The irregular wave condition, especially the oblique irregular wave condition, is the actual circumstances when trimaran is sailing in sea. In order to identify the characteristic of the wave-induced hydroelastic vibration in irregular waves, as well as investigate the change of vibration in different oblique irregular wave conditions, trimaran model tests were conducted to measure vibrations, wave impact, and motion under different azimuth and wave height. The vibration on main hull, side hull, and cross-desk is measured and analyzed separately to observe the influence of irregular wave in different structural parts. The longitudinal vibration, transverse vibration, and torsion are also included in the model tests measurement to investigate the relationship between these vibration deformation components and parameters of the irregular waves. The wave-induced hydroelastic vibrations and whipping effect is extracted and analyzed to find influence of whipping and springing on the total vibration. Based on the analysis, the dangerous positions and the critical waves condition is introduced to ensure that the subsequent structural strength assessment is more reliable.
Trimaran, as a kind of high performance ship, receives more and more attention. The new type ship is composed of one main hull, two side hulls, and two cross-decks. On the one hand, the advantageous wave interference caused by side hull gives trimaran a smaller resistance and better stability; on the other hand, complex cross-deck structure makes the investigation on trimaran’s vibration more difficult [
In fact, the distinctive transverse vibration and wave impact on cross-desk increase the complexity of research on trimaran’s wave-induced hydroelastic vibration greatly. In order to observe the wave-induced vibration more exactly, experts take numerous model tests. Hampshire et al. designed and carried out the load experiment at QinetiQ Rosyth by a segmented model [
So far, most cross-structure of trimaran model is idealized into a beam, which ignores the influence of wave slamming and air cushion on the wet cross-desk [
In this paper, the model design of trimaran and equipment is introduced. Then, these measured data are described and analyzed to study the characteristic of trimaran’s kinds of motion and vibration response in the oblique waves. Meanwhile, the vertical vibration proportion of side hull in the whole trimaran is illustrated. And the difference of side hull vibration between wave forward surface and wave backward surface is observed and compared. The whipping and spring phenomenon is also extracted and analyzed by Fourier spectral analysis. And the distribution of pressure on trimaran shell, especially the gap of side hull between inside shell and outside shell, is also found and studied. Through this experiment and data analysis, there is a comprehensive understanding of the structural response of the trimaran under oblique waves. The conclusion made in paper will play a great role in guiding the structural design of trimaran and subsequent structural strength assessment.
The trimaran model consists of three longitudinal steel backbone systems and two transverse backbone systems. A series of variable cross-section circle ring beams were used to keep longitudinal stiffness of the main hull. The thickness of the rings was changed to meet the variation of stiffness on main hull. Two rectangle ring beams were installed to satisfy the stiffness on side hull. There were also two transverse beams to ensure the transverse stiffness of the trimaran. The pedestal was made of wood and combines with steel clamp to fasten these backbones. The vibration response was measured by the electric strain gauges mounted on these steel backbones. The specific design of backbone systems is shown in Figure
Trimaran backbone systems design.
The shell of model is made of fibre-reinforced plastic (FRP) with the scale ratio of 1 : 25 to ensure similar shell geometry. It is accurate to provide buoyancy and water hydrodynamic force. Meanwhile, the wave slamming and air cushion on the wet cross-desk are also considered by full simulation of trimaran’s cross-desk. The trimaran shell is shown in Figure
Division location of model.
Division | Location from FP (m) | |
---|---|---|
Model | Prototype | |
P1 | 1.02 | 25.4 |
P2 | 1.56 | 39.0 |
P3 | 2.04 | 50.9 |
P4 | 2.72 | 67.9 |
P5 | 3.19 | 79.8 |
P6 | 4.28 | 107.0 |
Trimaran model shell.
In order to consider the influence of propeller on fluid and simulate the navigation of the trimaran, the propulsion system was installed in the last segment [
Model dimensions.
