An eigenfrequency study solves for the eigenfrequencies (natural frequencies) and the shapes of the corresponding eigenmodes.
where K is the stiffness matrix,
M is the mass matrix,
u is the eigenmode displacement vector, and
ω = 2πf is the angular frequency. In case of damping, the eigenvalue equation is expanded to
where C is the viscous damping matrix, and
K may be complex valued.
To compute modal participation factors, a Participation Factors node must be present under
Definitions in the current component. When you add an
Eigenfrequency study from the
Add Study window, such a node is automatically created.
You can also add it manually under Definitions>Variable Utilities. If you do that after an eigenfrequency study has been run, you need to do an
Update Solution in order to get access to the variables containing the participation factors.
The modal participation factors are available as global variables, and these can for example be displayed in a table using a Global Evaluation node under
Derived Values in the
Results branch. The participation factor results are available as predefined variables in the
Definitions submenu for the component. In
Table 2-1, the variables created from a
Participation Factors node is listed (assuming the default tag
mpf1).
If a Participation Factors node is present in the model when an eigenfrequency study is run, an evaluation group named
Participation Factors is automatically generated. It contains a table with the translational and rotational modal participation factors for all computed eigenfrequencies.
It is possible to compute eigenfrequencies for structures which are not fully constrained; this is sometimes referred to as free-free modes. For each possible rigid body mode, there is one eigenvalue which in theory is zero. The number of possible rigid body modes for different geometrical dimensions is shown in the table below.
To do a prestressed analysis, Include geometric nonlinearity must be selected in the
Eigenfrequency study step. This is automatic when you add the
Eigenfrequency, Prestressed study type.
In order to get a correct solution to Equation 2-3, the linearization point
ωL must be close to the actual eigenvalue
ω. This is in general possible only for one single eigenfrequency at a time. You must solve this problem either by manual iteration, or by using some type of scripting, for example through a model method.