(China Ship Scientific Research Center,Wuxi 214082,China)

Comparative Studies of the Transverse Structure Design Wave Loads for a Trimaran by Model Tests and Rule Calculations

WANG Xue-liang,HU Jia-jun,GU Xue-kang,GENG Yan-chao,XU Chun

(China Ship Scientific Research Center,Wuxi 214082,China)

It is very important to obtain the cross structure design wave loads of a trimaran for its transverse strength in structure design.In order to study the cross structure design wave loads of a trimaran,its model test was performed in a seakeeping tank.The model test conditions were composed of regular and irregular waves in head and quartering seas.Splitting moments Msp,splitting shear forces Qsp and transverse torsional moments Mtt of the cross structure were measured in model tests.RAOs and statistical properties were analyzed in detail.According to analysis of the cross structure wave loads from model tests,deductions and rule calculations,the full amplitude wave height to the calculation of those transverse wave loads might be 6.0 meters in LR rule.To different transverse wave loads,the extrapolated result of design wave loads with dependability 99%of transverse torsional moments Mtt was greater than that from rule calculation.However,the deductions of splitting moments Msp and splitting shear forces Qsp accorded with rule calculations.It can be concluded that the evaluation methods from LR rules are some nonconservative for the cross structure design of transverse torsional moments Mtt.This should be paid some attentions to ship designers in particular.

trimaran;cross structure;design wave load;rule;model test

Biography：WANG Xue-liang(1977-),male,Ph.D.student,senior engineer of CSSRC.

1 Introduction

Different from traditional monohull ship,trimaran will be exposed to transverse wave loads except for longitudinal wave loads when traveling at sea because of the existence of cross structure of this kind of ship.These transverse wave loads include splitting moments Msp,splitting shear forces Qsp and transverse torsional moments Mtt.There will have interaction from water between side hulls and main hull.Furthermore,the fluid force acting on a side hull will transfer to the main hull by cross structure.Then a trimaran will be exposed to different wave loads comparing to those of monohull ship when traveling at sea.

The measurement of wave loads of a trimaran should be given key consideration of the particularity of cross structure because of the different type of wave loads.The proper measurement method of transverse wave loads should be studied to Msp,Qsp and Mtt.And the wave loads measuring system should be designed to match this method.Wang(2009)[1]had given a further study on the measuring method of a trimaran wave loads.

John Hampshire et al(2004)[2]had taken a wave loads model test of a RV TRITON trimaran in the Ocean Basin at QinetiQ Haslar(UK).The model was divided into five segments along its length of the main hull and two segments in each side hull.A beam of varying stiffness connects both the main hull and side hull segments.The side hulls were attached to the main hull by two beams,one for each segment.The transverse wave loads which had been measured in model tests were vertical moments,vertical shear forces,horizontal moments,horizontal shear forces and torsional moments.

Kennell(2004)[3]had taken a model test of a high speed strategic sealift trimaran in David Taylor Model Basin(USA).The main hull of the model was converted into a six-segment hydrodynamic loads model using a calibrated beam or back-spline that linked together the segmented main hull.Segment breaks were at stations 4,7,10,13,and 16.Stations 4 and 16 were instrumented to measure vertical and lateral bending moments,torsional moments,and vertical and lateral shear forces.Stations 7,10,and 13 were instrumented to measure vertical and lateral bending moments only.Side hulls were connected to the cross structure through load cells to allow measurement of side hull bending,shear,and torsion.

Lloyd’s Register had its corresponding design wave loads rules for the classification of trimarans[4].The splitting moments,splitting shear forces and transverse torsional moments were given as provisions to cross structure of trimarans.

Dai et al(2007)[5]had pointed out that the ship design wave loads were determined by three principles:rationality,uniqueness and simplicity.Thus these three principles can be used to judge which value was suitable when ship designers use LR rules or model tests to determine the design wave loads.LR rules were used to evaluate the design wave loads of cross structure for a trimaran in this paper.And the evaluating values were compared and analyzed with model tests and their extrapolated values from Ochi[6]method.Then the applicability of LR rules to evaluate the design wave loads of cross structure for this trimaran was clear.The study result had certain significance to structural design of the same type trimaran.

2 Model tests and results analysis of a trimaran for its cross structure

This kind of trimaran had a high cruising speed and two side hulls located in post median of the main hull.The cross structure connected the main hull and two side hulls.The characteristic of this ship form made trimarans had a good seakeeping performance.The preconcerted service area of this trimaran had the wave height for cumulative distribution which was shown in Fig.1(introduced from reference[7]).It can be seen from this figure that waves took 71 per-cents within 2.5 meters height,91 percents within 4.0 meters height and 98.5 percents within 6.0 meters height of all waves.

