GB/T 43945-2024Cabin noise prediction for ships based on statistical energy analysis (English PDF)

3 Terms and definitions

Statistical energy analysis is defined as the analysis of energy transfer and balance between the parts of a system, using statistical averaging in time and space and taking energy as the independent variable to solve the medium and high frequency coupling problem between the solid structural vibration and the fluid sound field of a complex system.

A subsystem is a group of modes with similar resonant form. Modal density is the physical quantity describing the capacity of a subsystem to store energy. The damping loss factor is the ratio of the energy lost by a subsystem per unit time within a unit frequency, that is per vibration cycle, to the mean stored energy. The coupling loss factor is the percentage of transmission loss of vibrational energy at the connection of coupled subsystems.

The terms and definitions of GB/T 3947 also apply.

4 Symbols

Table 1 lists the symbols used in the document, each with its parameter name and its unit. The symbols cover the geometry and material properties of the beam, plate, sandwich panel and acoustic cavity subsystems, namely cross-sectional area, second moment of area, elastic modulus, density, thickness, surface density, bending stiffness, Poisson ratio, damping loss factor, panel perimeter and side lengths, rib spacing and total rib length, the thickness of the plate covering material and its properties, the equivalent fluid thickness of the plate, and the volume, surface area, perimeter, sound speed, fluid density and sound absorption coefficient of the cavity.

Table 1 also lists the quantities of the energy balance itself: the energy, input power and modal density of each subsystem, the internal loss factor and the coupling loss factor between two subsystems, the transmission efficiency between subsystems, the radiation efficiency from a plate to a cavity, the ratios of the thicknesses of pairs of plate subsystems, the mechanical impedance of a beam or plate at a common point and its real part, and the effective input mechanical impedance of the seating. The acoustic quantities listed are the sound pressure and sound pressure level of each cabin at each centre frequency, the reference sound pressure of two multiplied by ten to the power minus five pascals in air, the A-weighted cabin noise level, the A-weighting correction at each centre frequency, the sound pressure level and sound power level of the airborne noise of the equipment with a reference sound power of ten to the power minus twelve watts, the foot acceleration level of equipment vibration with a reference acceleration of ten to the power minus six metres per second squared, and its octave and one-third octave forms, together with the vibration isolation reduction from the equipment foot to the seating panel, the sound insulation of a component and of the common face between two cavities, the coincidence frequency of a plate, the frequency and the circular frequency, the surface area of the enveloping surface used for sound pressure measurement, and the distances from the excitation point to the nearest bracket and to the web.

5 General requirements

5.1 The airborne noise level is evaluated with the A-weighting curve, and since the A-weighted level is governed by the medium and high frequency noise, statistical energy analysis may be used as the calculation method for the cabin noise of a ship caused by the hull structural vibration excited by steadily running machinery. The result of the calculation is a statistical average in space and in frequency, and predicts with reasonable accuracy, in the statistical sense, the mean sound pressure level of the whole cabin when no resonance occurs between the structure and the equipment excitation. Using test data for the vibration and noise of the equipment and for the damping, sound insulation and sound absorption coefficient of the structure can raise the accuracy of the prediction.

5.2 The drawings and documents required are chiefly the arrangement drawings, the structural drawings and the electrical load calculation. The arrangement drawings include the general arrangement, the equipment arrangement, the fire insulation arrangement, the deck covering arrangement, the damping arrangement, the outfitting arrangement and the ventilation and air conditioning system arrangement. The structural drawings include every structural drawing of the region modelled, chiefly the basic structural drawing, the typical transverse section, the shell expansion, the superstructure structure, the engine room structure, the after body structure, the double bottom structure and the seating structure.

