Dynamic Characteristics of Complex Structure Under and Out of Water

Joural of Beijing Institute of Technology ,2003 , Vol.12 ,No.1Dynamic Characteristics of Complex Structure Underand Out of W aterFENG Hui-hus( 冯慧华)，LIAO Ri-dong廖日东)，ZU0 Zheng-xing(左正兴)，RONG Ke-li(荣克林尸( 1.School of Mechanical and Vehicular Engineering , Beiing Institute of Technology , Beijing 100081 , China ;2. Beijing Institute of Structure and Environment Engineering , Beijig 100034 , China )Abstract :To understand the dynamic characteristics of the whole period of a complex structure' s launching out of water ,on the basis of FEM formulations deduced for solving coupled fluid-structure problems with strong- coupled method , FEmodels used to simulate the structure surrounded with fluid domains are established. The modal experiment on the realstructure under shallow water shows great accordance with simulating results. Based on this verification , dynamic charac-ter parameters of all FE models simulating each phase of the structure' s launching out of water are abstracted with unsym-metric algorithm , which can comprehensively descibe the dynamic characters of the structure in its whole working pro-cess. Conclusions drawned from these calculations are scessfully applied in works of evaluating the structure' s perfor-mances and reliabilities.Key words : complex structure ; FEM ; structure-fluid coupling ; dynamic characteristicsCLC number :V414.1 .Document code :AArticle ID : 1004-0579( 2003 )01-0080-05The structure shown in Fig.1 , whose outer shell is aThis method has a relatively brief mathematical format andthin wall cylinder with sections different in thickness , be-the merit of requiring less computation cost ，thus it islongs to a complex revolving compound object. Based onwidely applied. But the precision the weak-coupledthe real working environment , dynamic characteristics ofmethod can reach is not high enough. The strong -coupledthe structure under shallow water and during each phasesmethod establishes motion equations of fluid and structureof launching out of water need to be understood. Owing toindividually , and synthetically solves the combined equa-its scale and dimension , completely relying on experi-tions with some kinds of the latest numerical techniques.ments is not economic ，even unexecutable ，numericalSo it could characterize the motion of fluid more exactly ,simulation techmiques must be introduced into the processand can reflect interaction between fluid and structureof investigation.more actually , therefore dynamic results of structure cou-front sectionmiddle sectionrear sectionpled with fluid acquired through this method are bound tobe close to the realities. In addition , with the developingof computer hardware and software as well as the improve-Fig.1 Contour of the structure to be studiedment of the numerical computing techmiques , consumingCalculating techniques for coupled fluid-structuretoo much of computer system resources , which used to beproblems can be divided into two categories : weak-cou-one of the chief defects of the strong coupled method , ispled method and strong- coupled method. For weak-cou-not prominent any more. It' s absolutely conceivable topled method , the fluid will be simplified so that its actionstud中国煤化工complex problems underon structure can be described as forms of fluid forces.concMYHC N M H G varying parameters. TheReceived 2002-05-21Biographies FENG Hui-hud( 1976 - ), doctoral student , fhbbit @ sina. com ; ZU0 Zheng-xinf 1963 - ) , professor , doctoral adviser.一80--FENG Hui-hud( 冯慧华)et al. / Dymamic Charateritics of Complex Struture Under and Out of Waterestablishment and solution of the structure and fluid ana-where M =- 2NN"dV , is the fluid mass matrix ;lytical models in this paper are all based on the strong-coupled method.K"=BB'dV is the fluid sifness matrix ; poR。=1 Basic Theories'21po |NnTN'TdS is the coupled mass matrix.1.1 Discretization of Fluid Wave EquationsIf the energy dissipation due to damping occurred onThe compressible , inviscid fluid satisfies the follow-ing assumptions : there is no mean flow of the fluid , thethe fluid-structure interface is taken into account , a dissi-mean density and pressure throughout the fluid uniform.pation temn should be added to the left side of Eq.( 5),The pressure wave equation could be simplified fromthat is given byNavier-Stokes equation and flow continuous motion formu-Cp="NN"d$p。,(6)lation aswhere r is the character impedance on the interface ; C。1吊7* Vp=0 ,(1)is the fluid damping matrix , andc2 72where c is the velocity of sound in the fluid medium ip isNN'dS.the acoustic pressure ; V* ( )and 7( ) are gradient anddivergence matrix operators respectively ,and V( )= L'1.2 Coupling of Fluid and Structure Dynamic For-=[ d/ax a/dy 8/az], 7( )= L.mulaUnder the assumptive conditions ，the normal pres-Suppose the fluid pressure load vector on the fluid-sure gradient of the fluid and the normal acceleration ofstructure interface is FR , the free vibration equation olthe structure on the fluid-structure interface S satisfy thethe structure coupled with the fluid can be written asfollowing relation :M。