A modal analysis setting ( MOS ) specifies the rules according to which the eigenvalues are calculated. Two standard analysis types are preset. You can adjust these types or create further modal analysis settings at any time.
Base
The Main tab manages the settings required for the modal analysis as well as some other elementary calculation parameters. RFEM and RSTAB provide different options for selecting the eigenvalue method.
Eigenvalue Method
In this dialog section, you can define which method is used to analyze the eigenvalue problem and how many mode shapes are determined.
Method for determining the number of eigenvalues
You can select three options in the list.
- User-defined
The user-defined method allows you to specify the number of the smallest modes to be calculated. It is possible to define up to 9,999 mode shapes. In addition to this limit, the model also represents a restriction on the number of possible mode shapes: It corresponds to the degrees of freedom that result from the number of free mass points multiplied by the number of the directions in which the masses act.
- Automatic, to reach effective modal mass factors
As many eigenmodes are determined until the preset effective modal mass factor is reached. The effective modal mass factors are analyzed for the specified translational directions (X, Y, Z).
- Automatic, to reach maximum natural frequency
As many eigenmodes are determined until the specified natural frequency is reached.
Method for Solving Eigenvalue Problem (for RFEM)
Three methods are available in the list for solving the eigenvalue problem. If you have set the automatic method for determining the number of eigenvalues, only one solving method is available.
For more information about each method, see Bathe [1] and Nurse [2].
- Lanczos
The Lanczos method is suitable as an iterative method to determine the lowest eigenvalues and the corresponding mode shapes of large models. In most cases, this algorithm allows to reach a quick convergence. Up to n/2 mode shapes can be calculated ( n : number of degrees of freedom of the model with mass).
You can find an introductory description at en.wikipedia.org/wiki/Lanczos_algorithm.
- Root of Characteristic Polynomial
This method is used to carry out the analytical solution of an eigenvalue problem in a direct method. The main advantage of this method is the precision of higher eigenvalues and the fact that all the eigenvalues of the model can be determined. For larger models, this method may be time-consuming.
You can find an introductory description at en.wikipedia.org/wiki/Characteristic_polynomial.
- Subspace Iteration
With this method, all eigenvalues are determined in one step. The spectrum of the stiffness matrix has a strong influence on the duration of the calculation when using this method. This method is therefore only recommended for large FE models and few eigenvalues to be calculated. The working memory limits the number of eigenvalues that can be determined within a reasonable amount of time.
You can find an introductory description at en.wikipedia.org/wiki/Krylov_subspace.
Method for Solving Eigenvalue Problem (for RSTAB)
Two methods are available in the list to solve the eigenvalue problem. If you have defined one of the automatic methods for determining the number of eigenvalues, only one solving method is available.
More information about each method can be found in Bathe [1].
- Subspace Iteration
With this method, all eigenvalues are determined in one step. The spectrum of the stiffness matrix has a strong influence on the duration of the calculation when using this method. This method is therefore only recommended for large FE models and few eigenvalues to be calculated. The working memory limits the number of eigenvalues that can be determined within a reasonable amount of time.
You can find an introductory description at en.wikipedia.org/wiki/Krylov_subspace.
- Shifted inverse power method
This method is based on assumptions for the eigenvectors of the mode shapes, which are iteratively approximated to a convergent solution in the course of the calculation. The advantage of this method is the short calculation time due to the rapid convergence. "Shift" means that this method can also be used to determine all results that exist between the largest and the smallest eigenvalue of the given matrix.
You can find an introductory description at en.wikipedia.org/wiki/Inverse_Iteration.
Mass Matrix Settings
In this dialog section, you can define which mass matrix is used and in or about which axes the masses are to act in the modal analysis.
Type of mass matrix
Three types of mass matrices are available for selection in the list.
