NOMENCLATURE
|
FRF |
Frequency
Response Function |
|
HD |
Drop
height |
|
Hw |
Wave
height |
|
P/D |
Probability
Distribution |
|
PEX
|
Extreme
peak pressure |
|
PP
|
Peak
pressure |
|
P/T |
Pressure
Transducer |
|
QI |
Impulse
quantity |
|
S/P |
Slam
Patch |
|
TD |
Duration
time |
|
TR |
Rise time |
|
V |
Speed of
boat |
INTRODUCTION
Weight is a governing factor for the speed of a racing yacht. To maximize speed
optimization of the structure is key whether the race area has calm water like
the
Starting with the work of von Karman
(1929), various research works have been carried out in naval architecture
(Ochi and Motter, 1973; Faltinsen, 2000; Kapsenberg et. al., 2003), on
motorboats (Heller and Jasper, 1961; Stavovy and Chuang, 1976; Savitsky and
Brown, 1976; Allen et. al., 1978), and on sailboats (Joubert, 1982; Reichard, 1984;
Hentinen and Holm, 1994; Joubert, 1996) in parallel with rules and regulations
(ABS, 1994; ISO, 2008; BV, 2008). Nonetheless, as pointed out by Manganelli
(2006), and Bunting and Sheahan (2009), a growing number of engineers and
researchers agree on the need for more accurate knowledge of the hydro-impact
problem in sailboats as new problems appear due to the continuously enhanced
performance of sailboats. In this regard, hydro-impact in the waves
during slamming is the subject of this study.
First, a specially built measurement system named ‘slam patch’ is designed and implemented with pressure transducers on a model boat and a series of hydro-impact tests are carried out. This slam patch system, which is based on force transmissibility, is designed to represent the local structure of the boat and/or a simple pressure/force transducer as a transition device between the pressure transducer and strain gauge. It is found that the slam patch system can be implemented to measure the total response of the local structure which can be divided into two components – hydro-impact load and vibration behaviour of the local structure under fluid-structure interaction.
Second, various measurement systems are installed in a scale model of an Open 60 and hydro-impact tests are carried out – a rotational drop test and a seakeeping-slamming test. In the drop test, it is found that as drop height increases, which means impact velocity increases, the transient response of the structure is significant and far exceeds the magnitude of the hydro-impact load itself measured at the pressure transducer. This is due either to the existence of resonance of the structure or the location of the pressure transducer, which is at the perimeter of the slam patch or sampling rate limitation. In the seakeeping-slamming test, because of the limitation of wave height, a maximum wave of 0.2 m was used in scale model to find the hydro-impact load. It was found that with a wave height of 0.2 m, the measured response of the slam patch system was pure hydro-impact load or slightly coupled with the structure’s resonance. The measured signals were processed statistically to predict the general trend of the hydro-impact phenomenon.
DESIGN OF SLAM PATCH SYSTEM
Various instruments can measure the hydro-impact load – pressure transducer, pressure panel, strain gauge, or accelerometer. Each instrument has its own advantages and disadvantages. For example, a pressure transducer can measure exact pressure at a given point but can miss the highest pressure value. A strain gauge and accelerometer can measure the total response of a structure when the structure impacts the fluid; however, the hydro-impact load from the fluid cannot be inferred when the exact response of the structure is unknown. The concept of the slam patch system, which belongs to the pressure panel category, is to measure the impact load by the fluid and/or to measure the response of the local structure. To design the system, the duration and the peak pressure of the hydro-impact caused by slamming must be known so the components of net hydro-impact load and response of structure can be either separated or coupled.
In the study of Manganelli et. al. (2003), a slam patch system is configured to find the hydro-impact load and hydro-elastic effect. In their study, the slam patch system is assumed as a 1-DOF system. The 80 by 80 mm slam patch is designed and tested in dry and wet modes[1]. It is found that in dry mode the linear range before the first resonance is between 300 Hz and 400 Hz. The corresponding linear range in wet mode is 200 Hz. After the slamming tests, hydro-impact signals are filtered to eliminate the resonant response of the slam patch system.
