Model reduction in a SOL 200 Model Update solution

Physical (Guyan) reduction

The full mass [M], stiffness [K], and damping [C] matrices are partitioned between omitted (O) and retained (A) degrees-of-freedom (DOF) as follows:

The transformation matrix between the omitted DOF set, {xO}, and the retained DOF set, {xA}, is defined as follows:

{xO} = [T] {xA}

The Model Update solution process gets the following reduced mass [MR] and stiffness [KR] matrices from SOL 200 Model Update solution results:

[MR] = [MAA] + [MOA]T [T] + [T]T [MOA] + [T]T [MOO] [T]

[KR] = [KAA] + [KOA]T [T] + [T]T [KOA] + [T]T [KOO] [T]

Modal reduction

The reduced modal matrices have a rank equal to the number of modes, n, retained in the SOL 200 Model Update solution. The reduced modal mass matrix that the Model Update solution process gets from the SOL 200 Model Update solution results is expressed as follows:

[R] = [Φ']T [M] [Φ']

where the eigenvectors [Φ'] are the mass normalized initial work mode shapes in physical coordinates.

If cross-orthogonality mode shape correlation is specified, the modal mass matrix can be transformed to the physical domain as follows:

[MR] ≈ [[Φ'] [R]-1[Φ]T]-1

The reduced modal stiffness matrix that the Model Update solution process gets from the SOL 200 Model Update solution results is expressed as follows:

[R] = [Φ']T [K] [Φ']

As the eigenvectors [Φ'] are mass normalized, [R] matrix contains the initial eigenvalues (mode frequencies).

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Reduced model sensitivities in SOL 200 Model Update solution

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