European Journal of Mechanics A/Solids 28 (2009) 591–598

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European Journal of Mechanics A/Solids

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Attenuating performance of a polymer layer coated onto floating structuressubjected to water blasts

Yong Chen a,∗, Zhiyi Zhang a, Yu Wang b, Hongxing Hua a, Houyu Gou a

a State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, 800 Dong Chuan Road, 200240, Shanghai, PR Chinab Naval Research Center, 100073, Beijing, Box 1303-14, PR China

a r t i c l e i n f o a b s t r a c t

Article history:Received 2 December 2007Accepted 9 October 2008Available online 17 October 2008

Keywords:Polymer coatingsWater blastsAttenuating performance

The water blast attenuating performance of a polymer layer coated onto floating structures has beenexperimentally investigated. A series of contrastive live fire tests were conducted on a rectangular metalbox before and after coating a layer of polymer on its outer hull. The blast responses of the box andwater pressure near the wet surface were monitored and analyzed. Test results show that the transmittedimpulse at the initial FSI stage can be reduced by almost 50%, owing to the rubber wall flexibility.Consequently, both acceleration and strain peaks of the box induced by the first shock wave can beeffectively reduced. Further shock response spectrum analysis indicates that the coating performs likea low pass filter with cutoff frequency at about 50 Hz. Response components higher than 50 Hz canbe attenuated effectively, but for components lower than the cutoff frequency, the attenuating effect islimited.

© 2008 Published by Elsevier Masson SAS.

1. Introduction

Many efforts have been taken to improve the blast resistanceof ships since WWI, for the devastating effects of underwater ex-plosions. The early measures taken include reinforcing the hull orbuilding multi-layer hull such as in “Julio Caesarea” Italy, 1938and “Iowa” USA, 1943. Their typical mine-blast protection solutionsprovided protection from the underwater explosion of 300–400 kgof TNT. Even though, very complex engineering constructions wereneeded and a big volume occupied. In addition, unmanned spacewas also needed at the range of 5–6 m. Such inconvenience pre-vented further use of this kind of techniques in modern ships.

Surface coating on the hull with homogeneous elastic mate-rial or visco-elastic rubber is another possible means explored.Kwon et al. (1994) studied the effects of surface coatings on metalcylinders in an underwater explosive environment. Their researchworks show that surface coatings appear to concentrate shock en-ergy under certain impact conditions. A threshold value for coatingstiffness may be determined for a particular application. Above thistheoretical value, a favorable dynamic response of a coated cylin-der to an underwater explosion will occur; but below this value,an adverse dynamic response will occur. More detailed researchby Brasek (1994) on one-dimensional system demonstrates thatthe threshold value may depend upon the geometry and materialproperties of both the coating and the structure. In elastic regime,

* Corresponding author. Tel.: +(86)02154744481-231.E-mail address: chenyong@sjtu.edu.cn (Y. Chen).

0997-7538/$ – see front matter © 2008 Published by Elsevier Masson SAS.doi:10.1016/j.euromechsol.2008.10.003

Gong and Lam (2002, 2006) presented some analyses on attenua-tion of floating structures response to underwater shock and someinsights on the improvement of floating structures to enhance theirresistance to underwater shock were deduced. Cichocki (1999) alsopresented some results of a study concerning the protective capac-ity of containment structures subjected to underwater explosion ofa spherical charge.

In recent a few years, sandwich structures were found to be ca-pable of increasing the total anti-blast resistance. Their dynamicperformance subjected to air and underwater shock became a hottopic. Parallel studies by Xue (Xue and Hutchinson, 2003) andFleck (Fleck and Deshpande, 2004) demonstrated that sandwichbeams have superior shock resistance to monolithic ones. By com-paring three core geometries: pyramidal truss, square honeycomband folded plate, Xue (Xue and Hutchinson, 2003) concluded that awell-designed sandwich plate can sustain significantly larger blastimpulses than a solid plate of the same weight. More detailed re-search works on the topic can be found in papers of Xue (Xueand Hutchinson, 2003), Hutchinson (Xue and Hutchinson, 2006),Rabczuk et al. (2004) Radford et al. (2006), Liang et al. (2007), Weiet al. (2007), McMeeking et al. (2008) and so on.