u.+ C。u。+ K。u。= FP，(7)r V p=-ρoIPu(2)where M。,C。, K。, respectively , are the mass matrix ,where n is the unit normal to the fluid structure interface ;damping matrix and stiffness matrix of the structure .FP can be acquired through integrating the pressurepo is the density of the fluid.Discretizing Eq.( 1 ) by using Galerkin process , andon the interface ，i.e.considering Eq.( 2 ) , the discrete form of the wave equa-F"= | N'pndS= | N'NI ndSp。= R。pe.( 8 )tion could be transformed intoEquation( 7 ) can be written as。五-2δp 2dV+ I( LTOpX Lp )IV=Mgue+ C。ue+ K。ue- R。pe=0. .( 9)(子By writing Eq.(5 )and Eq.( 6 ) as assembled form ,popn'u)ds.(3 )the following formula can be acquired :Introducing approximate shape functions into pres-M。sure p and displacement u i.e.l poR!p=N"pe ,l=N'Tue，(4)where N and N' are shape functions respectively forK。-R.]fu.0.( 10)pressure and displacement ; pe and u。are nodal pressure0K:」p。Jvector and displacement vector respectively.中国煤化工: complete finite elementBy substituting Eq.( 4 ) into Eq.( 3 ) and introducingdiscr.MYHC N M H Gture-fluid coupling prob-matrix B = LN' , the discrete wave equation in matrixlem , modal input such as natural frequencies and modalform can be acquired asshapes could be acquired by solving the character deter-M'p。+ K'pe+ poR[u=0,(5)minate and character equation.Journal of Beijing Institue of Technology ,2003 , Vol.12 ,No. 1portant characters of the structure properly , shell elements2 Establishment of Analytical Modelswith different real constants used to define different thick-The geometric model and finite element mesh of thenesses as well as hexahedron solid elements were adoptedstructure were established with CAD software I-DEASTM.to mesh the whole structure. The eventually received fi-A finite domain with certain dimensions was used to simu-nite element mesh of the whole problem ( structure underlate water area surrounding the structure , the type of hex-water) has 2 688 shell elements and 18 368 solid ele-ahedron element was adopted to divide the fluid domain .ments , among those 13 920 solid elements are used to de-According to the thickness of outer shell and inner struc-scribe the outer fluid. Figure 2a shows the FE mesh of theture' s characters of each section ，after properly simplify-structure under water. .ing the geometric model through eliminating some unim-2-(a) structure under water(b) struture partly out of waterFig.2 Finite element mesh of structure and fluid( prially amplfied)1 - fluid element ;2- shell element of the structure ;3 - solid element of inner structureFluid element properties( sound speed , reference a-ysis models were established individually , this could becoustic pressure , etc. ) and character impedance on the .fuflel by taking the fllowing steps : on the basis of un-fluid-structure interface are defined in ANSYS , the fluidderwater FE model which had been verified by experi-element layer which contacts with surface of the structurement , some contact fluid elements and correspondent fluidis designated , the fluid interactive load is applied to theinteractive loads on surfaces of structure were omitted ac-nodes in the contact surface between fluid and structure.cording to the distance between the top of the structureFor fluid structure interactive problems , since the systemand the water surface. A typically partially coupled FEmatrix is asymmetric , un-symmetric algorithm was em-model for simulating the process of the structure' s gettingployed to calculate dynamic characters of the FE models .out of water is shown in Fig. 2b.When carrying out the underwater modal( or the wetmodal , the opposite is called the dry modal , which pre-3 Dry and Wet Modal Test3-s]sents the modal characters of a structure in air ) test , the .By choosing steady sine signal as the excitationwhole process is complicated and costs much. Thereforesource , modal frequencies and shapes of the structureonly the modal test of completely immersed structure haswere identified and synthesized by phase resonancebeen implemented to verify the validity and reliability ofmethod. The modal tests were carried out in air and underthe analytical method and results calculated. Based onwater respectively to validate modeling methods and FEthese verifications , finite element numerical simulationsmodels. Figure 3 is the sketch map to illustrate the teston dynamic models of various phases of launching out fromsystem and environment of wet modal test. Except theunderwater have been carried out , so as to pre- estimatehang中国煤化Ihe configuration of modalthe structure' s dynamic behaviors in its whole workingtestYHC N M H Gs absolutely the same asprocess. As a result of logical theory and consistent calcu-that Fig. 3 shows. The comparison between test and simu-lation , such management is reasonable. Fourteen states oflation results is listed in Tab. 1.moving structure were chosen for investigation , their anal-Tab.1 Contradistinction between calculations and tests一82--FENG Hui-hud( 冯慧华)et al. / Dymamic Charateristics of Complex Struture Under and Out of Waterof all analytical model' results are referring to the all wetacceleration。