5.3 A cabin noise calculation model of the whole ship is to be built, covering the region from the noise source to the cabin analysed together with the region to which energy is transferred around it. The model is built chiefly from plate, beam and acoustic cavity subsystems: shell plating, decks and bulkheads and other ship structures are modelled as plate subsystems, pillars as beam subsystems, and accommodation cabins, offices and other ship spaces as acoustic cavity subsystems. Subsystems are to be as large as possible so that the number of modes in the analysis band of a subsystem is greater than 5. Plate subsystems are divided along the real boundaries of the ship structure, effective connection between them being ensured through common points and common edges. The shell plating and the tank bulkheads are divided into two plate subsystems at the waterline, and the subsystems below the waterline are to take account of the added effect of the fluid loading on the structure as clause 6 requires. Acoustic cavity subsystems generally follow the cabin arrangement of the ship and are effectively connected to the plate subsystems that bound them through common faces; large engine rooms, casings and stairways spanning several decks may be divided into several cavities bounded by the decks, and open regions are modelled by semi-infinite cavity subsystems. Doors and windows are treated as normally closed and may be replaced in the model by the plate subsystem of the ship structure, but the sound insulation computed for a composite component as 8.2.7 requires is to be assigned to that plate subsystem. Tables, chairs, berths and equipment inside a cabin need not be modelled, but their sound absorption coefficient is to be included in that acoustic cavity as 8.2.9 requires.

6 Calculation flow for cabin noise

6.1 and 6.2 The calculation flow is shown in Figure 1. Before modelling, the sailing condition or the specified calculation condition, the equipment that is running, the cabins to be checked and the noise control limits are to be settled from the technical specification.

6.3 and 6.4 From the arrangement and structural drawings required by 5.2, the noise source equipment, the insulation material, the deck covering, the composite rock wool panels and the damping material are to be established, together with the form, material and dimensions of the ship structure. From 8.1 and 7.2, the parameters to be supplied by the makers of the noise source equipment and of the outfitting material are to be listed, namely the foot acceleration level, the radiated sound power level and the isolation of the vibration isolators, and the elastic modulus, density, internal loss factor, sound insulation and sound absorption coefficient of the outfitting material; the design company and the yard pass the request to the suppliers.

6.5 and 6.6 The geometric mesh is built from the drawings or from the model supplied by the yard. Pre-processing software may be used to clean the geometry, delete or simplify secondary structures, divide plate subsystems by separating lines so that each face represents one plate subsystem, patch openings with faces, check the free edges of the model in wireframe view, cut cabins of irregular shape or excessive volume such as the engine room with faces, and output the geometric mesh file. In the statistical energy analysis software, octave analysis from 63 Hz to 8 000 Hz is set; the geometric mesh is imported with the correct system of units; the faces of the mesh are identified automatically and plate subsystems built, meshes for which the subsystem could not be generated being checked and patched by hand; cavities are created automatically from the closed plate subsystems that form a cabin, and cavities for open regions created by hand.

6.7 to 6.9 The input power is applied from the vibration and noise parameters as 8.1 requires: vibration data are converted into input power from the foot acceleration level, the isolation and the seating impedance; airborne noise data are to be radiated sound power levels, otherwise they are converted from the sound pressure level and the area of the measurement envelope. The properties of the beam, plate and cavity subsystems are set as 8.2 requires from the drawings and the material parameters, the subsystems being first grouped by drawing and material so that properties can be set and changed conveniently; the two faces of a plate subsystem are to be strictly distinguished so that the outfitting material and the fluid loading are set as they really are. The noise source equipment is then allocated to the several calculation conditions according to which equipment runs in each.

6.10 to 6.12 The cabin noise is computed with the statistical energy analysis software. If the calculation fails, the model is to be checked again; otherwise the A-weighted level of the accommodation and working cabins is extracted and compared with the cabin noise limits, a margin being kept according to the validity of the input parameters. If the result meets the requirement the calculation ends and the analysis report is written; otherwise the cabin arrangement is changed or vibration and noise reduction measures are drawn up following JT/T 781, and the calculation is repeated. The content of the report is given in Annex A and generally includes the basic information and principal dimensions of the ship, the cabin noise limits, the information on the main noise source equipment, the vibration and noise parameters and how they were obtained, the material property parameters and how they were obtained, the calculation method, the model and the modelling method, the results and their analysis, and the noise reduction measures.

7 Calculation method for cabin noise

7.1.1 For a statistical energy analysis model composed of several subsystems representing ship structures and cabins, the energy balance equation is computed by formula (1); solving it gives the energy of each structural and acoustic cavity subsystem. The formula is printed as a matrix equation whose coefficient matrix carries the internal loss factors and the coupling loss factors weighted by the modal densities; its layout is damaged in the extracted text and it is not reproduced here.

