Computation of normal modes

The eigenvalue solver of the Model Update solution process uses the LAPACKNOTE library to internally solve for the normal modes.

Physical (Guyan) reduction

When the physical (Guyan) reduction method is used, the undamped eigenvalues, λi, and eigenvectors, {Φi}, are computed solving the following matrix equation:

([KR] – λi [MR]) {Φi} = {0}

where the eigenvectors, {Φi}, are the current mode shapes and the current frequencies, fi, are calculated as follows:

Modal reduction

When the modal reduction method is used, the undamped eigenvalues, λi, and eigenvectors, {Ψi}, are computed solving the following matrix equation:

([R] – λi [R]) {Ψi} = {0}

where the eigenvectors, {Ψi}, are the current mode shapes in the modal domain.

The current mode shapes [Φ] in the physical domain, defined by the USET DOF, are related to the shapes [Ψ] in the modal domain by the following equation:

[Φ] = [Φ'] [Ψ]

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

The current frequencies are calculated in the same way as for the physical (Guyan) reduction.

Look up more details

Model reduction in a SOL 200 Model Update solution

Reduced model sensitivities in SOL 200 Model Update solution

Computation of frequency sensitivities

Computation of mode shape sensitivities

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Computation of normal modes, Simcenter 3D 2021.1 Series

© 2020 Siemens

Anderson et al., “LAPACK User's Guide”, Third Edition, 22 August 1999, 1999 by the Society for Industrial and Applied Mathematics.

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