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4.1 Vibration analysis of fresh water tank
It is difficult to predict the vibration response of a local structure due to the complicated transfer mechanism of excitation force and the difficulty of assuming the damping ratio. Traditionally, therefore, a vibration analysis considering the design of avoiding resonance is conducted to prevent the local vibration.
In this study, the vibration analysis of the fresh water tank is carried out by using NASTRAN which is a commercial finite element program and widely used for big structures like ships. The analysis model and arrangement of the fresh water tank are shown in Fig.
Fig. 4. Model and arrangement of fresh water tank.
4. Fig. 5 shows the design variables and boundary condition of the fresh water tank. Considering the precision of analysis and time-consuming modeling process, the range of modeling of fresh water tank is constrained to one side of the tank. The boundary conditions for the model are specified as follows: simple supports are used to the tank boundary area which is connected to the other bulkhead and deck. Table 3 shows the specification of main excitation sources.
In general, the design for avoiding local structure resonance in ships requires that the natural frequency of the structure must be two times higher than the blade passing frequency of the propeller under the maximum rpm of the main engine. In this study, the design target frequency is set as above 14.0Hz, which considers safety margins and twice blade passing frequency of the propeller (12.13Hz).
Fig. 6 shows the first three modes and natural frequencies of the fresh water tank by NASTRAN. These three modes frequently occur on the fresh water tank during a voyage. Especially, the 1st mode (8.60Hz) is a stiffener (stringer) mode which generates a strong vibration and much effect on the structure. In this model, the first natural frequency of the structure is also within the resonance region where the twice blade passing frequency of propeller is 12.13Hz. Therefore, the natural frequency of the structure is needed to be increased up to the target frequency under the condition that the tank is fully filled. The natural frequency of structure which is contacting fluid can be changed according to the water line of the tank. So, in order to design a safe structure, three modes of the fresh water tank are concerned in this study.
Table 3. Specification of main excitation sources.
Excitation source MCR Excitation
Order Frequency
Main engine (6S 70MC-C) 91 rpm 3rd
Fig. 5. Design variables and boundary conditions of fresh water tank.
Fig. 6. Mode shapes of fresh water tank.
4.2 Optimum design of fresh water tank
The main vibration modes on the fresh water tank are stiffener modes in transverse direction. One of the most important factors is the stiffness of the stiffeners. In this study, the stiffener size and plate thickness of fresh water tank in Fig. 4 are defined as design variables in equation (7).
x = {S1 S2 S3 S4 S5 S6 S7 S8 P1 P2}T (7)
where S and P mean stiffener size and plate thickness, respectively.
The web length of stiffener Lw is restricted as two categories such as Eq. (8) according to a shipyard’s practice.
150 ≤ Lw ≤ 450 mm for stiffeners (S1 - S7), 500 ≤ Lw ≤ 1000 mm for stringer (S8) (8)
Also, the basic concept of local vibration design is the minimization of the response at each point. However, it is difficult to evaluate how much the excitation force influences the local structure. So, to avoid resonance, the first natural frequency of the structure is restricted as Eq. (9) which considers a safety margin of about 15% with twice blade passing frequency of the propeller (12.14Hz).