Description | Model | Prototype |
---|---|---|
Overall length (m) | 5.64 | 141 |
Moulded breadth (m) | 1.06 | 26 |
Depth (m) | 0.47 | 12 |
Draft (m) | 0.2 | 5 |
Displacement (t) | 0.255 | 3987 |
VCG from BL (m) | 0.293 | 7.34 |
LCG from FP (m) | 2.98 | 74.51 |
Side hull length (m) | 2.44 | 61.00 |
Side hull breath (m) | 0.15 | 3.75 |
Side hull depth (m) | 0.33 | 8.25 |
Final design of trimaran model.
The four-degree-of-freedom monitoring instrument was used to measure trimaran model movements, which is shown in Figure
Four-degree-of-freedom monitoring instrument.
Three acceleration sensors were installed to monitor the intensity of the model motion in waves. The first acceleration sensor was put at 0.494 m from fore perpendicular (FP) to observe the acceleration at bow. The second acceleration sensor was fixed at VCG for monitoring the acceleration on the whole model. And the location of the third acceleration sensor was 4.5 m from FP to get the acceleration condition at stern.
In order to observe the phenomenon of slamming and study the water impact on the surface of the model more accurately, twenty pressure gauges were installed at different locations along the length of the trimaran model [
There are ten pressure gauges disposed at the first segment, as seen in Figure
Pressure gauges arrangement at bow.
Pressure gauges arrangement amidships.
Pressure gauges arrangement at stern.
Pressure gauges arrangement.
The experiment was carried out in ocean engineering tank of Harbin Engineering University. The length of tank is 50 m; the width is 30 m; and the depth is 10 m. The irregular waves were made by a hydraulically driven wave maker. The ISSC dual parameter spectrum is adopted in the irregular wave test [
Irregular waves time histories.
The irregular wave data is converted into the waves of the real ship by use of the similitude rule. And the curve of wave spectrum density (WSD) is drawn out and compared with the theoretical wave spectrum. Figure
Comparison of irregular waves parameter.
Scheme | Theory value | Experiment value | Deviation | |||
---|---|---|---|---|---|---|
| | | | | | |
W1 | 4.2 | 6.70 | 4.18 | 6.63 | 0.51% | 1.04% |
W2 | 4.0 | 6.70 | 3.98 | 6.59 | 0.42% | 1.64% |
W3 | 3.8 | 6.70 | 3.79 | 6.73 | 0.18% | 0.45% |
W4 | 3.6 | 6.70 | 3.58 | 6.67 | 0.48% | 0.45% |
W5 | 3.4 | 6.70 | 3.38 | 6.71 | 0.71% | 0.15% |
Comparison of wave spectral densities.
From the analyses of the irregular wave spectrum, it is found that the significant wave height measured is lower than the theoretical aim height. The deviation of the significant wave height is less than 1%. It can be explained that the irregular waves are attenuated when wave is propagating in tank. The zero-crossing period fluctuates around the theoretical target. And the error rate of the zero-crossing period is also less than 2%. Such results are considered as the influence of the tank boundary. All these errors are in the acceptance range of this model experiment.
When ship is traveling in irregular waves, all the response on the ship is random, such as motion and vibration. So the statistical characteristic value is used as an indicator to express severity of motion and structural response. Autocorrelation function based spectral processing of the measured data was conducted to obtain the significant amplitude values. And all the analyses of motion and vibration are based on the corresponded statistical significant values. In addition, the amplitude of measured data is converted by the similitude rule before statistical analyses. The trimaran model ran with different azimuths and weights. These wave azimuth conditions include head sea, bow sea, beam sea, quartering sea, and following sea. And the wave weight conditions are from W1 to W5.
The heave motion is one of the important indicators on trimaran seakeeping performance. Its intensity affects the vertical vibration and the bottom water impact directly. Figure
Time histories of heave in irregular waves.
Results of heave in irregular waves.
From Figure
The pitch motion is one of the factors that cause the bow and stern slamming. And the serious slamming at bow is often the main cause of longitudinal whipping phenomenon. So it is necessary to find out the relationship between the displacement of pitch and different wave azimuths. Figure
Time histories of pitch in irregular waves.
Results of pitch in irregular waves.
For a trimaran, roll is a kind of complex motion, when the interference of side hull is considered. Meanwhile, the severe roll will aggravate the extent of the impact on cross-deck, which may cause the transverse whipping phenomenon. So it is important to study the roll motion in oblique waves. Figure
Time histories of roll in irregular waves.