In this study, the dynamic behaviour of the slam patch system is
investigated to a further degree. Figure 1 shows the slam patch system used in this study.
|
|
|
|
Figure
1. Slam patch system (left: schematic,
right: prototype) |
|
To ensure that the frequency range of the hydro-impact load is not
near the resonance of the slam patch system, the boundary where the system is
attached is reinforced. Numerical calculation and modal testing are carried out to
measure the force transmissibilities in dry and wet modes. In the modal testing direct and
transfer FRF’s are obtained. However, in the wet mode direct FRF is impossible
to obtain, only transfer FRF’s are compared as shown in Figure 2.
|
|
|
Figure 2. Measurement in modal
testing |
It is found that the slam patch system behaves like a cantilever
beam with a mass at the free end, which is shown in equations (1), (2) and Figure 3.
|
|
(1) |
|
|
(2) |
where:
|
f,
ω = |
frequency in Hz and rad/sec,
respectively. |
|
kT,
kL = |
effective
stiffness of beam in transverse and longitudinal directions, respectively. |
|
meqT, meqL = |
effective mass in transverse and
longitudinal directions, respectively. |
|
M, m = |
mass at the free end of beam and
mass of beam, respectively. |
|
E = |
Young’s modulus of beam. |
|
A = |
section area of beam. |
|
I = |
moment of inertia of beam section. |
|
L = |
length of beam. |
|
|
|
Figure
3. Cantilever beam with a mass at the
free end |
In the numerical calculation the natural frequencies are 481, 580,
593, and 1343 Hz in dry mode and 345, 371, 535, and 805 Hz in wet mode. After
modal testing, the acceptable linear ranges where force transmissibility is
unity (= 1) are up to 500 Hz in dry mode and up to 250 Hz in wet mode. Figure 4 shows one (slam patch No.
3) of the transfer force transmissibilities of six slam patches in dry and wet
modes. In the figures of dry and wet mode, each line is the transmissibility
from one impact test whereas the bold line is the average transmissibility.
|
(a) Slam patch 3 in dry mode |
|
(b) Slam patch 3 in wet mode |
|
Figure
4. Force transmissibility (transfer
FRF’s) of slam patch No. 3 |
ROTATIONAL DROP TEST
The objectives of the rotational drop test are:
- To assess
the behaviour of
the slam patch when measuring the
hydro-impact load.
- To measure the hydro-impact load and/or the response of the local structure with regard to drop height.
The test is carried out with a 1/7-scale model of an Open 60
yacht in calm water with three slam patch systems, four pressure transducers, one potentiometer, and one accelerometer installed on the fore
body of the model. Figure 5 and Table 1 show the
details of the yacht in this study.
|
|
|
Figure 5. Body plan of Open 60 (Finot-Conq design, |
Table 1.
Principal characteristics of Open 60 (Finot-Conq design,
|
Principals |
Values |
|
Displacement |
11,290 (kg) |
|
LWL |
16.968 (m) |
|
BWL |
3.89 (m) |
|
Draught (bare hull) |
0.405 (m) |
|
Deadrise angle at 0.5 LWL (Station 5) |
20, 7.5, 4.5[2]
(degree) |
The fundamental hardware configuration in the drop test and the seakeeping-slamming test are given in Table 2.
Table 2. Key hardware
|
Item |
Model |
Remark |
|
A/D converter |
PCM-DAS08 |
24 kHz |
|
DAQ system |
Labview 8.0 Turboad |
Sampling rate: 3125 Hz Sampling rate: 1512 Hz |
|
Slam patch |
In house made |
± 40 kPa |
|
Pressure
transducer |
RDP A105 |
344.7 kPa |
|
Amplifier |
RDP 600 |
|
|
Accelerometer |
Endevco 2256 |
± 50 g |
|
Potentiometer |
In house made |
|
The locations of measurement and set
up in the drop test are shown in Figure 6. The accelerometer is attached to the
reinforcement structure over slam patch 2.