Fig.1 Wave height for cumulative distribution of preconcerted service sea area

2.1 Model feature

The test model of this trimaran was made by fiber reinforced plastics(FRP),and its main parameters were shown in Tab.1.In order to measure the longitudinal and transverse wave loads in different traveling status,segment breaks were at stations 4,8.5 and 13,see Fig.2.Beam stiffness at each segment break corresponded to that of the main hull.Thus the testing beam was a varying stiffness one along the main hull.Each side hull was cut into two segments at station 4 and was connected by a short beam.On the other hand,each side hull was attached to the main hull by a uniform beam which located at station 4.5.The height directions of these two beams were located in the center of gravity of each side hull.The measurement contents,methods and the locations in detail were presented in Tab.2.Thus,seven beams totally constituted the whole measuring frame of wave loads.

Tab.1 Main parameters of a trimaran model

Fig.2 Sketch map of the segmented model an their measuring beams

2.2 Model tests and data analyses

In order to give the comparison of model results and rule calculations,the testing states with speed 2.124m/s,wave height 131.6mm and heading sea 135°,90°and 45°in regular waves were performed.RAOs ofMsp,QspandMttin these states were shown in figures 3 to 5.And the results in irregular waves would be analyzed in next section’s comparisons.

From Fig.3 it can be seen thatMspwas bigger in beam wave than that in oblique wave.However,it was difficult to obtain theMspvalues in shorter wave lengths because of the limitation of wave making ability.The peak value ofMspin heading oblique waves was greater than that in following oblique waves,and the peak of responses located at the ratio of wave length to ship length being about 0.9.

It can be seen from Fig.4 thatQsphad the similar current toMspfor their relationships to wave direction.But the peak value in oblique waves moved to the direction to big ratio of wave length to ship length and some hypo-peak values appeared.

Fig.5 showed the RAOs of transverse torsional momentsMtt.It can be seen that the peak of RAOs curves had the highest value in following oblique waves,and there had the middle peak value in heading oblique waves,and the smallest peak value appeared in beam wave.Similar-ly,it was also difficult to obtain theMttvalues in shorter wave lengths because of the limitation of wave making ability.

Fig.3 RAOs of splitting moments

Fig.4 RAOs of splitting shear forces

3 Extrapolated design loads

According to Ochi methods,if the main short term statistics of wave loads had been obtained and their peaks obeyed the Rayleigh distribution,the short term extreme value γnof loads was given by the following formula.

Fig.5 RAOs of transverse torsional moments

where,α=probability that short term extreme value exceeds a specified value;n=number of observations;m0=area under spectral density function of loads responses.

It was generally taking α as 0.01 to global design loads.The extrapolated results denoted the likely encountered maximum of loads under a wind wave with 99 percents probability guarantee.

4 Rules calculation of design wave loads

LR rules for trimarans had defined the splitting momentsMspwhich was showed in Fig.6.MsphandMspswere according to moments of hogging and sagging respectively.And the corresponding locations were pointsIandO.In order to have the right comparison with model tests values,pointIwas chosen to calculate the splitting momentsMspin this paper.Furthermore,restrictions such as cruising speed and service sea area should be concluded in rules calculations.

5 Comparison analyses of design wave loads

Fig.6 The definition of splitting moments Msp

The comparison among cross structure wave loads from mod-el tests,extrapolation and LR rules were given in Tab.2.Here the sea states were heading oblique wave with the ratio of wave length to ship length 0.9,1.0 and 1.1,and wave height had different full amplitudes 2.5m,4.0m and 6.0m,and the speed was 2.124m/s,and the wave direction was 135°.Meanwhile,the model tests results and the extrapolated results corresponding to the significant wave height 2.5m and 4.0m in irregular waves were also given in Tab.2.

Tab.2 Comparison among cross structure wave loads from model tests,extrapolation and LR rules

From Tab.2 it can be seen that transverse wave loads of cross structure had a nonlinear increasing current with the wave height increment.As to the three regular wave lengths(λ/L=0.9,1.0 and 1.1),the nonlinear phenomena were not so much clear,and the reason might be the rather short distance among these three wave lengths.Mspin state with λ/L=1.0 and wave height 6.0m corresponded with the rules calculation.Qspin state with λ/L=0.9 and wave height 6.0m corresponded with the rules calculation.Mttin state with wave heights 2.5m to 4.0m corresponded with the rules calculation.On the other hand,the model tests results in irregular waves had an inapparent asymmetry of hogging and sagging parts of moments.And this might be caused by the lack of simulation of the whole wet deck of this trimaran,and thus it would result in the difference of hogging and sagging parts of cross structure wave loads became small.Rule calculations ofMspandQspwere bigger than those from model tests.This showed that the corresponding significant wave heights to rule calculations ofMspandQspshould have a bigger value than 4.0m.Comparing the extrapolated results to model tests results in irregular waves,the extrapolated results ofMspandQspcorresponded to those from rule calculations with significant wave height 4.0m and 2.5m to 4.0m,respectively.However,the extrapolated results ofMttwas greater than those from rule calculations with significant wave height 2.5m.

6 Results

Study of the cross structure design wave loads for a trimaran in regular and irregular waves using model testing method is presented in this paper.And the extrapolated results of these transverse wave loads were given using some model testing results in irregular wave.Evaluation of these transverse wave loads of a trimaran using LR rules was also performed in this paper.From the comparison among the above model testing results,extrapolated results and rule calculations,some valuable results were obtained:

(1)Mspwas bigger in beam wave than that in oblique wave.However,it was difficult to obtain theMspvalues in shorter wave lengths because of the limitation of wave making ability.The peak value ofMspin heading oblique waves was greater than that in following oblique waves,and the peak of responses located at the ratio of wave length to ship length being about 0.9.