These research works shows that the good blast resistance ca-pability of sandwich lies mainly in two aspects: Its good deflectioncapabilities provide volume to expand explosion gases and de-crease the shockwave pressure; the progressive damage mode andenergy absorbing mechanism of core permit relative small defor-mation of inner face plate. Especially, if the blast medium is water,the former advantage may become more prominent. Xue (Xue andHutchinson, 2003) and Fleck (Fleck and Deshpande, 2004) esti-

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mated the momentum transmitted into a sandwich plate usingthe Taylor analysis for a free standing front face sheet and drawvery optimistically conclusion. The fluid–structure interaction canreduce the momentum imparted to a sandwich plate by almosta factor of two relative to that imparted to a solid plate of thesame weight. Later Rabczuk et al. (2004) investigated the responseof sandwich beams subjected to underwater shocks by performingfully coupled FE fluid–structure interaction simulations. Makinen(1999) employed a one-dimensional finite difference scheme toinvestigate the fluid–structure interaction of polymer foam coresandwich beams with composite face sheets. These calculationssuggested that the benefits of employing sandwich constructionfor shock mitigation applications might be overestimated by theanalysis of Fleck (Fleck and Deshpande, 2004) and Xue (Xueand Hutchinson, 2003). More recently, Deshpande (Deshpande andFleck, 2005) made a deeply investigation on the one-dimensionalshock response of sandwich plates subject to an underwater pres-sure pulse. Both the propagation of an impinging acoustic shockwave within the fluid, and the propagation of a plastic shock wavewithin the sandwich core were accounted for. His analysis con-cluded that: (a) the momentum transmitted into the sandwichplates was substantially lower than that into a monolithic plateof same mass. (b) For a given core relative density, a smallerfraction of the shock impulse was transmitted into the sandwichplates with the bending-governed cores, which have lower com-pressive strength. Liang et al. (2007) elucidated two types of sand-wich response and labeled them as strong core and soft core typeresponses. Liang et al. (2007) suggested that the optimal perfor-mance of sandwich beams was attained for soft core designs. Itshowed that a core with a lower transverse strength reduced thetransmitted impulse more greatly during the initial FSI stage.

Though very promising in energy absorbing, the sandwichstructure with metal core is designed mainly to resist the contactor near-field explosions that are very powerful. The unrecoverabledeformation induced by shock wave often inevitably leads to highcosts and long cycle for repairing. But for far field explosions, theequipments are often more vulnerable than the hull structure. Un-der this condition, the protection capability of the metal sandwichseems limited for its compressive strength may be too large. Eventhough, the fact that the sandwich with soft core can lower themomentum transmitted to the hull seems very attractive. With aneye on this, the idea that coats ship hull with a layer of soft poly-mer is explored in this paper. The polymer coating is designed tobe shaped and sized to conform to the entire wet hull surface.Once impinged by the water blast waves, the coating can deformlargely and provide the desired shock mitigating and absorbing ca-pabilities. Aimed at the actual performance of polymer coating,a stiffened metal box is manufactured as testing platform. The wa-ter blast responses of the box before and after a layer of polymeris coated on its outer hull are measured and compared.

The outline of the paper is as follows: First, the geometry ofthe tested model and the polymer coating are introduced. Thenthe material characteristics and the quasi-static compressive be-havior of the coating are presented. In succession, the proceduresof the live fire tests are described in detail, including both measur-ing methods and instrumentations. Based on test results, extensiveanalysis are made on both shock responses and water pressure his-tories. Finally, some assessments are made on the performance ofthe polymer coating.

2. Experimental research

Our basic research scheme is to compare the shock responses ofa floating scaled metal box before and after coating a layer of poly-mer onto its outer hull when subjected to equal blasts loads. Aslong as consistent loading conditions are guaranteed, assessments

Fig. 1. Base structure and geometry of the metal box, named model I for conve-nience.

on the performance of the polymer coating can be made. Thoughmany other methods could be used to investigate the coating per-formance such as impact shock testing, the live fire test method isadopted because the fluid–structure interaction can be fully con-sidered. The bulk cavitation and other surface effects can also beconsidered as the floating box model is used. The box is designedas simple as possible, but it must have enough strength to with-stand the shock wave and keeps stable floating state once migratedby the upward expanding bubble.