(a) Test
set up |
|
|
(b)
Instrument installation |
(c)
Instrument installation |
|
Figure
6. Rotational drop test set up |
|
Figure 7 is a typical result of the drop test where, around the four corners of slam patch 3 (slam patch 380), four pressure transducers are installed. In this case, the drop height is 4 cm from the bottom of slam patch 3 (slam patch 380) to the water surface.
|
(a)Time histories of P/T’s |
(b) Power spectrums of P/T’s |
|
|
(c) Time histories of S/P’s |
(d) Power Spectrums of S/P’s |
|
|
(e) Time history of accelerometer |
(f) Time history at potentiometer |
|
|
Figure 7. Typical test result (drop height = 0.04 m) |
|
|
Note that the magnitude and power of the accelerometer is extremely
high, over 40 g. Consistent results are acquired during the other drop height where
the pressure at the slam patch is greater than the pressure at the pressure transducer. This is due to either the dynamic load factor (resonance) of the
structure being within the range of excitation, or the pressure transducer
being located at the perimeter of slam patch such that the first highest impact occurs at
the slam patch; however, the perimeter assumption can be rejected since the
three slam patches show a similar degree of pressure shown in (c) of Figure 7.
On the other hand, since it is
recommended that at least a 20 kHz sampling rate is needed to measure the
hydro-impact signals in pressure transducers (Campbell and Weynberg, 1979;
Wraith, 1998; Kwon et. al., 2005), the possibility of missing the peak at a
pressure transducer cannot be excluded because of the relatively low sampling
rate of 3125 Hz.
In the series of drop and sloshing tests by Kwon et al. (2005), it was found that at a sampling rate of over 20 kHz extraordinary high peak pressure which was undetected at the low sampling rate was found. Thus, pressure transducers underestimate the original signals of impact pressure in this case. Figure 8 supports the former case where the structure is flexible enough that the dynamic load factor or resonance plays a significant role. It shows a typical hydro-impact force and its power spectrum density as the drop height increases.
|
(a) Time
history of hydro-impacts |
(b)
Corresponding power spectra |
|
Figure 8. Four hydro-impacts
(1~4) and corresponding power spectra |
|
No. 4 in Figure 8 is the case of the lowest drop height where the hull bottom just
touches the water by surface tension effect. No. 1 is the case of
the highest height of 0.4 m where the signal is clipped off - the
maximum capacity of the slam patch system is 290 N (nominal capacity is 250 N). As the
drop height increases, the range of frequency that contributes to the power of
the hydro-impact also increases. This means that as the drop height increases,
the response of the structure includes the components of resonance of the
structure due to the extended frequency range.
Figure 9 shows the
relationships between various variables in the drop test. The data are fitted
by 1st and 2nd degree polynomials.
|
|
|
(a) Pp vs HD at P/T’s |
|
|
|
(b) Pp vs HD S/P’s |
|
|
|
(c) TD
vs HD at P/T’s |
|
|
|
(d) TD vs HD at S/P’s |
|
Figure 9. Hydro-impact characteristics in drop test |
The peak pressure has a linear
relationship to drop height for both the pressure transducers and slam patches
as shown in Figure 9 (a) and (b). Although the relationship between peak
pressure and impact velocity is omitted, it also has a linear relationship
since the impact velocity is the function of drop height. Duration time is an
important factor in the calculation of the structural response to the impulse.
In this case, both pressure transducers and slam patches show a converging
tendency as the drop height increases as shown at the Figure 9 (c) and (d),
even though it is interpolated by a linear function because of the scarcity of
the data. This will be investigated further in the seakeeping-slamming test
below.
In this drop test, it is found that:
- Low pressure is detected at the pressure
transducer because of the low sampling rate limit.
- As the drop height increases,
magnification is dominant in the slam patch. However, at present, it is
difficult to detect the fluid-structure interaction effect (for example,
reduction of peak pressure), because there is no evidence with regard to
the response of the slam patch in vacuo when the same impact load is
applied.
SEAKEEPING-SLAMMING
TEST
A series of seakeeping-slamming tests are carried out in regular waves. The test
matrix is given in Table 3, where wave frequency (fw), wave height (Hw), and boat speed (V) are parameters. The measurement location is shown at Figure 10
(a) where the slam patches are lined up on the centre of the fore-body (station
2.5 to 4) of the model. In contrast to the drop test, the sensors are
distributed to determine the longitudinal distribution of the hydro-impact
pressure.
