Complex modes analysis (SOL 402)

A complex modes analysis can help to evaluate the stability of a model, typically for rotating or aeroelastic systems, by analyzing the real part of complex eigenvalues. For example, you can use a complex modes analysis for a rotating system such as a shaft that is supported by bearings where the bearings are idealized by stiffness and damping coefficients. The complex modal analysis produces complex eigenvalues and complex eigenvectors.

Another advantage of a complex modes analysis is that it computes damped natural frequencies. The complex analysis is then able to check this change of frequency. For highly damped systems, this frequency can reach zero values, so the change can be very large.

Two options are available for you to set up a complex modes analysis, depending on whether you want to reduce the model first:

• To reduce the number of degrees of freedom in your model before extracting the modes, use the modal approach, which uses real modal analysis to reduce the system (damping is ignored), and then projects the real modes in the complex space. The modal approach uses both the real eigenvalue and complex eigenvalue methods, and is more appropriate for large models and when the damping values are not too big (real eigenmodes should not be too far from the complex ones). The modal approach is an approximation, but it requires less computation time.

• To extract the modes from your model without a modal reduction, use the direct approach. The direct approach uses the complex eigenvalue method to perform the complex eigenvalue analysis, and is more suitable for smaller models.The direct approach is more precise, but compared to the modal approach, it requires more computation time.

Both the modal and direct approach use the Lanczos method for extraction.

Unsymmetrical matrices

A complex modes subcase requires unsymmetrical matrices at the global level and at the subcase level, which are set by default:

• In the Nonlinear Control Parameter - Global modeling object, Matrix Symmetry (INLY) is set to Unsymmetry Activated.

• In the Nonlinear Control Parameter - Subcase modeling object, Unsymmetrical Stiffness, Damping and Mass Matrices for Complex (MATSYM) is set to Yes.Note: For complex eigenvalues, the solver sets MATSYM to yes, even if you change Unsymmetrical Stiffness, Damping and Mass Matrices for Complex (MATSYM) to No.

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Complex modes analysis (SOL 402), Simcenter 3D 2021.1 Series

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