Development of ship noise analysis program based on the combination of simplified Janssen method and SEA method

2.1 Structure-Borne Sound

As structure-borne sound is the most significant factor for ship noise prediction, it is necessary to apply an analytical method in order to numerically evaluate the sound energy transmission mechanism considering the various complex structures (material, shape, and size) and transmission factors of the sound power incident, reflection, absorption, radiation through transmitting route from the sound sources to cabins, instead of an empirical method such as the Janssen method.

Therefore, the SEA method is selected to be applied in this study, by simplifying the sound power transmission mechanism and the analysis structure model, as practically as possible.

By applying the statistical averaging procedure in specifying the frequency range, the transmitted power flow between adjacent elements is shown in Figure 1 and calculated by the fundamental power balance equation as shown in Equation (2). The transmitted power P_ij(=P_ij) depends on the difference of vibration energy levels of elements E_i , E_j and the internal power loss in element $$ P_i^d$$.

Figure 1:

Transmission of vibration energy between elements

where, ω is the center angular frequency in 1/3 or 1/1 octave band and η_i(ω) is the internal loss factor of the specific material of panel element on the frequency basis, which is experimentally verified and specified in the vibration transmission database.

The coupling loss factor η_ij(ω) is calculated by the group velocity of the flexural wave on flat panel element c_gi and the connected joint condition c_τ as per Equation (3) and Equation (4).

where, L_cij is the joint length between element i and j, and S_i is the area of element i. In addition, τ_ij is the vibration energy transmission efficiency at the joint which is computed by the fundamental formula of L. Cremer and M. Heckl [2] for each flat plate connection form as shown in Figure 2.

Figure 2:

Transmission of vibration energy between elements

Here, the vibration energy transmission is estimated by considering only the flexural vibration mode on the flat panel element as simplified.

Furthermore, the mode number N_i existing in the range of band width Δω at the center frequency ω is given as Equation (5).

where, S_i, M_i, and B_iare the area, surface density, and bending stiffness of the flat panel element, respectively.

Moreover, the radiation loss factor $$ {\eta }_i^r$$ , the boundary loss factor $$ {\eta }_i^b$$, and the damping loss factor $$ {\eta }_i^d$$ are introduced into the power balance equation, so that the influences of power losses on sea water under the ship draft, other structures out of the analysis modeling range, and the application of special damping construction are considered.

The resultant sound power transmission is calculated by solving the simultaneous equations for all the elements in the concerned model.

Figure 3 shows the analysis process for cabin noise due to structure-borne sound.

Figure 3:

Analysis model for structure-borne sound prediction

As we can estimate the vibration velocity level L_v on the deck structure under the concerned cabin, by the solution of the power balance equations, the cabin sound pressure level L_ps is predicted as the summation of the sound pressure level L_psf radiated by the floor vibration and sound pressure levels L_psi radiated by the surrounding walls and ceiling as per the following Equation (6) ~ (8), taking into consideration the floor insertion loss IL_nby special application such as the floating floor, the transmission loss ∆L_vwi from deck to wall, and the average acoustic radiation efficiency of members of the sound receiving room $$ \bar{\sigma }$$, which are experimentally verified and specified in the sound receiving room database, including the data of area of floor S_f and each walls S_i and the sound absorption area of the sound receiving room A_E.

2.2 Air-Borne Sound

The air- borne sound level L_pA in the sound receiving room is predicted by the sound pressure level L_p0 in the adjacent sound source room or by the sound power level L_w of the sound source device as shown in Figure 4 and as per Equation (9) and Equation (10). In addition, the calculation of the air- borne sound level L_pA requires the data of the sound absorption area in the sound source room A_S and the sound receiving room A_E, the sound transmission loss TL, and the area S of the partition wall/deck plate. The verified data measured at the shop test or sea trial are specified in the database.

Figure 4:

Analysis model for air-borne sound prediction

2.3 Air Conditioner and Ventilator Noise

As shown in Equation (11) and Equation (12), the sound pressure level L_AC in the cabin is given by the measured data or predicted by the power level of sound source L_ACw in front of the air outlet of the air conditioner or ventilator. Here, the directivity factor Q, the distance r from the point of the sound source, the room constant of sound receiving room R, the mean sound absorption coefficient $$ \bar{\alpha }$$, and the total surface area S of the cabin are taken into account.