Table 3.
Seakeeping-slamming test matrix
|
Item |
Model scale |
Full scale |
|
Wave
frequency (fw) |
0.4
~ 0.95 Hz with 0.05
Hz increment |
0.15 ~ 0.36 Hz |
|
Wave
height (Hw) |
0.1/ 0.15/ 0.2 m |
0.7/ 1.05/ 1.4 m |
|
Boat
speed (V) |
1.5/ 2/ 2.5 m/s |
7.7/ 10.3/ 12.8
knots |
|
(a) Measurement location |
(b) Testing |
|
Figure
10. Seakeeping-slamming test set up |
|
At specific locations
In the seakeeping-slamming test, the foremost area shows the greatest peak pressure consistently throughout the test matrix. The hydro-impact pressures measured at the slam patch are well within the capacity of the slam patch, which implicitly means that the drop height or impact velocity is relatively smaller than in the drop test. The results at the foremost area of pressure transducer 1 and slam patch 1 are processed statistically and presented in Figure 11 as the relationship based on various boat speeds.
|
(a) Pp
distribution at Hw = 0.1 m (P/T 1) |
(b) Pp
distribution at Hw = 0.2 m (P/T1) |
|
(c) Pp
distribution at Hw = 0.1 m
(S/P 1) |
(d) Pp
distribution at Hw = 0.2 m
(S/P 1) |
|
Figure
11. Peak pressure (Pp) vs
wave frequencies at P/T 1 and S/P 1 at wave height (Hw) of 0.1 and
0.2 m in seakeeping-slamming test |
|
In these test results, significant hydro-impact
pressures are detected at:
- The wave frequency of 0.65 ~ 0.75 Hz,
- The foremost area of pressure transducer 1
and slam patch 1,
- The higher wave height of 0.2 m.
Figure 12 and Figure 13 are the
corresponding histograms and probability distributions of pressure transducer 1
(P/T1) and slam patch 1 (S/P1) at the specific wave height and boat speed. The
histograms are fitted by Gamma and Weibull distribution functions. The Gamma
distribution shows a slightly better fit throughout the histograms (i.e., has a
greater maximum likelihood of 1% and a smaller variance of 3% than the Weibull
distribution in goodness-to-fit analysis).
(a) Hw=0.1
m, V=1.5 m/s |
(b) Hw
=0.1 m, V =2.0 m/s |
||
|
(c) Hw
=0.1 m, V =2.5 m/s |
(d) Hw
=0.2 m, V =1.5 m/s |
||
|
(e) Hw
=0.2 m, V =2.0 m/s |
(f) Hw
=0.2 m, V =2.5 m/s |
||
|
Figure 12. Histogram and probability of P/T 1 in seakeeping-slamming test |
|||
|
(a) Hw
=0.1 m, V =1.5 m/s |
(b) Hw
=0.1 m, V =2.0 m/s |
|
(c) Hw
=0.1 m, V =2.5 m/s |
(d) Hw
=0.2 m, V =1.5 m/s |
|
(e) Hw =0.2 m, V =2.0 m/s |
(f) Hw
=0.2 m, V =2.5 m/s |
|
Figure 13. Histogram and probability of S/P 1 in seakeeping-slamming test |
|
The highest peak pressure is not
necessarily a function of boat speed in the case of a wave height of 0.1 m,
whereas a wave height of 0.2 m shows the opposite situation where the highest
peak pressure depends on the boat speed.
At all locations in the entire test matrix
In the previous section, pressure
transducer 1 and slam patch 1 showed the highest and most significant
hydro-impact pressure. Figure 14 shows the hydro-impact characteristics at all
locations within the entire test matrix. By doing so, the hydro-impact
characteristics such as peak pressure (Pp), duration time (TD),
rise time (TR), and impulse quantity (QI) in the bottom
area of the model can be traced.
