One simple method that includes an approximation of the mass effect at omitted DOF is the dynamic reduction. In this case we start with (2.3.1-1) and include the mass terms at a “center” frequency w. The upper partition of (2.3.1-1) can be solved as:
(2.3.2-1)
The transformation matrix from the FEM DOF to the TAM DOF is:
(2.3.2-2)
or
(2.3.2-3)
The dynamic TAM is exact only at the “central” frequency w, but it is a better approximation than the static TAM at frequencies near w. If w is chosen as 0, dynamic reduction reduces to static reduction. In general w should be chosen in the frequency range of interest, typically near the frequency of the primary modes of the test article.
Note that if w
is chosen above the first eigenvalue of and
, the matrix
will
not be positive definite. Therefore w
should always be chosen below the first eigenvalue of
and
. Reference [10]
shows that all the TAM methods other than static have difficulty when
this criterion is not met. To find the eigenvalue of
and
, the user can replace
the ASET cards with SPC cards and perform a modal calculation.