Use of Modal Flexibility and Normalized Modal Difference(NMD) for Mode Shape Expansion

모드 유연도 및 정규화된 모드차를 이용한 모드형상 전개

In this paper, two possible ways for mode shape expansion are proposed and opened for discussion for future use. The first method minimizes the modal flexibility error between the experimental and analytical mode shapes corresponding to the measured DOFs to find the multiplication matrix which can be treated as the least-squares minimization problem. In the second method, Normalized Modal Difference (NMD) is used to calculate multiplication matrix using the analytical DOFs corresponding to measured DOfs. This matrix is then used to expand the measured mode shape to unmeasured DOFs. A simulated simply supported beam is used to demonstrate the performance of the methods. These methods are then compared with two most promising existing methods namely Kidder dynamic expansion and Modal expansion methods. It is observed that the performance of the modal flexibility method is comparable with existing methods. NMD also have the potential to expand the mode shapes though it is seen more sensitive to the distribution of error between FEM and actual test data.