Produce Craig-Bampton Modes for Multi-body Analysis
- Perform a normal analysis with fixed interface B.C.
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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.
- Perform a static analysis with subcases where unit displacement along each DOF of the interface nodes is applied at each subcase.
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Read results.
- Xc
- Constraint modes (displacement of static analysis).
- Fc
- Nodal forces at B.C. from static analysis.
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Form modal mass matrix MHAT:
MHAT=X'*m*X
Where,X=[Xn, Xc]
Form modal stiffness matrix KHAT:KHAT = |Dn 0| | 0 Fc|
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Solve the eigen problem to obtain N and D
KHAT*N=MHAT*N*D
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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.