rubber ropemodes ,i.e. modes with the same shape have the samewatersequence number as that of the wet modal results of thedomain二structurestructure. Since frequency descending degree caused by .water medium' s coupling effect upon different shapes mayshakervary，the phenomenon of mode sequence number ex-change will occur in the course of the structure moving outcharge一AD -ymodal analysisamplifierFL fiter 片convertersystemof water.4 Modal Results of Moving Out ofFig.3 Sketch map of wet modal testrelative errors of calculated .Watermodemodal shapemodal frequency/ %No.dry modalwet modalIn period of launching out of water , fourteen mo-1fist order bending0.86-2.16ments were chosen at which dynamic characters of the2local motion on tail coverstructure were calculated. Figure 4 shows frequencywiggling of front section3.83-2.91changing curves of the preceding seven modes againstfront section comeandgo2.772.69structure' s relative position described as the ratio of oversecond order bending4.425.91water height to the overall length of the structure. Thethird order bending3.487.29horizontal axis represents the percentage form of this ra-7twisting-1.932.06tio. As shown in this figure , frequency changing curves ofmode4 and mode 5 ,as well as mode 6 and mode 7 ,areForm data listed in Tab.1 we can see the results ofintersecting to each other respectively , which is the modesimulations and experiments in two environments accordsequence number exchanging phenomenon. Table 2 listswith each other very well : similar mode shapes , their rel-the natural frequency descending degrees of each modeative errors are all below 5% except for few modes. Sowhen the structure is all in water , compared with those ofthe requirement for calculating precision was met , phasesstructure' s dry mode. Several typical mode shapes areof getting out of water of the structure can be simulatedshown in Fig.5.with those modeling method as mentioned above. It isworthy to be pointed out that , for convenient comparison ,1.2mode sorting1.0mode 7,mode 50.'mode 30.4+◆◆◆0.2mode !20406080100percentage of structure out of water/%Fig.4 Changing curves of natural frequeney whenstructure moving out of water中国煤化工Tab.2 Influence of fluid on structure'.MHCNM HGmode No.2346eq. shif/ %-31.10- 10.20- 14.90- 0.10- 13. 10-7.70- 0.04一83-Journal of Beijing Institue of Technology ,2003 , Vol.12 ,No. 1(a) mode 1: first order bending(b) mode 3: wiggling of font section(C) mode 5: second order bending(d) mode 6: third order bendingFig.5 Some typical modes' modal shapein the course of the front one-fifth part of the structure5 Conclusionsmoving out of water , this is mainly attributed to the factBased on calculated results listed above ，we canthat the front section of the structure is the most activedraw conclusions as follows :part in most modal shapes .①In shallow water and period of moving out of wa-⑤The mode frequency of each bending mode is veryter , almost all dynamic modes are preserved from those ofsensitive to the influence of interaction between structurethe structure in air. Above all , as the results of fluid-and fluid , while come-and-go and twisting mode have rel-structure interaction , when contacting with water , theatively jarless resonance frequencies in the process whenstructure has more prolific modal shapes .contact area between water and structure was changing.②As a result of fluid-structure coupling effect ,modal frequencies of most modes of the structure underReferences :water dropped a lot compared with correspondent dry[ 1] Ansys Inc. Ansys theory manua[ M ] Canonsburg: AnsysInc. ,2001 .321- 328.modes. Especially for mode 1 , it had dropped about31.1% ,thus it can be seen that the fluid' s action on[2] Wang Xucheng , Shao Min. Basic theories and numericalmethods of finite element method[ M ] Beijing : Tsinghua U-structure researched in this paper is remarkable and couldniversity Press , 1997 .443-448.( in Chinese )not be neglected.[3 ] Xu Benwen , Jiao Qunying. Basis of mechanical vibration and③For modes with similar vibration character( formodal analysis[ M ]. Beijing : China Machine Press ，1998.example bending , etc. ), as the mode sequence number235 - 248.( in Chinese )increases , the influence of reducing mode frequencies be-[4] Liu Qingmao. Modal test investigation of complex body struc-came more and more feeble. For example , the wet modelture in wate[ J ]. Missiles and Space Vehicles ,1997( 4 ):23frequencies of the first order bending , second order bend-- 29.( in Chinese )ing and third order bending had decreased by about[5] Wu Jiaju , Zhu Xiquan , Xia Yilin. Investigation of dynamiccharacteristics of structure under wate[ J ] Chinese Joumal of31.1% ,13.1% and 7.7% , respectively.Applied Mechanics ,1997 ,14( 4):14 - 21.( in Chinese)④The maximum frequency dropping speed ocured中国煤化工MHCNMHG一84--