2.3.5.      Hybrid Reduction

A disadvantage of the modal reduction method is that only a small number of vectors (the FEM mode shapes) is used to develop the transformation matrix. This is much more limited than the Guyan or IRS methods which use unit deflection shapes at each TAM A‑set DOF. While the modal TAM will be numerically very accurate, it may not be robust for situations where the modes of the test article are significantly differ­ent than those predicted by the finite element model.

Additional work by Kammer [4] extended the capabilities of the modal TAM method. The new method, called the Hybrid TAM, combines the accuracy of the modal TAM with the robustness of the Guyan reduction. An oblique projector matrix is formed using the FEM mode shapes, the transformation matrix from the modal TAM, and the FEM mass matrix:

                               (2.3.5-1)

The transformation matrix for the hybrid TAM is the combination of the Guyan reduction and modal TAM methods:

                        (2.3.5-2)

The reduced mass and stiffness matrices are formed using (2.3.5-2) and (2.3-1).