Select from the list of How do I’s... to learn about creating various modes for multi-body analysis.
Procedures that involve finite element analysis are highlighted in red. Data that is obtained by the finite element analysis are highlighted in green.
MHAT=X'*m*X where X=[Xn, Xc] Form modal stiffness matrix KHAT: KHAT = |Dn 0|
KHAT*N=MHAT*N*D
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. |
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Fe = P*Fa where P=I-m*Xr*Xr' and Fa has unit force along each DOF of the interface nodes.
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KHAT | Dn Xn'*Fe | | Fe'*Xn Xa'*Fe | and modal mass matrix MHAT as: MHAT=X'*m*X where X is the combined mode: X=[Xn Xa] Orthogonalize X by solving the eigen problem: KHAT*N=MHAT*N*D If X is not independent, then one of the following occurs:
In either case the corresponding modes can be filtered out so this step removes dependent modes as well.
Y=X*N This is the mode set of rigid body modes, free-free normal modes, and the residual inertial relieve attachment 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. |
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( k - l * m ) * Xf = Fa where:
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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]
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.
Y=X*N This is the mode set of rigid body modes, free-free 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. |
This procedure is without the Guyan reduction procedure and without the special static analysis.
Xf = Xe * [( De - l * I )^(-1)] * Xe' * Fa where:
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]
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.
Y=X*N This is the mode set of rigid body modes, free-free normal modes, and the "frequency response mode" modes from the modified procedure. The generalized mass and stiffness matrixes are: M=N'*MHAT*N=I K=N'*KHAT*N=D
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