7.1.2 The modal density is computed by formulae (2) to (10): formula (2) for a beam, formulae (3) to (6) for a plate, including the surface density, the bending stiffness and the equivalent fluid thickness, formulae (7) to (9) for a sandwich panel, and formula (10) for an acoustic cavity, the cavity expression having three terms in the volume, the surface area and the perimeter.

7.1.3 The internal loss factor is computed by formulae (11) to (13), for a beam, for a plate and for an acoustic cavity respectively, each expression adding to the material or absorption term the sum of the coupling loss factors toward the other subsystems.

7.1.4 The coupling loss factor is computed by formulae (14) to (37). For plate to plate connections, formula (14) gives the coupling loss factor and formulae (15) to (23) the transmission efficiency for the four connection forms illustrated in Figures 2 to 5, namely the coaxial connection, the right-angle connection, the T connection and the cross connection. For beam to beam connections, formula (24) gives the coupling loss factor, the transmission efficiency being computed as for plates, with the ratio of the thicknesses of the plate subsystems replaced by the ratio of the cross-sectional areas of the beam subsystems. For cavity to cavity connections, formula (25) gives the coupling loss factor; the sound insulation of the common face is measured following GB/T 19889.3 and GB/T 19889.4, and for a single-layer structure it may be estimated by formula (26) where the surface density of the common face is not greater than 100 kg per square metre and by formula (27) where it is greater. For plate to cavity connections, formula (28) gives the coupling loss factor and formulae (29) to (33) the radiation efficiency, distinguishing the ranges below, at and above the coincidence frequency; where a plate is connected to an external semi-infinite cavity subsystem, only the coupling loss factor is computed and added into the internal loss factor of the plate. For beam to plate connections, formulae (34) to (36) give the coupling loss factor and the mechanical impedances at the common point. Once the coupling loss factor from one subsystem to another has been obtained, the reciprocal coupling loss factor is computed by formula (37) from the ratio of the modal densities.

7.2 to 7.4 The airborne sound pressure is computed by formula (38) from the energy of the cavity, its volume and the density and sound speed of air; the sound pressure level by formula (39) from the sound pressure and the reference sound pressure; and the cabin noise level by formula (40) as the energy sum over the eight octave bands of the sound pressure levels corrected by the A-weighting values. Table 2 fixes those A-weighting correction values against the octave centre frequencies 63 Hz, 125 Hz, 250 Hz, 500 Hz, 1 000 Hz, 2 000 Hz, 4 000 Hz and 8 000 Hz as -26.2 dB, -16.1 dB, -8.6 dB, -3.2 dB, 0 dB, 1.2 dB, 1.0 dB and -1.1 dB.

8 Input parameters for cabin noise calculation

8.1.1 to 8.1.3 The noise sources are the machines running in the sailing condition or in the specified calculation condition, generally the main engine, the diesel generating sets, the propulsor, the engine room fans, the pumps and the ventilation and air conditioning plant. After the cabin noise caused by the machinery has been computed by statistical energy analysis, the cabin noise caused by piping noise is added by energy summation; alternatively the cabin noise caused by the ventilation and air conditioning system travelling through the ducts may be applied to the corresponding cavity subsystem as an airborne noise source. The source parameter of a machine is the input power in octave form, coming chiefly from the vibration transmitted through the feet into the plate subsystem and from the noise radiated directly into the air and reaching the cavity subsystem.

8.1.4 The input power of equipment vibration into the ship seating structure is computed by formula (41) from the foot acceleration level, the vibration isolation reduction, the frequency and the effective input mechanical impedance of the seating. That impedance is obtained by test following GB/T 11349.2 and GB/T 11349.3; where no measured data exist it may be computed by the finite element method or estimated by formulae (42) and (43).

8.1.5 and 8.1.6 The input power of the airborne noise of the equipment into the cabin is computed by formula (44) from the sound power level, or from the sound pressure level together with the area of the measurement envelope. Where the equipment vibration is supplied in one-third octave form it may be converted to octave form by formula (45) on the principle of energy summation, the sound power level and sound pressure level of the airborne noise being converted in the same way.

