Use of Modal Flexibility and Normalized Modal Difference for Vibration Mode Shape Expansion

Proposed herein are two possible ways for mode shape expansion for future use. The first method minimizes the modal flexibility error between the experimental and analytical mode shapes corresponding to the measured degrees of freedom (DOFs) to determine the multiplication matrix. In the second method, Normalized Modal Difference (NMD) is used to calculate the multiplication matrix using the analytical DOFs corresponding to the 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 the Kidder dynamic expansion and the 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 to be more sensitive to the distribution of error between finite element method and actual test data.