2.1. Target scaled models

The base structure of the target model is a stiffened metal box,as shown in Fig. 1. Its main body is an open welded metal box withglobal dimensions 2 m×1 m×0.7 m. All the outer plates are madeby 10 mm thick mild steel plate except two side plates at bothends, which are 12 mm in thickness. The bottom and side platesare reinforced by one longitudinal and three transverse stiffeners.All stiffeners are made by 10 mm thick hot rolled steel sheet. Themetal material used is the common mild steel A4, with yieldingstress beyond 250 MPa. The total mass of the box including allaccessories is about 800 kg. Two steel cylinders, each weighting16 kg, are welded at both bottom ends by angle irons. As counter-weights, the cylinders can lower the mass center of the wholemodel. This is very helpful in keeping balance when migrated bythe expanding bubble.

For convenience, we refer to the metal box without polymercoating as model I, and name it model II once its outer hull be-neath waterline is covered with polymer coating. The coating isenvisaged as a protective layer that can be used on surface ship orfloating platform to mitigate the shock energy produced by under-water explosions. The other potential advantage may be its goodsound isolation capability, which is very helpful for the acousticstealth of ships. The model after coated with polymer layer (i.e.model II) is shown in Fig. 2. The sooty parts indicated by the whitearrowheads are just the polymer coatings.

2.2. Geometry of the coating

Sixteen pieces of polymer coatings are plastered onto the outerhull with epoxy resin glue. The geometry of a single piece ofcoating is shown in Fig. 3. Its global dimensions are 500 mm ×600 mm × 42 mm, divided by 4 mm thick vertical walls into six-teen segments along the longitudinal direction and eight alongthe transverse direction. The coatings are molded wholly piece bypiece beforehand. The basic material is neoprene with shore hard-ness number 65. The neoprene is a kind of synthetic rubber with

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Fig. 2. Test model with coated polymer layer, named model II for convenience. Theblack tiles pointed by white arrowheads are polymer coating. Altogether sixteenpieces, four pieces on the bottom and twelve on the four sides, are plastered onthe outer hull. The gaps between neighboring pieces are filled with asphalt to keepsmoothness.

good flexibility and wearability that is produced by polymerizationof chloroprene. To enhance the strength and toughness, the outerface sheet is strengthened by interwoven nylon lines as that in au-tomobile tire. Fig. 4 shows the stress-strain curves of three kindsof neoprene with different hardness. Both tensile and compressivebehaviors are included. The materials exhibit excellent flexibilityas the tested specimen can be elongated up to 300% without anyvisible damage.

Besides the mechanical properties of the base material, knowl-edge about the dynamic compression behavior of the coating fa-cilitates the comprehension on its performance in underwater ex-plosion environment. Unfortunately, a single piece of coating is solarge that it is very difficult to test a whole piece directly on com-mon material test machines. As a substitution, a small piece ofcoating together with the steel plate is cut from the box after livefire tests has been finished. The dimensions of the cut specimen is250 mm × 250 mm as shown if Fig. 5. It contains five longitudinaland three transverse cells. The uni-axial compression test is per-formed on a 100 KN Zwick general material test machine. Duringtests, the specimen is clamped between two thick circular plates.Only quasi-static compression test is performed. The compressionvelocity is selected as 10 mm per minute. Fig. 5 presents the com-pressive stress-strain curve. Three distinct stages can be observed:at small strains (<12%) the specimen deforms in a linear elasticmanner due to cell wall bending. The next stage is a plateau ofdeformation at almost constant stress around 1 Mpa, caused bythe elastic buckling of the cell walls. Once the nominal strain ex-ceeds 70%, the densification region begins, where the cell wallscrush together, resulting in a rapid increase of compressive stress.

2.3. Underwater explosion tests

Two groups of contrastive live fire tests are conducted in orderto compare the shock responses of models I and II to identical blastloads. All tests are conducted in an artificial lake that is 15 metersin depth and 60 meters in diameter. As shown in Fig. 6, the modelsare located in the middle of two interconnected floating platforms,which are supported by two buoyancy tanks and used to placeinstruments. The explosive device is fixed by the nylon cords thatare fastened on the platforms. By adjusting the length of the cords,the explosive can be fixed at a scheduled position.

