Application discussion of perturbed force approach in modal expansion

The perturbed force approach is a modal shape expansion method, it can also be derived from the perturbed eigenvalue equation. Here, the simplification of this method was discussed when tested eigenvalues were very much close to FE model eigenvalues to cause a singularity problem of eigen-matrix. Again using perturbation analysis, an arbitrary small shift was introduced to eliminate the matrix singularity and simplify the modal expansion matrix expressing. To avoid computation of a full matrix in actual application, the expansion of the generalized inverse of a matrix could be used to obtain a more efficient modal expansion scheme. Through implementing the generalized inverse expansion, the necessary conditions for the perturbed force approach being equivalent to SEREP method were gained. Finally, some criteria for FE modal base selection were proposed to choose lower order modal shapes and determine the number of modal expansion bases, a notched beam modal test demo was conducted to validate the discussion.