The Frequency Analysis simulation type allows the computation of natural (under no external load excitation) frequencies of oscillation of a structure and the corresponding oscillation mode shapes. The resulting frequencies and deformation modes are dependent on the geometry and material distribution of the structure, with or without the displacement constraints. In SimScale, the Code Aster solver is used to perform the frequency analysis.

The results from a frequency analysis enable you to evaluate the overall rigidity of your structure, as well as the rigidity of local regions. The lower frequencies of oscillation can be used as input for the seismic or wind load assessment and computation of structures. Also, in parts and structures subjected to variable frequency loads, the fundamental frequencies are used to avoid resonance between the natural oscillation modes and the applied load.

To create a frequency analysis, first select the desired geometry from the top of the simulation tree on the left, and then click on **‘Create Simulation**‘:

The simulation library window will appear with all the available analysis types:

Select ‘**Frequency Analysis’** from the list and confirm the choice by clicking on the ‘**Create Simulation**‘ button. A new element will appear in the simulation tree with all the available settings:

In the next sections, the different simulations settings that need to be defined to run the simulation are described:

The global settings are accessed by clicking on the simulation name, in this case, *‘Frequency Analysis’*, from the simulation tree. For this type of analysis, there are no further parameters to change. For more information, please refer to the global settings page.

The geometry panel contains the CAD model used for the simulation. Details of CAD handling and manipulation are described in the pre-processing page. Additionally, if you are facing problems with CAD complexities and uploading then it is advised to visit this documentation.

Geometrical models consisting of multiple bodies require connections to be defined on faces that make contact. The possible choices are:

**Bonded contact**: The master faces are rigidly connected to the slave faces, creating continuity on the deformation and compliance of forces.**Sliding contact**: The master faces are connected to the slave faces, but the local tangential displacements and forces are not transmitted.

Upon creating the simulation, all interfaces are automatically detected and defined as bonded contacts, but they can be further configured. More information about contacts here.

The element technology refers to the type of solid element you are using. Possible choices are:

**Standard:**- Used in first-order meshes, the element technology parameter has no effect in this case.
- Used in second-order meshes, the simulation will require more memory and time to complete due to the increased number of nodes and the computation of the equations.

**Reduced integration second-order solids:**- Used in second-order meshes, and saves on computation time with respect to fully integrated second-order elements. On the other hand, the reduced integration of Gauss might cause hour-glass deformation modes.

First-order solids are less expensive to use in terms of computational resources but require a finer mesh to properly capture some modes of deformation. In thin-walled parts, we recommend the use of second-order elements. Using reduced integration second-order elements will reduce computation time, but some artificial deformations can be obtained, due to numerical errors (hour-glassing of elements).

What is an hour-glass deformation mode?

Hour-glass deformation of elements is a numerical error phenomenon that can arise in reduced integration, second-order mesh elements. The error causes the elements to deform under no stress condition, creating a lack of precision in the results. If you detect strange, irregular deformations in your results, try changing back to standard second-order elements and compare.

Select a material from the materials library or customize the material model with your own parameters. Then, assign the created material models to each volume in the geometry. Please see the materials section for more details.

In frequency analysis, you will find that only displacement constraints are available. This is due to the assumption that the body is vibrating without the effect of any external load. If the analysis aims to compute the free body motion modes of vibration, no displacement restriction must be imposed. For an overview of all the boundary conditions available, please check this page.

The parameters of the modal and linear equations solvers are controlled in *Numerics*. For most cases, the default choices should be enough to get accurate results. You can find more information on numeric settings in the following blog post:

How to Choose a Solver for FEM Problems: Direct or Iterative?

The computation mode is specified under *Simulation control*. The available choices are:

**First modes:**Compute the first*‘Number of modes’*, according to the lower vibration frequencies.**Frequency range:**Compute all the modes in the band of frequencies ranging from*‘Start frequency’*to*‘End frequency’*.

If there is a need to compute the free body motion modes, the *‘Start frequency’* should be a small negative number, such as -0.1. You can find more details on the simulation control documentation page.

Under result control, the user can select desired output fields from the computation. In the case of frequency analysis, the only available field is *displacement*. It is important to note that the magnitude of the displacements only has a relative meaning and no physical interpretation.

For a frequency analysis, the *Standard* and *Tet-dominant *meshing algorithms are available. For more information about meshing in SimScale, please refer to the dedicated page.

After a successful simulation run, you will find the results in the following items:

Opens the online post-processor to visualize the deformed shape for each computed natural frequency of oscillation. Notice that the numerical values of the deformations not absolute, thus they do not contain any physical meaning, besides the relative deformations in the mode shapes.

The magnitudes of the deformations are normalized according to a ‘Translational-Rotational’ criteria. This means that all the computed deformations are divided by the largest value among all of the degrees of freedom, to achieve a maximum value of 1 on the component with highest deformation, and the other components are scaled proportionally.

Presents a table (labeled ‘Statistical data’) with the numerical results from the frequency analysis. The results are presented as a list of:

**Eigenmode**number,**Eigenfrequency**, the oscillation frequency for the mode,**Modal Effective Mass (MEM)**, in**DX**,**DY**and**DZ**directions,**Normalized Modal Effective Mass**, in**DX**,**DY**, and**DZ**directions,**Cumulative Normalized Modal Effective Mass**, in**DX**,**DY**and**DZ**directions.

For a total of 11 data columns. The result data can be downloaded in a text CSV table form.

Presents the results of the frequency analysis as line plots for the following quantities:

**Eigenfrequency plot**, shows the natural frequency vs mode number.**Modal effective mass plot**, shows a plot for each direction vs mode number.**Accumulated normalized modal effective mass plot**, shows a plot for each direction vs mode number.

What are these modal quantities?

For an explanation of what modal effective mass quantities are, its derivatives and applications, please refer to this page.

Last updated: March 3rd, 2022

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