In (a) and (b) of Figure 14, it is
confirmed that pressure transducer 1 and slam patch 1 show the highest
distribution of the peak pressure. As
the peak pressure increases, the duration time and rise time converge.
|
(a) Pp
at P/T’s |
(b) Pp
at S/P’s |
|
|
|
(c) Pp
vs TD at P/T’s |
(d) Pp
vs TD at S/P’s |
|
|
|
(e) Pp
vs TD at S/P 1 |
(f) TR
at P/Ts |
||
|
(g) TR
at S/P’s |
(h) TR
at S/P 1 |
||
|
(i) QI
at P/T’s |
(j) QI
at S/P’s |
||
|
Figure
14. Hydro-impact characteristics at
all locations in the entire test matrix |
|||
Corresponding histograms and
probability distributions (P/D) in the entire test matrix are shown in Figure
15. The pressure at slam patches 2 and 3 and the acceleration approach
exponential distributions, which is the area where relatively lower pressure
occurs. Note that the pressure 40 kPa in model scale corresponds to 280 kPa in
full-scale based on Froude’s law. The exceptionally high acceleration of 50 g
in Figure 15 (h) is the response of the local structure. It must be noted that
the local structure where the accelerometer is attached is in vacuo and was not
investigated in this case; however, it is inferred that the excessive power up
to higher frequency range contributes to this extraordinary acceleration.
|
(a) Histogram
and P/D at P/T 1 |
(b)
Histogram and P/D at P/T 2 |
|
(c)
Histogram and P/D at P/T 3 |
(d)
Histogram and P/D at P/T 4 |
|
(e)
Histogram and P/D at S/P 1 |
(f)
Histogram and P/D at S/P 2 |
|
(g) Histogram P/D at S/P 3 |
(h) Histogram P/D at Accelerations |
|
Figure
15. Histogram and Histogram P/D at all
locations in the entire test matrix |
|
The extreme peak pressures (PEX)
are selected from each run and used in the calculation of the extreme value
distribution. Figure 16 shows the extreme value distribution in which the
concave start in the QQ plot suggests a Fréchet-type distribution. Extremely
high peak pressures such as 80 kPa (which corresponds to 560 kPa in full-scale)
can be expected with very low probability.
|
(a) QQ
plot of PEX at P/T’s and S/P’s |
(b) Extreme value distribution (Fréchet-type) |
|
(c) CDF of
extreme value |
|
|
Figure
16. Extreme value distribution |
|
NOTE ON SCALE METHODOLOGY
Scaling the test results up to full-scale is another
challenge to solve. Since the boundary condition and natural behaviour of the slam patch are different from the hull plate of the prototype it is difficult to
justify the use of the system. However, if reasonable assumptions can be made as described below, then the slam patch system represents a scale model of the hull
plate of the prototype.
First of all, the slam patch system measures a force response to an
external force. The measured force has two components; i.e., the net
hydro-impact force and
the structural response of the slam patch system
itself. Segregation of the components of forces solely depends on the system’s
natural behaviour and the characteristics of the external force. In some of
the drop test cases, because
the measured data contains the structure’s natural
behaviour, it is difficult to separate the net hydro-impact force and structure’s resonant response. However, by using a filtering process to eliminate the component of frequencies
where resonance of the structure exists, the
hydro-impact force can be estimated. In the case of the seakeeping-slamming
test, the response is mainly hydro-impact force because the frequency range is well below the
structure’s resonance range. It can therefore be justified to use the slam
patch to measure the external hydro-impact load, slightly coupled with the structure’s
resonance.
Second, in this test, the first
objective is to measure the hydro-impact force and the second is to find the
hydro-elastic effect of the local structure under hydro-impact. So, to find the
natural characteristics of the slam patch system, FRF of force transmissibility
is plotted. If the force transmissibility between the
model and prototype are assumed to be the same, Froude’s law can be applied, where frequency is scaled as 1/λ1/2 and the force transmissibility
remains the same. Here,
the force transmissibility is receptance/receptance (Mead, 2000), where one familiar receptance used in naval architecture is the transfer function.
Furthermore, since the impulse has the dimensions of force and time,
if the force is scaled by λ3 or pressure by λ
and time by λ1/2, the quantity of (force) impulse can be
scaled up by λ7/2, or quantity of pressure impulse by λ3/2. Further study may be needed to find the exact scale law for the hydro-impact and
FSI problem so that Froude’s law can be adapted to the hydro-impact problem.
