Finite element analysis of global ship vibrations

Abstract

With the increase of ship size and speed, shipboard vibration becomes a great concern in the design and construction of the vessels. The flexibility of vessels which are needed to meet the demand in sea trans-portation, causes ship vibrations. In addition to un-desired effects on passenger comfort and crew hab-itability, excessive ship vibration may result in the fatigue failure of local structural members or mal-function of machinery and equipment. The im-portance of the solutions of vibration problems which are addressed at the earliest design stage and the great cost in later correction efforts are clear. It is possible to avoid great vibration problems by means of simple studies in the early design stage. Besides local vibrations, global vibrations are of great importance to ship safety. In this study, global ship hull free vibration problems are studied under two conditions which are free – free (dry) and in wa-ter (wet) using finite element analysis. Excessive ship vibration is of great importance to the perfor-mance of precious navigation equipments and usual-ly cause them to malfunction. In the condition of resonance which the propulsion frequency collides with the global natural frequency of the ship and during manoeuvres, the amplitude of oscillations on local structures exceeds certain limits. Concept design is where the vibration avoidance process must begin. It is clear that if the vibration problems, repeatedly identified by experience as the most important, are addressed at the earliest design stage, ultimately serious problems, involving great cost in correction efforts, may be avoided. The focus is on planning for vibration early at the concept de-sign stage, where there has been no development of details. If as much as possible can be done in con-cept design with the simple tools and rules of thumb available at that level, it will help to avoid major vibration problems. The major potential problems may often be present in the crude concept design definition. Just identifying and addressing those po-tential problems in terms of the minimal technology available at the concept design stage is considered very important to the success of ship design. The de-sign and construction of a ship free of excessive vi-bration continues to be a major concern and, as such, it is prudent to investigate, through analysis, the likelihood of vibration problems early in the de-sign stage. Vibration analysis is aimed at the con-firmation of the many design considerations associ-ated with stern configuration, main propulsion ma-chinery, propeller/shafting system and location and configuration of major structural assemblies. The ship hull structure includes the outer shell plating and all internal members, which collectively provide the necessary strength to satisfactorily perform the design functions in the expected sea environment. The hull structure responds as a free – free beam (both ends free) when subjected to dynamic loads. The vibration induced by the propulsion system is a common source of ship vibration. The vibration from this source manifests itself in several ways. Dynamic forces from the shafting system are transmitted to the hull through shaft bearings. The propeller in-duces fluctuating pressures on the surface of the hull, which induces vibration in the hull structure. The main and auxiliary engines can directly cause vibrations through dynamic forces transmitted through their supports and foundations. The re-sponse to this forcing can cause the vibration of the hull girder, deckhouse, deck and other structures, local structures and equipment. When attempting to determine the source of vibration, it is necessary to establish the frequency of excitation and to relate the frequency of excitation to the shaft rotational frequency by determining the number of oscillations per shaft revolution. Ship structures are complex and may be analyzed after idealization of the structure. Several simplify-ing assumptions are made in the finite element ideal-ization of the hull structure. The modeling require-ments are that all significant structural sections are to be captured and deflection/ velocity/acceleration are to be sufficiently predicted. A three-dimensional finite element model representing the entire ship hull, including the deckhouse and machinery propul-sion system, needs to be developed for vibration analysis. If a global model exists from any previous tasks such as stress analysis, it needs to be condi-tioned for vibration analysis. In the section which the global vibrations are studied, a three – dimen-sional ship model is prepared using a solid model-ling software and the natural frequencies and mode shapes are determined using finite element analysis. In this way, the resonance frequencies and behav-iour of the ship are determined.

Özet

Gemi boyut ve hızlarındaki büyük artış nedeniyle gemi titreşimleri, gemi tasarımı ve yapımında bü-yük önem taşır hale gelmiştir. Gemi tasarımındaki son gelişmeler, daha büyük stroklu ve daha güç-lü dizel motorların kullanıldığı, daha büyük boyutlarda, daha hafif, daha esnek teknelerin yapılma-sına yol açmıştır. Deniz taşımacılığında artan talebi karşılamak için ihtiyaç duyulan bu yapıların daha esnek olması titreşim problemlerini de beraberinde getirmektedir. Aşırı gemi titreşimleri, yol-cu konforunu ve mürettebat yaşamını önemli ölçüde etkilemektedir. İnsan üzerindeki istenmeyen etkilerinin yanında, aşırı gemi titreşimleri, makina ve cihazlarda bozulmalara neden olmakla birlik-te yapısal elemanlarda da yorulma hasarına neden olmaktadır. Gemilerde titreşim problemlerinin çözüm kaynağının erken safhadaki tasarım aşamasında belirlenmesinin önemi ve sonradan yapıla-cak olan düzeltmelerin çok ağır maliyetler gerektirdiği bilinmektedir. Tasarım aşamasında yapıla-cak olan bir takım basit çalışmalarla ileride ortaya çıkacak büyük titreşim problemlerinin önlenme-si sağlanabilmektedir. Gemi titreşimleri bakımından, yerel titreşim problemlerinin yanı sıra gemi-nin bütününde ortaya çıkan global titreşimler de gemi emniyeti açısından büyük önem taşımaktadır. Bu çalışma kapsamında tüm gemi, sonlu eleman analizi yöntemiyle global olarak serbest – serbest (susuz) ve su içinde olmak üzere serbest titreşim açısından incelenerek, tüm geminin doğal frekans-larının ve mod şekillerinin belirlenmesine çalışılmıştır. Bu şekilde geminin hangi frekanslarda re-zonansa gireceği ve nasıl davranışlar sergileyeceği belirlenmiştir. Ayrıca sonlu eleman yöntemiyle hesaplanan doğal frekans değerleri, klas kuruluşları tarafından kullanılan ampirik formüllerle he-saplanan doğal frekans değerleri ile karşılaştırılarak, sonlu eleman analizinin gerekliliği üzerinde durulmuştur.