The explosive devices are constructed from common TNT, endinitiated with an exploding bridge wire detonator. The TNT is fab-ricated in the shape of a right cylinder formed by pressing it intoa hollow tube constructed from PMMA. All experiments are de-signed to detect the response of the models to loadings from boththe shock wave and the bubble pulse. For consistency, altogetherseven events are attempted at the same stand-off 5 m, three timesfor model I and four for model II, respectively. Only in one case,the target is split by the load at the position of the accelerometermount; the other six events are all well recorded.

2.4. Instrumentation

Three PCB 138A05 pressure transducers, linear within 2% up to35 MPa, are used to monitor water pressure. As indicated in Fig. 7,one transducer (P1), monitoring the free field pressure change, issuspended from the corners of the support platform at the depthof 5 m and kept 3 m away from the explosive center in horizon-

Fig. 4. Stress–strain curves of several kind of neoprene.

Fig. 3. Detailed geometry of the rubber coating.

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Fig. 5. Quisi-static compressive behavior of the cut specimen.

Fig. 6. Underwater explosion tests.

Fig. 7. Sketch of the measurement system and locations of pressure transducers.

tal direction. The other two transducers (P2 and P3) are placed tomonitor the pressure fluctuation near the fluid–structure interface.Both P2 and P3 are suspended in the water right beneath the bot-tom hull as shown in Fig. 7. P2 is just located below the centerof the model and P3 0.9 m distant from P2 in the horizontal di-rection. For both models, the wall pressure transducers are 40 mmvertically distant from the wet surface of the bottom.

Five accelerometers and six strain gauges are used to monitorthe shock responses of the main structure. All measurement pointsare distributed on the inner bottom hull and stiffeners. Fig. 8 de-

Fig. 8. Locations of accelerometers (bottom view).

Fig. 9. Locations of strain gauges (bottom view).

picts the positions of the accelerometers, viewed from the bottomview. Since the bottom plate is divided into eight lattices by thecrossed stiffeners, A2 is just mounted at the center of the bottomplate; A1 and A3 are located near the intersections of the stiffen-ers. All accelerometers mounted on stiffeners are used to measureglobal motions of the box. A5 is the only one mounted at the cen-ter of a lattice to measure the local motion. The accelerometersused are B&K 4393 piezoelectric accelerometers that have a maxi-mum operational shock range of ±25 000 g, with upper frequencylimit 16.5 kHz. In order to avoid overloading, all accelerometersare fixed at aluminum adaptors that are used as mechanical filters,with cut-off frequency around 3 KHz.

Unlike accelerometers, most strain gauges are used to mea-sure the local deformations. All gauges are of resistance style, with350 ohm resistance. Their locations are indicated by the little solidsquares in Fig. 9. Four bidirectional gauges are on the hull plates(S1, S2, S3 and S4) and two unidirectional ones on stiffeners (S5,S6). S1 and S4 are just located at the center of a lattice; S2 andS3 are 60 mm distant from the neighboring stiffeners. S5 and S6are located perpendicularly nearly at the center of the bottom. Al-together ten signal channels are used to record strain.

A suit of 32-channel Odyssey high speed data recording de-vice is used to record all electrical signals for a period of 300 msafter detonation of the explosive. Data are recorded with a maxi-mum sampling frequency of 1 MHz/Ch and 12 bit resolution. The300 ms recording span is sufficient to include both the shock wavephase and the first bubble collapse of 1 kg charges. The selectedsampling rate is 10 KHz/Ch and 20 KHz/Ch, respectively for ac-celeration and strain records. The maximum 1 MHz sampling rateis selected for the pressure records. Altogether 18 channels arerecorded at the same time. The filter band for pressure is 100 kHz,and 5 kHz for strain and acceleration records, respectively.

3. Results and discussions

Test results are presented in three sections. We begin with adetailed analysis on the pressure records to distinguish blast loads,and explore the fluid–structure interaction as well as the wave re-flection characteristics with different targets. This is followed by adetailed presentation of the target responses to the shock loads intime domain, including both the acceleration and strain histories.The shock response spectrum (SRS) analysis is also made in orderto comprehend the coating performance in frequency domain.