- Diagonal
In the case of the diagonal mass matrix M, the masses are assumed to be concentrated on the FE nodes. The input in the matrix are the concentrated masses in the translational directions X, Y and Z as well as the rotational directions about the global axes X (φX ), Y (φY ) and Z (φZ ). The following two cases must be distinguished:
– Diagonal matrix with only translational degrees of freedom: If only the translational directions are activated, the diagonal matrix results in:
– Diagonal matrix with translational degrees of freedom and rotational degrees of freedom: If the translational directions as well as the rotational directions are activated, the diagonal matrix results in:
| m | Mass |
| IX, IY, IZ | Mass moments of inertia (RFEM 6) |
- Consistent
The consistent mass matrix is a complete mass matrix of finite elements. Therefore, the masses are not concentrated on the FE nodes. Instead, the shape functions are used for a more realistic distribution of masses within the finite elements. With this mass matrix, non-diagonal entries in the matrix are considered, so that a rotation of the masses is generally taken into account. The consistent mass matrix is structured as follows (the shape functions are neglected for the sake of simplicity):
- Unit
The unit matrix overwrites all previously defined masses. This matrix is a consistent matrix where all diagonal elements are 1 kg. The mass is set to 1 at each FE node. Translations and rotations of masses are taken into account. This mathematical approach should be used for numerical analyses only.
More information about matrix types and, in particular, about using the unit matrix can be found in Barth/Rustier[3].
In direction / About axis
The six check boxes control in which direction or about which axes the masses act when determining the eigenvalues. The masses can act in the global displacement directions X, Y, or Z, and rotate about the X, Y, and Z axes. Select the corresponding check boxes. At least one direction or axis must be activated for the eigenvalues to be calculated.
Options
The last dialog section in the 'Main' tab provides an important setting option for the modal analysis.
Find modes beyond frequency
If individual members or surfaces in the model have a very low natural frequency, they occur first as local eigenmodes. If you tick the check box, you can only calculate the eigenvalues that lie above a certain value 'f' of the natural frequency. In this way, you can reduce the number of results and restrict it to the eigenvalues that are relevant for the entire model.
Settings
The 'Settings' tab manages further settings required for the modal analysis as well as elementary calculation parameters.
Mass Conversion Type
This dialog section controls the import of masses for the modal analysis. By default, only the 'Z-components' are taken into account. This refers to the load components acting in both directions of the Z-axis – positive and negative.
When you select the 'Z load components (in the direction of gravity)', the program applies only the load components that are effective in the direction of gravity. Gravity is determined by the orientation of the global Z-axis (see Chapter Orientation of Axes of the RFEM manual): It acts in the direction of the global Z-axis if it is directed downwards. If the global Z-axis is still oriented upwards, it has the opposite effect
Select the 'Full Loads as Mass' option to import all loads and apply all components as masses.
Neglect Masses
The modal analysis takes into account all masses that are defined for a model. This section provides the possibility to neglect the mass of parts of the model, for example the mass in all fixed nodal and line supports. You can also make a user-defined object selection.
When you select the 'User-defined' option, the additional tab 'Neglect Masses' appears. You can specify the mass-free objects there.
You can create the list of objects (nodes, lines, members, and so on) directly using the object numbers. Alternatively, use the
button in the field of the 'Object List' to select the objects graphically. You can use the
button to preset only fixed supports.
Use the check boxes for the displacement directions uX, uY, and uZ, as well as the rotations φX, φY, and φZ to define in which direction the masses are to be neglected.
The stiffness of the objects whose masses are neglected is nevertheless considered in the matrix. If you also want to neglect the stiffness of these objects, you can use the Structure Modification to adjust the stiffnesses individually. It is also possible to deactivate the objects for the calculation (see Chapter Base of the RFEM manual).
Minimum Axial Strain for Cables and Membranes
In order to enter the cable members and Membrane Surfaces chapter requires a minimum change in length. If the limit is set too low, the reached eigenvalues are not realistic and only local eigenmodes are determined. The default value of the initial prestress for emin is suitable in most cases.
