Kernel safe basins of the rolling motion under excitation

Abstract

Rolling motion of the ship has always been popular subject of the researchers. The reason for this can be IMO rules or the present IS (Intact Stability) code of the ships is based on the rules which are not based on rational reasoning and which was accepted 30 years ago or rolling motion of the ship could not be explained completely by researchers. Although the ships especially the small ships such as fishing vessels and research vessels ensure IMO stability criteria or the present IS code, they could still capsize due to combined environmental effects. The present stability criteria are insufficient because the rules are only based on the static stability at calm water and they do not include any effect of nature of the sea and dynamic response of the ships directly. Thus, IMO should renew its rules to include dynamic effects. Oscillatory sudden capsizing, oscillatory symmetric and anti-symmetric build-up capsizing can not be explained by present stability criteria. Only non-oscillatory capsizing can be explained by current rules. In this study, the kernel safe basin concept was presented to improve the present stability criteria. Kernel safe basin is the smallest safe basin in the roll angle and roll angular velocity phase space. If the ship is stable or not in a dangerous situation, there is no erosion at kernel safe basin of the ship. The condition which causes erosion at kernel safe basin more than an agreed amount can be named as dangerous situation. The boundary of kernel safe basin is determined by using the Lyapunov function of the non-excited roll motion and defines a reserve energy level. The maximum roll angle of the kernel safe basin is dependant on the working environment of the vessel. In this study, it was assumed to be 25° for external excitation case and 20° for parametric excitation case. However, kernel safe basins that have different sizes, were also investigated in the PhD. Thesis. Although the rolling motion is strongly coupled with sway and yaw motion, in this study it was assumed to be uncoupled with other ship motions by defining roll center. The uncoupled roll motion was examined by using the integrity curves which show the amount of erosion occurred at kernel safe basin under the influence of external and parametric excitation. In this study, the importance of damping moment, excitation amplitude, excitation frequency and bias angle on the stability of the ships were shown from the investigation of the uncoupled rolling motion under external excitation. Increment of damping moment caused to decrease the risk of capsizes. Thus, the ship could survive or operate for rougher waves. Both increment of wave height (excitation amplitude) and bias angle caused to increase the erosion occurred at kernel safe basin. Thus it could be said that the ship should operate at smaller waves when the bias exists. When excitation frequency to natural frequency ratio is around 0.8, the maximum erosion occurred at kernel safe basin. Thus it can be concluded that main resonance case is the most critical case for safety of vessel in beam seas. While examining the protection of kernel safe basins under the influence of parametric and external excitation, the ratio of metacentre height variation of the ship was assumed to be function of the heading angle and the ratio of the component of wave length in the direction of ship heading to ship length. In addition, it was assumed that there was constant wind effect while modeling rolling motion. The results showed that the small increment of metacentre height (GM) over the value defined by IMO caused the increment of erosion occurred at kernel safe basin for stern quartering waves whereas the waves which come from the stern of the ship with an angle (0°-15°), caused less erosion at kernel safe basin. The small decrement of GM under the value defined by IMO caused to decrease the erosion occurred at kernel safe basin for stern quartering waves whereas the erosion increased for stern waves (0°-15°). If the value of GM is too small than the IMO defined value, both stern and stern quartering waves caused too much erosion at kernel safe basin. However, it should not be forgotten that the encounter frequency and angle are also operational variables (they can take different values by changing the velocity and heading of the ship) for following seas so in the evaluation of the transverse stability of the ships not only the design factors but also the operational factors should be considered.

Özet

Gemilerin yalpa hareketi bilim adamları ve araştırmacıların her zaman popüler bir araştırma konusu olmuştur. Bunun sebebi IMO kurallarının ve şu anki mevcut IS kodunun rasyonel temellere dayanmayan ve en az 30 yıl önce kabul edilmiş kurallara dayanması, ya da yalpa hareketinin araştırmacılar tarafından tamamıyla açıklanamamış olmasına bağlanabilir. Bu konu üzerine çalışma yapmamızın sebebi de mevcut IS kodunu geliştirilmesine bir katkı sağlamaktır. Bu makalede, gemilerin enine stabilitesinin matematiksel yöntemlerle irdelenmesinde yeni bir yaklaşım olarak “çekirdek güvenli bölge kavramı” ortaya çıkarılmıştır. Çekirdek güvenli bölge, yalpa açısı ve yalpa açısal hızından oluşan faz uzayındaki sağlanması gereken en küçük güvenli bölgedir. Bu bölgenin dış sınırı zorlanmamış yalpa hareketinin Lyapunov fonksiyonu kullanılarak belirlenmektedir. İzin verilen en büyük yalpa açısı ise geminin çalışma koşullarına bağlı olarak çıkartılmaktadır. Çekirdek güvenli bölgenin belli bir miktardan fazla erozyona uğraması, geminin stabilitesinin büyük bir tehlike içerisinde olduğu anlamına gelmektedir. Dışarıdan ve parametrik zorlama etkisi altında, rüzgar ve sönüm kuvvetlerinin çekirdek güvenli bölgenin büyüklüğü üzerindeki etkileri gösterilmiş ve geminin çalışma koşullarına bağlı olarak stabil olup olmadığı ortaya konulmuştur. Karşılaşma frekansı doğal frekans civarında olduğu zaman en tehlikeli durumlar gözlemlenmiş, sönümün arttırılması geminin devrilme olayının daha büyük dalgalarda oluşmasını sağlamıştır. Ön meyil açısının arttırılması ise daha küçük yükseklikli dalgaların tehlikeli hale gelmesine yol açmıştır. Kıç omuzluktan gelen dalgalarda enine metasantr yüksekliğinin IMO tarafından belirlenen sınırın biraz üzerine çıkarılması, kıçtan gelen dalgalarda ise enine metasantr yüksekliğinin sınırın biraz altına indirilmesi geminin devrilme riskini arttırmıştır.