3.1. Pressure-time profiles

The typical free field pressure recorded by P1 in test event 1is shown in Fig. 10. For definition, the shock wave within 1 ms is

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Fig. 10. Free field pressure history of P1 (test case 1): pressure record within 250 ms including both the shock wave and the bubble pulse and shock wave within 1 ms ismagnified.

Table 1Valid experimental events.

EnventNo.

Model Charge stand-off(m)

Charge size(kg)

P1(MPa)

P2(MPa)

P3(MPa)

1 I 5 1 8.47 8.23 8.352 I 5 1 8.59 8.70 8.743 I 5 1 8.44 8.59 8.414 II 5 1 8.28 8.62 8.585 II 5 1 8.39 8.26 9.016 II 5 1 8.67 8.64 8.62

magnified. It can be seen that the incident shock wave arrives at0.2 ms, with peak pressure of 8.47 MPa, and then decays rapidlywithin 0.3 ms. The following first bubble pulse arrives at about210 ms, with broader profile and lower peak (1.63 MPa). The reflec-tion wave from the structure can be distinguished, arriving at P1about 7.3 ms after the shock wave. The time corresponds to thetraveling distance of about 10 m, double the standoff distance. Ta-ble 1 lists all the pressure peaks recorded at P1 in different events.It is shown that the pressure peaks range from 8.28 MPa (event 4)to 8.67 MPa (event 6). The bias within 5% demonstrates that theexplosion processes are very consistent, which ensures that the fol-lowing comparisons are authentic.

Fig. 11 compares the typical wall pressure recorded at P2 andP3 in event 1 and 4, respectively for model I and II. For the recordsof model I, several distinct phases including incidence, cavitationand reflection, can be observed. The whole process begins with thedirect shock wave from the explosive, which is followed almost im-mediately by a tension wave produced by the onset of cavitation at

the hull bottom, and later the first reflective wave. The subsequentbroad pressure wave indicates the repeating elastic deformation ofthe outer hull.

Both the incidence and cavitation phases can be identified forthe records of model II. But compared with that of model I, thereflective signal of model II is much smaller and more faded. Thisis mainly attributed to the lower reflective characteristic of poly-mer coating compared with that of sole metal. Another distinctdifference between the records of both models is that the cavita-tion for model II takes place much earlier than that for model I,which results in much narrower time span of the first incidentshock wave. The negative pressure for model II is also lower thanthat for model I. This should be attributed to the soft core, whichdeforms much easier and faster when the shock wave impingesthe face sheet. As the face sheet moves immediately on the ar-riving of incident wave, the fluid–structure interaction mechanismchanges and the reflection is greatly reduced. Note that the totalpressure is the sum of both incident and reflective wave, the to-tal impulse induced should be reduced. This phenomenon verifiesthe conclusion drawn by Deshpande and Fleck (2005). In view ofthe fact that the rubber core is softer than the metal core, the re-duction effect may be more outstanding. As a comparison, Table 2lists the total impulses and time spans of the first incident wavesbefore cavitation takes place. The total impulses are numericallyintegrated from the pressure histories. It is shown that the aver-aged time span is reduced from 26 ms to 14 ms, and the averagetotal impulse is reduced from 84.05 N s to 36.75 N s by almost 56%after the polymer being coated. As a result, lower structure re-sponses excited by the shock wave are anticipated.

(a) (b)

Fig. 11. Wall pressure comparison between two models: (a) P2, event 1 and event 4; (b) P3, event 1 and event 4.

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Table 2Comparison between the wave crest of both models.

Test No. Impulse (N s) Time span (μs)

Model I Model II Model I Model II

1 (4) 81.61 34.91 27 152 (5) 87.31 37.08 24 133 (6) 83.22 38.27 26 14Average 84.05 36.75 26 14

3.2. Acceleration and velocity records

The details of the center mounted accelerometer (A2) responsesof model I (event 1) and model II (event 4) are shown in Fig. 12.Abrupt jump of signal at the instants corresponding to the shockwave arrival and the first bubble pulse indicates that the targetsrespond to loads from both of these events. Comparing the tworecords, it can be found that the initial acceleration peak drasti-cally reduces from 7619 g to 693 g after the polymer is coated.The acceleration peaks induced by the fist bubble pulse is also re-duced from 201 g to 102 g. In addition, it can be seen that thereexists more high-frequency components in the record of model Ithan that of model II, which will be verified by the later spectraanalysis.