Results of roll in irregular wave.
The vertical acceleration in the motion is also recorded and analyzed. Figure
Time histories of acceleration in beam sea.
Results of acceleration in irregular waves.
Dynamic wave load, which is the reflection of vibration response, is monitored by the steel backbone systems under irregular waves. The longitudinal steel backbone system on main hull recorded three kinds of vibration deformation on the main hull, such as vertical bending moment (VBM), horizontal bending moment (HBM), and torque. Two longitudinal steel backbone systems on the side hull also monitored the vertical bending moment of the side hull. And the splitting moments (SM) and transverse torsional moments (TTM) were observed by the transverse backbone systems. The data was collected and converted into corresponding statistical significant values. Then the analyses of these wave loads are done, respectively, as follows.
Firstly, the vertical bending moment on the main hull is observed and studied. Figure
VBM time histories of main hull in beam sea.
Power spectral density functions of VBM.
The reason of deviation between natural frequency and frequency peak of the hydroelastic vibration is analyzed. The low order natural frequency was measured by impact hammer test in calm water. In fact, when model was sailing in irregular waves, ship wetted surface was changed rapidly and all kinds of vibration responses by waves and experimental equipment were mutual interference. The surrounding flow field interference of model propeller and the vibration generated by propeller operation are considered as the reasons for the deviation between the natural frequency and measured high frequency peak. And some high frequency vibration caused by water slamming at both main hull and side hull’s bow can also lead to this deviation.
Springing is a steady and periodic hull vibration by wave-induced forces. And this phenomenon occurs in the condition that the wave’s encountered frequency or higher harmonic frequency matches with hull lower order natural frequency. Irregular waves contain a variety of waves with different frequencies, and it is relatively easy to stimulate this vibration. In Figure
VBM time histories of springing.
The maximum location of VBM can be found in Figure
Longitudinal distribution of VBM in beam sea.
VBM of main hull in different azimuths.
Figure
VBM time histories of main and side hull.
VBM of side hull in difference azimuths.
The general significant vertical bending moment on the whole trimaran is often regarded as the sum of these three VBM components. So the significant vertical bending moment on the three structures is counted, and the ratios of VBM on each part to the general significant vertical bending moment are showed in Figure
Ratios of VBM on main hull and side hull.
Figure
Longitudinal distribution of HBM.
HBM of main hull in different azimuths.
The power spectral density function of HBM is calculated by Fourier spectral analysis, as shown in Figure
Power spectral density functions of HBM.
Longitudinal distribution of torque.
Figure
The phenomenon that torsion deformation in beam sea is more serve than the deformation in other azimuths is observed in Figure
Torque of main hull in different azimuths.
The Fourier spectral analysis is also made in torque time history. Only one frequency peak is found in the frequency domain. And the high frequency peak does not appear. Obviously, the torsion natural frequency is too high to be stimulated. From above analyses it is known that the stern of trimaran structure in beam sea is the critical cross-section for structure strength analyses.
The observation on transverse deformation of trimaran is one of the aims of the model experiment. The individual transverse load for trimaran is splitting moment and transverse torsional moment, which is the potential cause of cross-deck structural break. The transverse backbone systems measure the potential danger and these data are analyzed as follows.
Figure
SM time histories in beam sea.
Splitting moment in different azimuths.
Splitting moment in different wave height.
TTM time histories in beam sea.
Transverse torsional moment in different azimuths.
The power spectral density functions of TTM are shown in Figure
Power spectral density functions of TTM.
The impact of waves always causes high frequency vibration. And the high frequency vibration accelerates the fatigue failure of trimaran’s structure. By arranging the pressure gauges on the shell of trimaran model, the rule of wave impact is studied.
The pressure sensors 1–10 are arranged at three cross-sections to observe the rule of pressure at the bow segment. The first cross-section includes the pressure sensors 1–3, whose locations are above the waterline. The number 1 pressure sensor, whose location is lowest in the three sensors, suffers more types of wave impact in the three pressure sensors. And the three pressure sensors reached the maximum value at 63.48 s, as seen in Figure
Time histories of pressure in bow sea.
