Produce S. Dietz's "frequency response mode" for Multibody Analysis

Perform a normal analysis without constraint
(freefree).
Read results.
 m
 System mass matrix (Lumped mass).
 Xn
 FreeFree normal modes including the rigid body modes
(Xn=[Xr,X1,X2,....,Xk])
.  Dn
 Diagonals are the eigenvalues associated with Xn.

Perform a "special" static analysis without
constraint in FE:
( k  l * m ) * Xf = Fa
where, k
 System stiffness matrix.
 l
 A scalar, usually half of the first nonzero frequency of the freefree normal analysis in step 1.
 m
 System mass matrix (Lumped mass).
 Fa
 Attachment forces at junction nodes, not necessarily unit loads.
Read results. Xf
 The "frequency respond mode" associated with l and Fa (the displacement from the "special" static analysis).

Form modal stiffness matrix KHAT as:
KHAT=  Dn Xn'*Fb   Fb'*Xn Xf'*Fb 
where Fb is the balancing force and is defined as:Fb = Fa + l*m*Xf
Form modal mass matrix MHAT as:MHAT=X'*m*X
where X is the combined mode:X=[Xn Xf]

Orthogonalize X by solving the following eigen problem:
KHAT*N=MHAT*N*D
If X is not independent, then one of the following occurs: The eigenvalues/vectors are complex
 Some highest eigenvalues are infinite
 Extra zero eigenvalue rigid body modes
In either case, the corresponding modes can be filtered out so this step removes dependent modes as well.

Transform X to orthoginalized modes Y:
Y=X*N
This is the mode set of rigid body modes, freefree normal modes, and S.Dietz's "frequency response mode" modes.
The generalized mass and stiffness matrix are:M=N'*MHAT*N=I K=N'*KHAT*N=D
Y, D, and m are used to calculate the flexible MB input file.