(2)The transverse wave loads of cross structure had a notable nonlinearity to wave heights.These transverse wave loads from LR rule calculations might correspond to the regular wave height(full amplitude)6.0m.

(3)The inapparent asymmetry of hogging and sagging parts of moment from rule calculations was much more notable than that from model test results.It might be caused by more considerations of nonlinear features of these cross structure wave loads.

(4)For different type of transverse wave loads,the extrapolated value with 99 percents probability guarantee to transverse torsionalMttwas greater than that from rule calculations.However,the extrapolated value of splitting momentsMspand splitting shear forceQspwere corresponding to that from rule calculations.It indicates that the evaluation methods from LR rules are nonconservative for the cross structure design of transverse torsional momentsMtt.

[1]Wang Xueliang.Study report of the technology for wave-induced loads testing of catamarans and trimarans[R].Wuxi:China Ship Scientific Research Center,2009.

[2]John Hampshire,Sarah Erskine,Neill Halliday,Magnus Arason,QinetiQ,Rosyth,UK.Trimaran structural design and assessment[C]//Design and Operation of Trimaran Ships.London,UK,2004.

[3]Kennell C,David Taylor Model Basin,USA.Model test results for a 55 Knots high speed sealift trimaran[C]//Design and Operation of Trimaran Ships.London,UK,2004.

[4]LLOYD’S REGISTER(LR).Rules for the Classification of Trimarans[S].2006.

[5]Dai Yangshan,Shen Jinwei,Song Jingzheng.Ship Wave Loads[M].Beijing:National Deference Industry Press,2007.

[6]Ochi M K.On prediction of extreme values[J].Journal of Ship Research,1973,17:29-37.

[7]Fang Zhongsheng,Jin Chengyi,Miao Quanming.Wave statistics of northwest pacific[M].Beijing:National Defense Industry Press,1996.

三體船橫向結(jié)構(gòu)波浪設(shè)計(jì)載荷試驗(yàn)與規(guī)范比較研究

汪雪良，胡嘉駿，顧學(xué)康，耿彥超，徐 春

（中國(guó)船舶科學(xué)研究中心，江蘇 無(wú)錫 214082）

三體船連接橋結(jié)構(gòu)波浪設(shè)計(jì)載荷的確定對(duì)結(jié)構(gòu)設(shè)計(jì)中關(guān)注的橫向強(qiáng)度問(wèn)題來(lái)說(shuō)是非常重要的。為了研究一艘三體船連接橋橫向波浪載荷，進(jìn)行了該三體船的水池模型試驗(yàn)，包含不同浪向下規(guī)則波與不規(guī)則波試驗(yàn)。試驗(yàn)對(duì)連接橋遭受的分離彎矩Msp、分離剪力Qsp和橫向扭矩Mtt進(jìn)行了測(cè)量，分析了其傳遞函數(shù)和統(tǒng)計(jì)的特性。根據(jù)對(duì)這些連接橋橫向波浪載荷在試驗(yàn)值、推斷值與規(guī)范計(jì)算值之間的比較分析表明：勞氏規(guī)范關(guān)于這些橫向波浪載荷的計(jì)算值可能對(duì)應(yīng)于規(guī)則波雙幅波高6.0m；對(duì)于不同的橫向波浪載荷來(lái)說(shuō)，保證率為99%的設(shè)計(jì)載荷推斷值對(duì)橫向扭矩Mtt來(lái)說(shuō)要大于規(guī)范計(jì)算值，而分離彎矩Msp和分離剪力Qsp的推斷值對(duì)應(yīng)的規(guī)范計(jì)算值則相當(dāng)，這意味著設(shè)計(jì)人員在用勞氏規(guī)范進(jìn)行校核時(shí)，橫向扭矩Mtt的規(guī)范計(jì)算值是偏向于冒險(xiǎn)的，應(yīng)給予特別關(guān)注。

三體船；連接橋；波浪設(shè)計(jì)載荷；規(guī)范；模型試驗(yàn)

U661.72

A

汪雪良（1977－），男，中國(guó)船舶科學(xué)研究中心高級(jí)工程師，博士研究生，研究方向?yàn)榇芭c海洋工程波浪載荷、結(jié)構(gòu)響應(yīng)與試驗(yàn)研究等，E-mail:wsnowolf@126.com；

徐 春（1980-），男，中國(guó)船舶科學(xué)研究中心工程師。

U661.72

A

1007-7294（2011）03-0269-07

date：2011-01-21

胡嘉駿（1965-），男，中國(guó)船舶科學(xué)研究中心研究員；

顧學(xué)康（1963-），男，中國(guó)船舶科學(xué)研究中心研究員；

耿彥超（1982-），男，中國(guó)船舶科學(xué)研究中心助理工程師；