Bow slamming in bow sea.
Bow slamming
Bow emerges from water after slamming
The vertical bending moment in the period of bow slamming is extracted and studied in Figure
VBM time histories at slamming moment.
VBM time histories at bow
VBM time histories amidships
In Figure
The similar relationship is found between the slamming of cross-deck and the splitting moment on transverse structure. The whipping response in transverse structure also exists by the slamming on cross-deck. From Table
Pressure in different azimuths.
Number | Pressure (Kpa) | ||
---|---|---|---|
Bow sea | Beam sea | Quartering sea | |
1 | 59.86 | 24.37 | 29.60 |
2 | 37.33 | 20.85 | 25.64 |
3 | 15.38 | 0.00 | 0.00 |
4 | 36.93 | 28.03 | 27.65 |
5 | 30.54 | 21.45 | 22.10 |
6 | 26.41 | 15.32 | 20.28 |
7 | 34.13 | 20.73 | 26.93 |
8 | 29.03 | 19.45 | 25.65 |
9 | 30.18 | 25.24 | 26.17 |
10 | 25.67 | 16.44 | 21.24 |
11 | 23.48 | 18.99 | 23.82 |
12 | 25.65 | 22.94 | 28.70 |
13 | 20.38 | 16.75 | 21.06 |
14 | 17.85 | 10.43 | 18.06 |
15 | 28.77 | 25.43 | 31.34 |
16 | 36.39 | 30.74 | 38.74 |
17 | 23.14 | 19.83 | 24.56 |
18 | 18.81 | 10.02 | 19.48 |
19 | 20.79 | 14.88 | 20.99 |
20 | 18.32 | 17.34 | 23.22 |
In this paper, the trimaran’s response of motion and wave-induced vibration in irregular oblique waves was studied by experiment. A scaled segmented trimaran model that matched the vibration characteristics of prototype was designed and tested in tank with different azimuths and wave heights. The experimental results of motion, load, and wave impact are analyzed, respectively. And the conclusions are made as follows: The motion of trimaran with side hull at stern has its own characteristics in oblique waves. The motion of heave and roll in beam sea is more sensitive than the response of other azimuths. And the following sea condition is the most dangerous case for the trimaran motion of pitch. In oblique waves, the bow acceleration is motivated most intensely in quartering sea and beam sea and replaced by stern acceleration in bow sea. The different kinds of vibration deformation should be considered separately in oblique waves. The position amidships always suffers vertical bending deformation most severely, and the maximum torsional deformation often happens at stern. But the longitudinal distribution of horizontal bending deformation is not stable and changes with different azimuths. In oblique waves, the bow sea condition often causes more severe vertical and horizontal bending vibration than the response in other oblique wave conditions. And the consistent fluctuation of vertical bending vibration between the main hull and side hull exists. The vertical bending vibration of side hull makes an important contribution to total vertical bending vibration at stern and cannot be ignored. Through spectral analysis, the hydroelastic vibrations are found in VBM and HBM. The springing effect should be paid more attention in the structure strength assessment of vertical and horizontal bending deformation. The characteristics of transverse deformation in oblique waves should be concerned. The splitting moment reaches a maximum peak in beam sea and tends to gentle in quartering sea with increase of wave height. And the transverse torsional moment in beam sea gets minimum with different azimuths. The cross-bridge structure at wave forward side always suffers more severe transverse deformation and should be strengthened in structural design. The drastic slamming and the severe high frequency impact load will appear, when ship encounters high waves. The enormous instantaneous loads caused by whipping increase the total load greatly at the slamming moment and should be taken seriously for the structural assessment. In addition, the local structure of trimaran’s shell near the waterline and at stern should be strengthened to resist more violent wave impact.
In the present research, all the experiment is based on low speed to ensure relative position invariant. The irregular wave response of vibration and slamming in different high speed will be studied in further research. More factors that cause load nonlinearity will be recorded to make the experiment results more credible.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported by the National Natural Science Foundations of China (nos. 51209054 and 51079034). The authors express their gratitude to these foundations.