Modal Analysis

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Pro/MECHANICA: Structure and Thermal Analysis 9–1

Chapter 9 Modal Analysis

Objective This chapter introduces:

Natural FrequencyMode ShapesDefining a Modal Analysis

Modal analyses are sometimes called natural frequency analyses.

A modal analysis in Pro/MECHANICA helps you determine the frequency and mode shape of a model. Modal analyses report the dynamic response of structures characterized by resonance frequencies (natural frequencies), mode shape and damping. These factors are important for models that are subjected to cyclic or vibration loads. You can calculate natural frequencies and model shapes for the following types of parts:

• A free part (when it has six rigid body modes)• A partially fixed part (when the number of rigid body modes is less

than six)• A full fixed part (when there are no rigid body modes)

NaturalFrequency

All models have a natural frequency. If a dynamic load is applied to a model close to its natural frequency, the model exhibits a larger than normal oscillation. Without proper damping, the oscillation can become uncontrollable and cause the model to collapse.

Resonance occurs when the frequency of the forced vibrations approaches or coincides with the natural frequency of the system.

To prevent this problem, Pro/MECHANICA predicts the natural frequency of your model so that you can analyze the model under specific, dynamic constraints. The results of a modal analysis helps determine whether a model requires more or less damping to prevent failure. Use a modal analysis to find the resonant frequencies for a structure under specific constraints.

Degrees ofFreedom

Any object that vibrates has a degree of freedom. The degrees of freedom is the number of directions in which the object can vibrate. An object with a single degree of freedom can move back and forth in one direction only. An object with multiple degrees of freedom can move back and forth in more than one direction.

Frequency = number cycles in a unit time.

Degrees of freedom can also be defined by the number of objects that move. For example, take two objects attached with a spring. The first object can move back and forth in only one direction. The second object can move back and forth in only the same direction as the first. The two-object system has two degrees of freedom.

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9–2 Pro/MECHANICA: Structure and Thermal Analysis

If your system has more than one degree of freedom, the combined forces of the two objects can yield a frequency that affects your part. Pro/MECHANICA can automatically calculate the degrees of freedom.

Damping Damping is used to dissipate the vibrational energy in a model or part. All models and parts have some inherent damping; however, the amount of damping can be increased to dissipate energy in particular modes.

After you run a modal analysis, you can decide whether more or less damping is required.

Modes Modes measure the vibration of an object at a particular frequency. Each mode is assigned a number. The lowest speed at which a structure vibrates after all external loads are removed is assigned to mode 1. This mode is called the free vibration mode because it is not damped.

Each mode is assigned a different frequency. For example, mode 1 (the free vibration mode) for a part could be 255.6Hz. and mode 2 for the part could be 868.7Hz. Any number of modes can apply to a particular part. Pro/MECHANICA can analyze up to 9999 different modes.

Mode Shape Each mode is characterized by a deformed shape called the mode shape. Any number of mode shapes can apply to a particular part. Using Pro/MECHANICA, you can visualize these shapes and the frequency that is associated with them. Four mode shapes are shown in Figure 9–1. By viewing mode shapes, you can see how a part reacts to different frequencies.

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Figure 9–1

255.6Hz 868.8Hz

1026.7Hz 1440.4Hz

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Defining a ModalAnalysis

Modal analysis parameters are defined in the Modal Analysis Definition dialog box, as shown in Figure 9–2.

Figure 9–2

The options in the Modal Analysis dialog box are described in Table 9–1.

Table 9–1

Option Description

Name Enter a name for the analysis in this field.

Description Enter a description of the analysis in this field (optional).

Constraints Enables you to define the constraint set using the following options:P

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Constrained Use this option to select a constraint set, if one is available.

Unconstrained Use this option if you do not want to use a constraint.

With rigid mode search

Use this option if you are not using a constraint. This option is automatically selected if no constraint set is available. Pro/MECHANICA reports any rigid body modes that it finds.