2.4 Exterior Fan Noise

As shown in Equation (13) ~ Equation (15), the sound pressure L_FN in the cabin caused by the exterior fan noise is predicted by the measured sound pressure level L_FNp or sound power level L_FNw at a distance of 1 m from the exterior fan, and the attenuation of the distance r from the fan to the sound receiving room. In addition, the sound transmission loss TL of the walls and roof, and the directivity factor Q are taken into account. Here, the effect of sound diffraction is not considered.

2.5 Funnel Exhaust Noise

Similarly to the exterior fan noise, the sound pressure L_EX in the cabin caused by the funnel exhaust noise is predicted by the measured sound pressure level L_EXp or sound power level L_EXw at a distance of 1 m apart from the funnel top, as per Equation (16) ~ Equation (18).

3.1 Supporting Database System

All necessary data for the model creation and noise prediction analysis are defined in the supporting database system (hereinafter, DB) as per the formulated MS Excel format as shown in Table 2, which are specified and updated on the basis of the data verified by shop tests, measurements at sea trial, and so on, by each user.

Table 2:

Contents of database (DB) definition

The entire DB can be automatically controlled by the DB control function in the DB system which enables the following functions:

① Selecting and importing necessary data files from the DB

② Data format conversion to TSV

③ Data check, error detection, and notification

3.2 Model Creation Program

The 2D forms of the relevant frame sections of the hull structure are defined by using the point, line, and surface layer data that are extracted from AutoCAD data (dxf format) by the layer control method. Then, the 3D analytical model can be automatically created on the platform of TSV by placing the 2D forms in the order of the identified frame number and connecting the adjacent points, lines and surfaces as per the following steps as shown in Figure 6 and Figure 7.

Figure 6:

Model creation procedure

Figure 7:

3D model assembly

Step-1: Import the 2D cross-sectional data from AutoCAD data and identify their frame position data.

Step-2: Project the cross-sectional lines onto the cross-section plane.

Step-3: Connect the adjacent frames’ data and create surfaces.

Step-4: Edit (cut, add or delete) surfaces, as needed.

As shown in Figure 8, the simplified model is composed from flat panels of the significant structures for energy transmission elements, such as shell, deck, and wall, excluding stiffeners.

Figure 8:

Structural modeling for analysis

The effectiveness and accuracy of the prediction using these simplified models has been validated by comparison of the measured results in actual ships and the predicted results.

Thus, it is confirmed that the easy and quick creation of analysis models has a significant impact on saving the time and effort required for ship noise analysis thereby providing a high potential tool for the optimum design of ship noise control.

3.3 Noise Prediction Program

Here, the simplified SEA method is applied, where only the sound energy transmission due to the flexural vibration modes of an element is taken into account.

The effects caused by the simplified analysis can be adjusted by introducing a tuning process for the loss factors such as the internal loss factor η_i and the coupling loss factor η_i as shown in Figure 9. The effectiveness of this procedure has been experimentally validated [3].

Figure 9:

Program flow of noise prediction function

Moreover, the operation of the noise prediction is easily executed by one-push, using the simplified model and the formulated DB system, according to the following six functional steps by the work bench as shown in Figure 10.

Figure 10:

Work Bench for SNA function

① Create model function (Model read on to TSV)

② Modify model function (Model merge, add parts, and delete)

③ Set property function (Read DB, and define calculation condition, material and thickness, damping material, pillar, draft, tank and boundary condition)

④ Set source function (Define sound source of Structure-borne, Air-borne, AC &Vent, Ex. Fan and Exhaust sound)

⑤ Run solver (Perform analysis as per the program flow shown in Figure 9, by 1/1 or 1/3 Octave band basis, and recalculate due to the modification of the model and DB for tuning operation.

⑥ Show result function (Display of analysis results for confirmation, by overall value, octave band curve, and contour figure (vibration velocity/acceleration/energy, sound pressure, element thickness, mode number, and loss factors)

3.4 Result View Program

To verify the analysis results in comparison with the measured data, the following two functional steps are performed after step ⑥ in the previous subsection.

⑦ Plot function (Output of calculation result for verification study by plotting the response of elements, frequency and cabin on the basis of frequency or element)

⑧ Tuning function (MS Excel file output of factors for tuning)

The cycle of steps from ⑧ back to ⑤is repeated for the tuning operation as shown in Figure 9, which is the most important and invaluable function for practical ship noise control procedures with reference to the measured data.