Mode Shape Reduction, Expansion And Their Applications

In the fields of aeronautics, astronautics and mechanics, a precise mathematical model of thestructure is important for response prediction, condition monitoring and engineering performancecontrol. The mathematical model can be obtained by combining the test model and finite elementanalysis model of the structure. By the reduction of analysis model, a test/analysis model (TAM)having the same number of degrees of freedom (DOFs) with the test modelcan be established. Amodel within a complete DOF space can be obtained by expanding the test model.In this thesis, the methods of mode shape reduction and expansion are systematicallystudied. Forthe mode shape reduction, several common sensor placement methods are researched, and a two-stagesensor placement method，which is a combination of the addition method based on QR decompositionof the mode matrix and the reduction method based on the Effective Independence method, wasproposed. The method and other three methods are applied in the modal test of a cantilever beam anda model frame of a vehicle. By comparing the evaluation criteria, the measurement DOFs identifiedby this two-stage method can not only meet the requirement of modes matching, but guarantee themodes independence. For the mode shape expansion, four classical methods which can be classifiedinto two categories, namely, methods based on mass and stiffness matrix and methods based on modecoordinate, are researched. The four methods are used to expand the test mode shapes of the cantileverbeam and the model frame, and the effects of the expansion are compared. The relationship of thedisplacement modes and the strain modes is also researched. The equations for the transformation ofthe four-node plate element strain are deduced and utilized in the computationof the strain modes ofthe cantilever beam. Modal tests using the sensor placementobtained by the two-stage method wereconducted on the cantilever beamand model frame to obtain their dynamic characteristics. Themodeshape correlations are computed to validate the modal result. Finally, based on MATLABGUItechniques, a toolbox with good human-computer interaction is developed for the mode shapereduction and expansion.