COMSOL 6.4 - Bracket — Eigenfrequency Analysis

In this example, you learn how to perform an eigenfrequency analysis for an unloaded structure as well as for a prestressed structure.

When the structure is subjected to a constant external load, the stiffness generated by the stress may affect the natural frequencies of the structure. Tensile stresses tend to increase the natural frequencies, while compressive stresses tend to decrease them.

It is recommended you review the Introduction to the Structural Mechanics Module, which includes background information and discusses the bracket_basic.mph model relevant to this example.


	In the Structural Mechanics Modeling chapter of the Structural Mechanics Module User’s Guide: Eigenfrequency Analysis.

Model Definition

This tutorial is an extension of the example described in the section “The Fundamentals: A Static Linear Analysis” in the Introduction to the Structural Mechanics Module.

The geometry is shown in Figure 1.

Figure 1: Geometry of the bracket.

In the first case, the natural frequencies of the unloaded bracket are studied, while in the second case it is considered how the natural frequencies are affected by a static external load. The static load is applied to the pin holes, and the left arm is under a pure compressive load while the right arm is under a pure tensile load.

Results and Discussion

Figure 2 and Figure 3 show the first six eigenmodes for the unloaded and the prestressed case, respectively. The difference in the two first mode shapes between the two load cases is significant. For the unloaded structure, there is a full symmetry, leading to the two closely spaced first eigenfrequencies. With prestress, the first eigenmodes for the two arms become distinct. The problem is no longer symmetric, since one arm is loaded in tension and the other one in compression.

The two first mode shapes consist of bending in the x direction in the bracket arms. For the unloaded case the corresponding eigenfrequencies are expected to be approximately equal because of the symmetry. For the prestressed case, there will be a difference because of stress stiffening (right arm) and stress softening (left arm).

Figure 2: Six first eigenmode shapes for the unloaded case.

Figure 3: Six first eigenmode shapes for the prestressed case.

When comparing eigenmodes, it should be noted that the modes may be computed with reversed signs. This can even happen when the same study is run twice. Note also that the magnitude of an eigenmode does not have any physical significance; that is why the default mode shape plots do not have a color legend.

In Figure 4, the stress state from the static preload is shown.

Figure 4: Equivalent stress from the preload. Note the nonlinear color scale.

In Figure 5 below, the frequency shifts in the two first eigenmodes are clearly visible.

Figure 5: The six first eigenfrequencies for the unloaded case (stars) and the prestressed case (circles).

For the unloaded case, the two first eigenfrequencies are approximately 114 Hz. They correspond to the bending mode in the x direction for the two bracket arms. For the prestressed load case, the eigenfrequencies for the bending modes are 105 Hz for the left arm and 128 Hz for the right arm. Such a frequency shift is expected since a tensile load causes stress stiffening, while a compressive load causes stress softening. The other eigenmodes are not significantly affected by the prestress.

Notes About the COMSOL Implementation

For a structural mechanics physics interface in COMSOL Multiphysics, there are two predefined study types available for eigenfrequency analysis: and .

The plain eigenfrequency analysis computes the natural frequencies of the unloaded structure. The contribution of any traction boundary condition is disregarded and prescribed displacement constraints are considered as having the value zero.

In the prestressed eigenfrequency analysis, a stationary analysis is first performed to take into account the different loads and nonzero displacement constraints. The resulting stress is then automatically taken into account in the stiffness used in the eigenfrequency calculation.

As a default, the checkbox is selected in the study step used for computing the prestress solution. In many cases, you can choose to clear that checkbox. In this example, that would change the natural frequencies only by about 1%.

If there are no other nonlinearities in the model, you can shorten the analysis time by using an assumption about geometrical linearity, since no iterations are then needed in the first study step.

Structural_Mechanics_Module/Tutorials/bracket_eigenfrequency

Modeling Instructions

Application Libraries

From the menu, choose .

In the window, select > > in the tree.

Click

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Study 1

Step 1: Eigenfrequency

In the study node you have the possibility to select the number of eigenfrequencies to compute, and the frequency around which you would like to search for these frequencies. By default, the eigenvalue solver finds the six lowest frequencies.

In the window for , locate the section.

Select the checkbox. In the associated text field, type 10.

In the toolbar, click