Produce Craig-Bampton Modes for Multibody Analysis

  1. Perform a normal analysis with fixed interface B.C.
  2. Read results.
    m
    System mass matrix (Lumped mass).
    Xn
    Fixed-interface modes (displacement of normal analysis).
    Dn
    Diagonals are the eigenvalues from the normal analysis.
  3. Perform a static analysis with subcases where unit displacement along each DOF of the interface nodes is applied at each subcase.
  4. Read results.
    Xc
    Constraint modes (displacement of static analysis).
    Fc
    Nodal forces at B.C. from static analysis.
  5. Form modal mass matrix MHAT: 
    MHAT=X'*m*X
    Where,
    X=[Xn, Xc]
    Form modal stiffness matrix KHAT:
    KHAT =	|Dn  0|
	| 0 Fc|
  6. Solve the eigen problem to obtain N and D 
    KHAT*N=MHAT*N*D
  7. Transform the X to orthoginalized modes Y: 
    Y=X*N
    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.