Section 4 Mass

4.1.1 Structural mass is represented by including mass density in the definition of structural material properties. It is usually necessary to make a small increase to the material density to allow for minor structural details that are not specifically included in a model, in order to align with a defined mass of material.

4.2.1 Outfit masses can be categorised into two types: those which can be considered to be of a distributed nature, and those which are concentrated. The former consists of items such as systems, insulation and minor equipment. The latter can include, for example, engines, generators, steering gear, rudders and propellers, which would then be specifically defined in a model.

4.2.2 Distributed outfit masses can be included by factoring up the structural material mass density. In order to do this appropriately, it is usually necessary to divide the ship into material zones, because distributed outfit mass varies depending upon the type of compartment. Typically for a cargo ship, material zones would be arranged for aft peak, machinery spaces, the remainder of the hull, and the superstructure.

4.2.4 Outfit mass on accommodation decks can sometimes be available for an analysis, but often it is not. It has been found that an average value of 75 kg/m² is usually representative for internal accommodation deck panels, which includes deck coverings and fittings on the deck, together with systems and insulation attached below. However, variation between lightly and heavily loaded areas can often encompass a range such as 50 - 100 kg/m², so specific information should be obtained from the Shipbuilder or designer, if possible. A value of 30 kg/m² can be considered reasonable for an external deck panels above accommodation areas having only attachments beneath.

4.3.1 For ships having large variations in loading conditions, such as tankers, LNG ships and container ships, it is usual to study a loaded and a ballast condition. For passenger ships, it is normally adequate to investigate a single loading condition.

4.3.2 Internal fluids can comprise fuel, water ballast and fresh water, together with fluid cargo, for example oil or LNG. Other notable types of cargo are: containers, vehicles on Ro-Ro ships, and bulk cargoes such as grain and ore.

4.3.3 The most rigorous approach for representation of internal fluids in a finite element model may initially appear to be fluid finite elements. However, for large scale global vibration models, this is unnecessarily complicated and impractical in computational terms. While use of boundary elements, such as those which can be employed to represent external fluids, is satisfactory for studying vibration behaviour of tank boundaries, they are not appropriate with respect to participation of the whole tank contents in global ship vibration.

4.3.4 Distribution of cargo tank fluid masses at the tank boundaries is satisfactory in relation to vertical and horizontal ship vibration modes, but not for hull torsion modes because of incorrect mass radius of gyration. However, normally this is not important, as hull torsion modes are not usually significant with regard to the acceptability of ship vibration behaviour. This method is satisfactory for small tanks in relation to all global vibration modes.

4.3.5 The facility of ‘motion-weighted average elements’ for representation of internal fluids and cargo in a finite element model is useful, whereby a total mass is specified at the centre of gravity and averaged to an array of specified node points. This method can be used for tank fluids, bulk carrier cargoes, and blocks of containers in holds or on the upper deck. In this connection, it is important that longitudinal divisions of motion weighted average elements correspond to sections having ASET points that are arranged for dynamic reduction (see Ch 1, 2.3 Dynamic reduction). For example, while container ships may have sufficient open and watertight bulkheads to be natural choices for the positioning of ASET points, a membrane LNG ship may have only four holds. This would typically necessitate each hold being artificially divided into at least three parts with respect to ASET sections and motion weighted average elements, in order to obtain adequate definition relating to relevant hull vibration modes.

4.3.6 In relation to vehicle decks in Ro-Ro ships, the interface between vehicle masses and the decks comprises shock absorbers and tyres, or in other words, springs and dampers. Since the stiffness of these would be significantly weaker than that of the deck structure, they could be considered to be equivalent to a system of resilient mounts, thereby mostly isolating the vehicles from the deck.

4.4.1 Sea water surrounding a ship has an inertial effect on its dynamic behaviour. This can be treated as mass additional to the mass of a ship, and is known as ‘added mass’ or ‘virtual mass’. It is of significant magnitude: for a ship of full form in the vertical sense, it can be of the same order as the mass of the ship.

4.4.2 In early times, before the advent of sophisticated computational techniques, added mass was a difficult aspect to deal with in the dynamic analysis of ships.

4.4.3 The early method most commonly used was by Lewis: using a half-submerged cylinder of infinite length with a cross-section approximating to the midship section. Such a procedure exaggerates the effect of the water since it implies an assumption that the water can only move in a two-dimensional manner around the girth of a section. Since ship sections can vary rapidly along their length, the motion of water would not be so confined. Hence, a three-dimensional correction factor was incorporated into the method, which was based upon an equivalent ellipsoid of revolution.

4.4.4 Later methods that were developed included more specific definition of ship section shapes, such as the Frank Close Fit Method.

4.4.5 The added mass of sea water varies with the direction of the dynamic motion and frequency. Early methods could reasonably account for direction in terms of the basic vertical and transverse modes, but essentially did not include the possibility of addressing the other variations.

4.4.6 With the availability of powerful computers, ‘boundary elements’, also known as ‘infinite elements’, defined on the wetted surface of ship finite element models, emerged as an efficient and accurate way of allowing for the virtual mass of sea water vibrating with a ship. The NASTRAN finite element program includes such a facility, where potential flow theory is used and the boundary elements constitute point sources.

4.4.7 Computational fluid dynamics (CFD) also affords increasing capabilities in relation to fluid-structure interaction and, in future, FEA and CFD may become more interrelated.

4.5.1 Shallow water may be considered as a sea depth whose value is less than five times the vessel draught. It has the effect of increasing the virtual mass of entrained sea water, thereby reducing the vertical hull natural frequencies compared to those of a vessel travelling in deep water.

4.5.2 Horizontal modes are not significantly affected by the proximity of the sea bed; they are more affected if the vessel is travelling in a narrow channel.

4.5.3 The influence of the sea bed on the hull by way of virtual mass of entrained water is inversely proportional to the square of the distance between the sea bed and a hull.

4.5.4 Arbitrary plate elements together with boundary elements can be used to represent the sea bed or channel sides in order to produce the appropriate effect on added mass.