Bracket — Eigenfrequency Analysis

In this example you learn how to perform an eigenfrequency analysis for both an unloaded structure and 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.

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 model geometry is represented in Figure 1.

Figure 1: Geometry of the bracket.

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

Results and Discussion

Figure 2 and Figure 3 show the first six eigenmodes for both the unloaded and the prestressed case, respectively. The mode shapes are listed in order from left to right and top to bottom. The difference in the two first mode shapes between the two load cases is significant.

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

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

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

In Figure 4 below, the frequency shift in the two first eigenmodes is clearly visible.

Figure 4: Six first eigenfrequencies for the unloaded case (stars) and the prestressed case (circles).

For the unloaded case, the two first eigenfrequencies are 115 Hz and 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 107 Hz for one of the arms and 128 Hz for the other. Such a frequency shift is expected since a tensile load causes stress stiffening, while a compressive load causes stress softening. The other mode shapes are not significantly affected by the prestress load case.

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 load boundary condition is disregarded and the 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.

Structural_Mechanics_Module/Tutorials/bracket_eigenfrequency

Modeling Instructions

From the menu, choose .

Browse to the model’s Application Libraries folder and double-click the file bracket_basic.mph.

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select .

Click 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.