A DIRECT MODE SHAPE EXPANSION METHOD

Traditional methods dealing with spatial incompleteness is by employing transformation matrix for model reduction and modal expansion. This article presents a different mode shape expansion method without obtaining transformation matrix, i.e., a direct mode shape expansion method. A hybrid vector is employed, which is constructed by values corresponding to master degrees of freedom (DOF) and values corresponding to slave DOFs. Spatial complete mode shape is estimated by modifying the above values at slave DOFs based on information such as measured spatial incomplete mode shape and stiffness and mass matrices from the analytical model. A five DOFs mass-spring system is used to examine the accuracy of the proposed method; and a planar frame structure is used to identify the performance for lower order mode shapes estimation. Numerical results show that: 1) Mass normalization and scaling for mode shapes are not needed in the proposed method; and 2) The proposed method outperforms traditional expansion method for lower order mode shape expansion, and a certain modeling errors are permitted in finite element model of the test structure.