TRANSIENT RESPONSE OF SIMPLE STRUCTURE
Carrying out the transient response
of an Open 60 yacht under the hydro-impact based on the test results is left
for further study. Before that, a simple structure is studied to give insight
into the structural dynamics under an impulse. In this study, a cantilever beam
and a simply supported plate under half-sine impulse are studied analytically
and numerically.
A qualitative approach is tried to see the “relativity” between the structure’s natural characteristics and the applied impulse load. An impulse is quantified by the shape of the impulse and its duration time and is a key factor in the calculation of the structure’s transient response where the impulse is applied (Harris and Piersol, 2002). Since the shapes are varied in the test, it is difficult to determine the representative shape of the impulse and its duration time. This is left for further study. In this calculation, a half-sine function is employed to see the relativity.
Clamped beam
Two cases are of interest. One is where the relative time difference
between the structure’s first natural frequency and the duration time of the
impulse is high, low and zero, respectively, by changing the Young’s modulus of
the material, and the other is by adding mass on the beam. To clarify the
response easily, “clamped beam” is selected and simulated in the commercial finite element analysis program ANSYS™. The main parameters in this simulation are listed in
Table 4 and Table 5.
Table
4. Parameter 1 - Changing the Young’s modulus
|
Geometry |
1 m × 0.05 m × 0.05 m |
|
Young’s modulus |
2, 32, 128 GPa |
|
Poisson’s ratio |
0.3 |
|
Density |
2100 kg/m3 |
|
Load magnitude |
5000 N |
|
Duration of impulse |
5 ms |
|
Impulse shape |
Half sine |
|
1st fn of structure |
50, 200, 500 Hz |
Table 5. Parameter 2 - Adding mass
|
Geometry |
1 m × 0.05 m × 0.05 m |
|
Young’s modulus |
108.6 GPa |
|
Poisson’s ratio |
0.35 |
|
Density |
1700 kg/m3 |
|
Added mass (per unit length) |
0, 5, 10, 20, 30 kg |
|
Load magnitude |
5000 N |
|
Duration of impulse |
5 ms |
|
Impulse shape |
Half sine |
The transient responses at the midpoint of the clamped beam with
various Young’s moduli are shown in Figure 17 and Table 6.
|
a) fn =50 Hz |
b) fn =200 Hz |
c) fn =400 Hz |
|
Figure 17. Deflections to half-sine impulse with
various Young’s moduli |
||
Table
6. Responses at various Young’s moduli
|
fn |
Static (mm) |
Ratio to 50 Hz (%) |
Transient (mm) |
Ratio to static (%) |
|
50 |
25.04 |
100 |
23.08 |
92 |
|
200 |
1.56 |
6.23 |
2.65 |
170 |
|
400 |
0.39 |
1.55 |
0.491 |
126 |
It can be seen from the results that when the relativity is zero (in
this case fn is 200 Hz and the duration time of impulse is 5 ms),
the transient/static ratio (170%) is larger than the other cases (92% for fn=50Hz
and 126% for fn=400 Hz). However, as the natural frequency of the structure increases, the
responses to static and impulse loads significantly decreases.
The transient responses at the midpoint of the clamped beam with various added mass are shown in Figure 18 and Table 7.
|
a) Mass =
0 kg |
b) Mass =
5 kg |
c) Mass =
10 kg |
|
Figure 18. Deflections to half-sine impulse with
various added mass |
||
Table
7. Responses at various added mass
|
Added mass |
fn |
Static (mm) |
Transient (mm) |
Ratio to static (%) |
|
0 |
410 |
0.46 |
0.57 |
123 |
|
5 |
278 |
0.46 |
0.70 |
152 |
|
10 |
224 |
0.46 |
0.76 |
165 |
Similar results can be found such that as the added mass increases,
fn decreases. At the same time the transient deflection and the
transient/static ratio also increase. Generally when a simple structure is
in or on the water, because of the role of added mass of water, the natural
frequency of the boat in terms of local and global structure decreases (Kwak, 1996; Ramachandra
and Meyer-Piening, 1996).
