1、2011China InternationaI Boat Show&HPMV Conference 14-17 April，201 12Finite element identification modalFEM is a efficient and resonable method to analysis huge stnlctu增。 which basic idea is to dispersethe continuse stfllctllre to many small part called elementThe elements are linked by node。which is
2、used to transfer load and distortionThe communal nodes between elements must satisfy with distortionharmony and load equationThe basic steps are stnJcture separation。element property calculation，assembled strcture analysisWhen analysised dynamic problems，the continuse structme problem istransform to
3、 MDOF problem according to FEMBecause this paper use the basical frequency resonance as the criterions of calcilation，we can usebeam theroy to illuminate the calculation courseWe Can get the MDOF systems vibrancy equation basedon proportional viscous after we separate the ship s仃ucture with element：
4、【Mj)+【C】童+【K】工=LF(t) (o1)where。M】is the systemS mass matrix。C】is the systemS viscous matrix，K】is thesystemsstiffness matrix，扛)is the systems node displacement vector。犯)is the load distributionmatrix，尸(，)is the excitionS time process functionUsed the mode shapeS orthonormality of undamped free vibrat
5、ions，we can transform the solution ofvibration equation from physical coordinates to mode coordinates 。 achievinguncouplingUndamped free vibrationsequation is：M】戈)+【K】x=0 (02)Suppose expression ofx)=簟Isin(cot+O)is the equationS root above。 矽)is the swing of thenodeput it into equation(22)，we get the
6、 systemS eigenproblem：IK-Mc02矽)=0 (03)Reffering to the equationsnon-zero root above，we get the result below from Cramer principle：lK-c02【MI=o (04)According to the equation(24)，we can get the systemS co蛐atural frequency q(i_1，2，n)Put it into equation(23)。we get swing vectorf。which is the systemS natu
7、ralmode shape and normalize with mass matrix and stiffness matrixTo underdamped system，the coercive vibrationS solution isx)=溉誓 (o5)i=1where Z is the modal coordinate，and changes with timen is the digree number of the systemPut expression(25)into(21)then multiply the both sides ofexpression(21)with
8、some mode vector矽)，rWe will get an ordinary differential equation：霉+2爵w，毒+wr2，：=峄(。6)E28-220l lChina International Boat Show&HPMV Conference 1417 April201 1where q is natural frequency of undamped free system， 岳is modal damping ratio矽rTLF(t)is the modal force，M=纠，r【M】缈，is modal massWhen the distribu
9、tion ofthe load and the change rule with time are given，we carl solve equation(25)toget the displacement response of the nodeFor our discussion，the screw propellerS bearing frequencyload is F(r)=sin万t。万is frequency。which is the rotate speed of the propeller shaftThen the IeRofequation(26)can be writ
10、ten嬲fk sinwt。k=l2一m means the discrete node，k=lis the swing of modal force located at excitation pointSolving the equation(26)，五2专(1-+(2爵眦。1彪sn(研一印(o7)whe聆墨=缈)，rK】缈)，is m。dal stiffness， 屏兰旦is the rati。load fiequ饥cy to natural皱quency=恤-l(筹)and吣1800After we get鬈(，)(i=1，2，刀)through(27)，we put the resul
11、ts into(25)to get the steadydisplacement ofthe nodeGenerally speaking，We can use the first 20 ftequency mode shape to calculate the steady response ofthe structure。which wull give an satisfactory resultWhen load frequency is closed to the resonantfrequency especially。we can use the mode shape the re
12、sonant frequency correspond to to calculate theresponse ofthe structureThus五蜘溉=一慨表c。s加c。s研(蚰)Identification espression：办，r犯)妒)，=2考rX) (O9)whereX)is the resonant amplitude of the displacement from experimental dataDiesel engine is the the main machine which provide the energy when shippingThe vibrati
13、on responsecontain the airscrewS contribution and the effection of diesel engineBut The effection Can be eliminatedwhen the diesel engine is at the place of zero point of the mode shapeWe see the effection Can be ignoredfrom expression(27)when the load frequency is closed to some natural frequency，as one of the twocases below：Firstly。the load frequency is far from the natural frequency；Secondly，the plce the loadE283