The time histories of velocity at point A2 of both models ob-tained by numerical integration of acceleration records are plot-ted in Fig. 13. Like acceleration records, the velocity histories can

also be divided into the shock wave and bubble pulse phases. Formodel I, velocity achieves the maximum 4.67 m/s immediately af-ter it is impinged by the first incident shock wave. For model II,the velocity achieves the maximum 1.79 m/s within 6.25 ms. Thepeak of model II is much less than that of model I, which provesthat the maximum kinetic energy of the structure is decreased af-ter the polymer is coated. It is consistent with the total impulsereduction conclusion drawn in Section 3.1.

After a few cycles of motion, the instantaneous velocities ofboth models decrease to zero almost at the same time about65 ms. After then, both models move in the opposite directiondue to the contraction of the bubble. From the moment about150 ms, the velocities of both models increase again with the sec-ond expansion of the bubble. Model I achieves another peak at204.8 ms while model II at 217 ms. Compared with that in thefirst shock wave phase, the difference between the velocity peaksof the two model reduces greatly from 2.88 m/s to 0.21 m/s. Thisphenomenon is attributed to the fact that the loading of fluid ismainly from the retarded flow of water and not the wave dur-ing the bubble pulse phase. Because of the much smaller magni-tude of loading, the deformation of the coatings in this stage isgreatly reduced. As a result, the difference between two models ismuch smaller compared with the loading phase of the first shockwave.

Table 3 lists the peaks of the acceleration, velocity and displace-ment at location A2 of both models in all six events. The average

Fig. 12. Comparison between typical acceleration histories of both models at location A2 (for event 1 and 4).

Fig. 13. Comparison between velocity histories of both models at location A2 (events 1 and 4).

Y. Chen et al. / European Journal of Mechanics A/Solids 28 (2009) 591–598 597

Table 3Comparisons between acceleration, velocity and displacement peaks at location A2.

Test No. Acceleration (g) Velocity (m/s) Displacement (mm)

Model I (without coating)/Model II (with coatings)

1/4 7619/693 4.67/1.79 85.2/89.32/5 7595/694 3.35/1.74 92.1/97.93/6 8262/689 4.72/1.77 93.4/95.0Average 7825/692 4.25/1.77 90.2/94.1Ratio 11.31 2.40 0.96

values of the respective three events corresponding to each modelare also presented. Though there are some differences in the differ-ent events of each model, the basic trends are consistent that afterthe polymer is coated, the average acceleration peak is greatly re-duced from 7820 g to 692 g. The ratio between the average peaksof the two models reaches 11.3. As expected, the average veloc-ity peak is also reduced from 4.25 m/s to 1.77 m/s, and the ratiois 2.4. It is a little surprising that the average displacement is notreduced. On the contrary, it is increased slightly from 90.2 mm to94.1 mm. This is perhaps attributed to the fact that the global dis-placement of structure is mainly controlled by the bubble motion.As indicated by the velocity curves, the polymer coating does notplay an evident role during this phase.

3.3. Shock response spectrum analysis

The SRS analysis is an effective measure in understanding thefrequency components of the dynamic response of the structuresubjected to the shock input. The pseudo velocity shock responsespectra from the acceleration at A2 in events 1 and 4 are plottedin Fig. 14. The analysis frequency band is between 1 Hz and 4 kHz.Both the positive and negative spectral curves of each model aredisplayed. But the curves are approximately coincident, which in-dicates that the acceleration records are in good condition and nosaturation or zero drift occurs.

It can be seen that within the frequency band lower than 50 Hz,the difference between spectra velocities of two models is verysmall. The frequency band between 15 Hz and 50 Hz is magnifica-tion region. Several peaks corresponding to 5, 9, 15 and 19 Hz keep

almost unchanged after the polymer is coated. This demonstratesthat after the polymer is coated, the low order eigen-frequency ofmodel I had not been changed, at least in low frequency band.On the other hand, a prominent difference can be observed in fre-quency range higher than 50 Hz. In high frequency band, there isdistinct reduction of SRS value after the polymer is coated. Thehigher the frequency, the more obvious the attenuation effect isrevealed. As an analogy, it can be concluded that the elastic coat-ings perform like a low pass filter with cutoff frequency at about50 Hz. Response components higher than the cutoff frequency canbe attenuated effectively, but for components lower than the cut-off frequency, the attenuating effect is small. The cutoff frequencyis a critical parameter, which should be determined mainly by themass of the main structure and the stiffness of the coating, espe-cially that of the core.

