Yalpa Hareketinin Melnikov Metodu İle İncelenmesi
Karışık Dalgalarda Nonlineer Yalpa Hareketinin Melnikov Metodu İle İncelenmesi
Dosyalar
Tarih
Yazarlar
İşçi, Mustafa
Süreli Yayın başlığı
Süreli Yayın ISSN
Cilt Başlığı
Yayınevi
Fen Bilimleri Enstitüsü
Institute of Science and Technology
Institute of Science and Technology
Özet
Bu çalışmada, bordadan gelen karışık dalgalarda gemilerin yaptığı nonlineer yalpa hareketleri Melnikov Metodu ile incelenmiştir. Zorlayıcı dalga momenti etkisi ile yalpa hareketi yapan bir geminin faz uzayı akısının, güvenli havuzun dışına taşınımı uygun bir Melnikov fonksiyonu ve faz uzayı taşınımı teknikleri ile tespit edilmiştir. Deniz ortamı, sıfır ortalama değerli, Gauss olasılık dağılımına uyan rasgele bir proses olarak kabul edilmiştir. Öncelikle, seçilen referans makaledeki gemi için yöntem uygulanmış ve doğru sonuçlar elde edildikten sonra, çok farklı stabilite özelliklerine sahip bir gemi için uygulamalar yapılmıştır. Yeni uygulamada, orjinal yöntemden farklı olarak, keyfi bir yalpa açısı seçilmiş ve gemiye ait GZ eğrisi quintik polinomla ifade edilmiştir. Melnikov yöntemi ile bulunan sonuçlar, Runge –Kutta simülasyonu ile elde edilen sonuçlarla karşılaştırılmış ve benzer sonuçlar elde edildiği görülmüştür. Faz uzayı akısı taşınımının, küçük dalga yüksekliklerinden itibaren başladığı gösterilmiştir. Bu sonuçtan, teorik de olsa, düşük dalga yüksekliklerinde bile yeteri kadar uzun süre kalan bir geminin devrilme olasılığının her zaman olduğu anlaşılmıştır.
In this study, the nonlinear roll motion of a ship which was excited by random beam waves was investigated by using Melnikov method. The phase space flux transportation of a ship, which is excited by waves, can be determined by a suitable Melnikov function and a phase space flux transportation techniques. Sea state was assumed as a random process with zero mean and Gauss probability distribution. First, the mentioned method was applied on a ship which was given in a reference article. After true and same results with reference article had found out, method was applied on a ship which was chosen by the author of this study. The new ship had very different stability specifications compared to first ship. In this study, a different application from the reference article was given. An arbitrary roll angle was chosen instead of using the vanishing stability roll angle. Besides, GZ curve was defined with a quintic polynomial. The results that was reached with Melnikov method, compared with the results that was found with Runge-Kutta simulations. It was seen that phase space flux transportation begins even if the wave amplitudes are small. This findings led us to reach an agreement that there is always a probability of the capsize, even for moderate wave amplitudes, if ship stays long enough in that sea state.
In this study, the nonlinear roll motion of a ship which was excited by random beam waves was investigated by using Melnikov method. The phase space flux transportation of a ship, which is excited by waves, can be determined by a suitable Melnikov function and a phase space flux transportation techniques. Sea state was assumed as a random process with zero mean and Gauss probability distribution. First, the mentioned method was applied on a ship which was given in a reference article. After true and same results with reference article had found out, method was applied on a ship which was chosen by the author of this study. The new ship had very different stability specifications compared to first ship. In this study, a different application from the reference article was given. An arbitrary roll angle was chosen instead of using the vanishing stability roll angle. Besides, GZ curve was defined with a quintic polynomial. The results that was reached with Melnikov method, compared with the results that was found with Runge-Kutta simulations. It was seen that phase space flux transportation begins even if the wave amplitudes are small. This findings led us to reach an agreement that there is always a probability of the capsize, even for moderate wave amplitudes, if ship stays long enough in that sea state.
Açıklama
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2002
Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2002
Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2002
Anahtar kelimeler
Melnikov Metodu,
Faz uzayı akı taşınımı,
Melnikov Method,
Phase Space Flux Transportation