Analysis of Natural Vibrations
Modal Analysis | Features
- Automatic consideration of masses from self-weight
- Direct import of masses from load cases or load combinations
- Optional definition of additional masses (nodal, linear, or surface masses, as well as inertia masses) directly in the load cases
- Optional neglect of masses (for example, mass of foundations)
- Combination of masses in different load cases and load combinations
- Preset combination coefficients for various standards (EC 8, SIA 261, ASCE 7,...)
- Optional import of initial states (for example, to consider prestress and imperfection)
- Structure Modification
- Consideration of failed supports or members/surfaces/solids
- Definition of several modal analyses (for example, to analyze different masses or stiffness modifications)
- Selection of mass matrix type (diagonal matrix, consistent matrix, unit matrix), including user-defined specification of translational and rotational degrees of freedom
- Methods for determining the number of mode shapes (user-defined, automatic - to reach effective modal mass factors, automatic - to reach the maximum natural frequency - only available in RSTAB)
- Determination of mode shapes and masses in nodes or FE mesh points
- Results of eigenvalue, angular frequency, natural frequency, and period
- Output of modal masses, effective modal masses, modal mass factors, and participation factors
- Masses in mesh points displayed in tables and graphics
- Visualization and animation of mode shapes
- Various scaling options for mode shapes
- Documentation of numerical and graphical results in printout report
Modal Analysis | Input
In the modal analysis settings, you have to enter all data that are necessary for the determination of the natural frequencies. These are, for example, mass shapes and eigenvalue solvers.
The Modal Analysis add-on determines the lowest eigenvalues of the structure. Either you adjust the number of eigenvalues or let them determined automatically. Thus, you should reach either effective modal mass factors or maximum natural frequencies. Masses are imported directly from load cases and load combinations. In this case, you have the option to consider the total mass, load components in the global Z-direction, or only the load component in the direction of gravity.
You can manually define additional masses at nodes, lines, members, or surfaces. Furthermore, you can influence the stiffness matrix by importing axial forces or stiffness modifications of a load case or load combination.
Modal Analysis | Calculation
In RFEM, you can use these three powerful eigenvalue solvers:
- Root of Characteristic Polynomial
- Method by Lanczos
- Subspace Iteration
RSTAB, on the other hand, provides you with these two eigenvalue solvers:
- Subspace Iteration
- Shifted inverse power method
The selection of the eigenvalue solver depends primarily on your model size.
Modal Analysis | Results
As soon as the program has completed the calculation, the eigenvalues, natural frequencies and periods are listed. These result windows are integrated in the main program RFEM/RSTAB. You can find all mode shapes of the structure in tables and also have an option to display them graphically and to animate them.
All result tables and graphics are part of the RFEM/RSTAB printout report. In this way, you can ensure clearly arranged documentation. You can also export the tables to MS Excel.
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In the Modal Analysis add-on, you have the option to automatically increase the sought eigenvalues until reaching a defined effective modal mass factor. All translational directions activated as masses for the modal analysis are taken into account.
Thus, it is possible to easily calculate the required 90% of the effective modal mass for the response spectrum method.
The Concrete Design add-on allows you to perform the seismic design of reinforced concrete members according to EC 8. This includes, among other things, the following functionalities:
- Seismic design configurations
- Differentiation of the ductility classes DCL, DCM, DCH
- Option to transfer the behavior factor from a dynamic analysis
- Check of the limit value for the behavior factor
- Capacity design checks of "Strong column - weak beam"
- Detailing and particular rules for curvature ductility factor
- Detailing and particular rules for local ductility
Have you already discovered the tabular and graphical output of masses in mesh points? That's right, this is also part of the modal analysis results in RFEM 6. This way, you can check the imported masses that depend on various settings of the modal analysis. They can be displayed in the Masses in Mesh Points tab of the Results table. The table provides you with an overview of the following results: Mass - Translational Direction (mX, mY, mZ), Mass - Rotational Direction (mφX, mφY, mφZ), and the Sum of Masses. Would it be best for you to have a graphical evaluation as quickly as possible? Then you can also graphically display the masses in mesh points.
As you've already learned, the results of a Modal Analysis load case are displayed in the program after a successful calculation. You can thus immediately see the first mode shape graphically or as an animation. You can also easily adjust the representation of the mode shape standardization. Do that directly in the Results navigator, where you have one of four options for the visualization of the mode shapes available for the selection:
- Scaling the value of the mode shape vector uj to 1 (considers the translation components only)
- Selecting the maximum translational component of the eigenvector and setting it to 1
- Considering the entire eigenvector (including the rotation components), selecting the maximum, and setting it to 1
- Setting the modal mass mi for each mode shape to 1 kg
You can find a detailed explanation of the mode shape standardization in the OnlineManual here.