Shock response spectra corresponding to the other accelerom-eters are not presented since the basic trends are consistent thatthe protective effect of rubber coatings at high-frequencies is moreobvious than that at low-frequencies.

3.4. Strain records

Strain records within 300 ms recorded at S1 by events 1 and 4are shown in Fig. 15. Like acceleration and velocity histories, re-sponses induced by both the shock wave and the bubble pulse canbe seen clearly. In addition, the same phenomenon is also observedthat the strain peaks induced by the shock wave are attenuatedgreatly after polymer is coated, but in the bubble pulse phase thedifference is small.

Table 4 lists all strain peaks measured by strain gages at S1to S6 in all events. The average values of each model are alsopresented. It is shown that values at all measurement points aredecreased to a great extent. The last column of Table 4 lists the ra-tios between the averaged values of two models. The ratios rangefrom 2.4 to 3.7, which proves that good attenuation effect canbe obtained by the polymer coatings. Observed from the differentmeasurement locations, the values of gauge S1 and S4 are muchlarger than that of other gauges, regardless whether the polymeris coated or not. This fact indicates that the attenuating effects of

Fig. 14. Pseudo velocity shock response spectra of two models (measurement location A2, events 1 and 4).

598 Y. Chen et al. / European Journal of Mechanics A/Solids 28 (2009) 591–598

Fig. 15. Comparison between the strain records of the two models.

Table 4Strain peaks of all gages in different test cases.

Gauge TestNo. 1

TestNo. 2

TestNo. 3

AverageI

TestNo. 4

TestNo. 5

TestNo. 6

AverageII

RatioI/II

S1-X 1463 1237 1464 1388 503.7 477.6 448.3 476.4 2.9S1-Y 1304 1149 1312 1255 470.9 470.4 431.4 457.6 2.7S2-X 196.8 253.4 199.1 216.4 75.1 77.3 61.8 71.4 3.0S2-Y 285.7 340.2 329.7 318.5 89.6 84.7 82.3 85.5 3.7S3-X 349.5 366.1 396.2 370.4 117.9 108.9 110.6 112.3 3.3S3-Y 202.3 177.4 134.1 171.3 60.4 51.8 48.6 53.6 3.2S4-X 1478 1292 1349 1373 505.4 497.2 456.7 486.4 2.8S4-Y 1151 1115 1053 1106 437.8 389.9 374.3 400.7 2.7S5 347.3 367.8 187.8 300.9 157.4 87.6 98.1 114.4 2.6S6 869.2 703 852.5 808.2 377.6 324.5 291.4 331.4 2.4

the coatings are global in nature, not just restricted to local areaof the protected structure. Combined with the discussion on theacceleration records in Section 3.1, it can be concluded that thepolymer coatings show good protective effects especially for thefirst shock wave.

4. Concluding remarks

This paper experimentally explores the attenuating effects andmechanism of a layer of hollow polymer coated onto the hull offloating structure subjected to water blasts. It is seen from thetest results that the structure shock responses induced by thefirst shock wave can be lowered greatly after the polymer layer iscoated. Wall pressure recorded near the bottom hull also approvesthat the soft core can substantially reduce the transmitted impulseduring the initial fluid–structure interaction stage, which is verybeneficial for the protection of the water blast loaded structures.Further shock response spectrum analysis indicates that the coat-ing performs as a low pass filter with cutoff frequency at about50 Hz. The attenuating effect higher than 50 Hz is distinct, but forresponses lower than 50 Hz, the effect is neglectable.

In future work, detailed numerical analysis is necessary on thedynamic compressive behavior of the rubber honeycomb core. Thegeneral relationship between the core compression behaviors andthe protective capabilities of the coating also needs to be illumi-nated.

Acknowledgements

The authors would like to thank the National Natural ScienceFoundation of China for financially supporting this research underthe contract No. 10672181.

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