As shown in Figure 17 and Figure 18, when the
duration time of the impulse approaches the 1st natural period of
the structure, the ratio of transient deflection to static deflection increases. This is
what the structural designer of boat must avoid. Higher stiffness does not
guarantee a safe hull unless the effect of the added virtual mass or the
behaviour of the structure in wet mode under hydro-impact is known.
Simply supported plate
Firstly, a simply supported plate in
dry mode under half-sine impulse (impulse pressure on the plate with half-sine
shape in time domain) is studied. Using the modal superposition method and
Duhamel’s integral, an analytical solution of the transient response of a
simply supported plate under half-sine impulse can be obtained. On the other
hand, a numerical solution using the commercial finite element analysis code is
found to compare well with the results to the analytical solution. Table
8 shows the comparison.
Table
8. Responses of a simply supported
square plate
(a)
Specification of calculation
|
Geometry |
1
m × 1 m × 0.005 m |
|
Material |
Steel |
|
Load magnitude |
5 kPa |
|
Duration of impulse |
0.04, 0.1, 1 sec |
|
Impulse shape |
Half-sine |
|
1st fn of structure |
50, 200, 500 Hz |
(b) Natural
frequency of the plate in Hz
|
Mode |
Mode shape |
Analytical |
Numerical |
Difference (%) |
|
1 |
(1,1) |
25.40 |
25.33 |
0.27 |
|
2 |
(1,2) |
63.52 |
63.19 |
0.51 |
|
3 |
(2,1) |
63.52 |
63.19 |
0.51 |
|
4 |
(2,2) |
101.63 |
100.53 |
1.08 |
(c) Maximum
deflections in mm to various loadings
|
|
Maximum deflection (mm) |
||
|
Loading type |
Analytical |
Numerical |
Difference (%) |
|
Static |
8.87 |
8.79 |
0.90 |
|
Dynamic (duration time=0.04 sec) |
15.46 |
15.37 |
0.58 |
|
Dynamic (duration time =0.1sec) |
9.75 |
9.99 |
2.40 |
|
Dynamic (duration time =1 sec) |
9.03 |
9.04 |
0.11 |
So far, the calculation results are
based on a relatively very simple structure. The structure of the boat is
relatively complex, and it is expected that the local complexity (which means
that the natural characteristics will be vary from area by area) will play an
important role in the dynamic response in terms of deflection, stress or strain
with or without the water.
CONCLUSIONS
Through this study, it was found that:
- A slam patch system can be used to measure the hydro-impact load and/or the local structure’s response to an external load if well designed to represent the local structure in terms of force transmissibility.
- To segregate the components of the slam patch’s response to the net hydro-impact load from the fluid and the resonant response of slam patch, the resonant frequencies of the slam patch must be well beyond the hydro-impact load range. On the other hand, in the case of trying to find the response that has a specific representative structure’s natural characteristics from full-scale prototype, the slam patch must be designed and implemented in terms of the same transmissibility between the model and full scale.
- The natural frequencies in the dry mode are consistently decreased compared to the slam patch in wet mode.
- In the drop test, as drop height increases, the slam patch’s measurement is consistently greater that the pressure transducer’s because of the existence of the slam patch’s natural characteristics of resonance. However, the possibility of the sampling rate problem still exists.
- In the seakeeping-slamming test, the measured force/pressure is far lower than the drop test result and since the measurement is well below the structure’s resonance range, it can be said that the measurement is net hydro-impact load.
- Gamma and Weibull distributions show good agreement with the histograms.
- As the relativity between external impulse and natural behaviour of the structure approach zero, the transient response increases in terms of transient/static deflection ratio in the simple structures.
- Qualitatively, the local structures will respond to the external hydro-impact load as the slam patch responds.
Nonetheless, some recommendations
for further research can be provided:
- The slam patch must be studied in further
detail to overcome the resonant problem when the objective is to measure
the net hydro-impact load.
- The wave matrix in the seakeeping-slamming
test must reflect the real sea condition where the boat operates, for
example, irregular waves, steep waves or higher wave height.
- The sampling rate must be re-considered
over 20 kHz to investigate the accuracy of the hydro-impact pressure.
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