8.1.7 to 8.1.10 Measured vibration and noise data of the equipment should normally be used as input, the measurement method meeting GB/T 3767, GB/T 3768, GB/T 6882 and GB/T 9911; where test data cannot be obtained, the methods of Annex B may be used for a first estimate. From the equipment arrangement drawing, the vibration and the airborne noise of the equipment are converted into input power and applied to the corresponding plate and cavity subsystems. Where several noise sources act on the same subsystem, the total input power is obtained by energy summation before being applied; where one noise source acts on several subsystems, the input power is distributed among them before being applied.

8.2.1 to 8.2.6 The material property parameters of the ship structure are chiefly the elastic modulus, the Poisson ratio, the density and the loss factor in octave form; they are supplied by the maker or looked up in material handbooks, the loss factor test method meeting GB/T 16406 and GB/T 18258. The property parameters of a plate subsystem are chiefly the material properties, the thickness, the stiffener data such as area, second moment of area and spacing, and the interior lining data such as material properties and thickness, and are taken from the structural drawings, a plate subsystem generally being a stiffened structure. The property parameters of a cavity subsystem are chiefly the medium properties, that is sound speed and density, and the sound absorption coefficient in octave form. The interior lining of a cabin is modelled from the drawings, the maker supplying the material composition, the material properties, the sound insulation and the sound absorption coefficient; sound insulation is measured following GB/T 19889.3 and GB/T 19889.4 and sound absorption following GB/T 20247.

8.2.7 to 8.2.9 The sound insulation of a component should be taken from measured data; the sound insulation of a composite component such as a door, window, window recess, opening or bulkhead is computed by formula (46) from the areas and the sound insulation values of its parts. The structural loss factor should likewise be taken from measured data; where none exists, Table 3 gives the loss factor of steel against the eight octave centre frequencies from 63 Hz to 8 000 Hz as 0.30 %, 0.26 %, 0.24 %, 0.21 %, 0.19 %, 0.18 %, 0.17 % and 0.16 %. The sound absorption coefficient of a cabin should also be taken from measured data; where none exists it may be computed by formula (47) from the areas and absorption coefficients of the surfaces and of the interior lining, or taken from Table 4, which gives against the same eight frequencies the values for the main engine room, auxiliary machinery room and after peak as 0.04, 0.08, 0.11, 0.14, 0.17, 0.20, 0.24 and 0.27; for the steering gear room and the refrigerated room as 0.04, 0.06, 0.08, 0.10, 0.13, 0.15, 0.18 and 0.20; for crew cabins as 0.12, 0.21, 0.25, 0.27, 0.28, 0.29, 0.29 and 0.29; and for public spaces and offices as 0.12, 0.17, 0.19, 0.20, 0.21, 0.21, 0.22 and 0.22.

B Annex B (informative) Estimation of vibration and noise source parameters of equipment

B.1 For diesel engines, formula (B.1) estimates the foot acceleration level of a low-speed engine from its rated speed, mass, rated power, working speed and the octave centre frequency; formula (B.2) estimates that of a medium and high speed engine from its mass, rated power, working speed, rated speed and an octave correction given in Table B.1; and formula (B.3) estimates the radiated sound power level from the rated power and an octave correction given in Table B.2, which distinguishes engines above and below 600 r/min. The reference acceleration is ten to the power minus six metres per second squared and the reference sound power ten to the power minus twelve watts.

B.2 For reduction gearboxes, formula (B.4) estimates the radiated sound power level from the rated power, the gear meshing frequency, that is the product of the gear rotational frequency and the number of teeth, the analysis frequency, and a manufacturing error coefficient given in Table B.3 for the grades B3, C1, C2, C3, D1, D2 and D3 as 0 dB, 2.5 dB, 5 dB, 7.5 dB, 10 dB, 12.5 dB and 15 dB.

B.3 For electric machines, formula (B.5) estimates the acceleration level from the rated power, the rated speed and an octave correction given in Table B.4, and formula (B.6) estimates the radiated sound power level from the rated power, the rated speed and an octave correction given in Table B.5, which distinguishes alternating current from direct current machines.

B.4 For pumps, formula (B.7) estimates the acceleration level of a non-reciprocating pump from the rated power of the driving machine and an octave correction given in Table B.6, which distinguishes centrifugal pumps from gear pumps, and formula (B.8) estimates the acceleration level of a reciprocating piston pump from the rated power of the driving machine, the rated pressure of the pump set and an octave correction given in Table B.7.