Output Define the output for the analysis in the Output tab. This tab contains the following options:

Calculate With this option, you select the stresses, rotations, and/or reactions to calculates quantity values.

Plot With this option, you can enter a plotting grid density. Pro/MECHANICA calculates quantity values at the intersection of grid lines; therefore, grid density is important.

Convergence Select a convergence method using the Method pull-down menu in the Convergence tab.

Modes Define the modes for the analysis in the Modes tab. This tab contains the following options:

Number of Modes

Use this option to specify the number of modes for Pro/MECHANICA to calculate. This number is added to the specified frequency.

All Modes in Frequency Range

Use this option to specify all modes within a frequency range in the Min Frequency and Max Frequency fields.

Number of modes

Use this pull-down menu to specify the number of modes above the specified frequency that you want Pro/MECHANICA to calculate. The number must be between 1 and 9999. You can only change this number if the Number of Modes option is selected.

Minimum Frequency

Use this option to specify the minimum frequency of a frequency range. You can only specify this if the All Mode in Frequency Range option is selected.

Maximum Frequency

Use this option to specify the maximum frequency of a frequency range. You can only specify this if the All Mode in Frequency Range option is selected.

Option Description

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Exercise 9a Modal Analysis (Natural Modes of Vibration)

Goal After you complete this exercise, you will be able to:

Create user-defined measuresSet up and run a modal analysis for a Quick Check convergenceSet up and run a Multi-Pass Adaptive analysisDisplay the results

A modal analysis enables you to find the natural frequencies and corresponding principal mode shapes of the hook under a specific constraint set.

In this exercise, you set up and run a modal analysis on a hook model, as shown in Figure 9–3. You use the shell idealization to represent the thin sections of the model as a FEA model.

Figure 9–3

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Modeling Tasks

Task 1: Open the part called modal_hook_1 in Pro/ENGINEER and launch Pro/MECHANICA.

1. Open modal_hook_1.prt. The unshaded part appears as shown in Figure 9–4.

Figure 9–4

2. Make sure that the unit systems is set to mmNs.

3. Launch Pro/MECHANICA Structure.

4. Make sure the model type is set to 3D.

Task 2: Define shell elements.

1. Create a mid-surface shell for the hook entities shown in Figure 9–5.

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Figure 9–5

2. Click Compress > Shells and Solids > ShowCompress to ensure that the compression of the shells worked. The model appears as shown in Figure 9–6.

Figure 9–6

Shell these entities

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Task 3: Apply loads.

In this task, you apply a bearing load to the hook hole.

1. Click Insert > Bearing Load or select the icon. The Bearing Load dialog box appears as shown in Figure 9–7.

The Dir Point & Mag and Dir Vector & Mag are other options in the Force pull-down menu.

Figure 9–7

1. Enter [hole_load] in the Name field.

2. Select the surface of the hole shown in Figure 9–8.

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Figure 9–8

3. Enter [-1500] in the Y field and select . The model appears as shown in Figure 9–9.

Use the Simulation Display dialog box to turn the load values off.

Figure 9–9

Select this surface

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Task 4: Apply the constraints.

In this task, you apply constraints to the top and bottom surfaces of

the hook using the icon, as shown in Figure 9–10.

Figure 9–10

1. Enter [surface_fix] in the Name field.

2. Constrain these surfaces in all directions. The model appears as shown in Figure 9–11.

Figure 9–11

Fix these surfaces

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Task 5: Apply the material.

1. Assign STEEL to the hook model.

The model’s material properties should be as stated.

The following values are the default material properties for HS-low-alloy steel (STEEL):• Poisson = 0.27• Young’s modulus = 199948 N/mm2• Coeff of thermal expansion = 1.17e-5 /C• Density = 7.82708e-9 tonne/mm^3

2. Select to check your material properties.

Task 6: Mesh the model.

1. Make sure the AutoGEM Settings are the default limits in the Limits tab of the AutoGEM Settings dialog box, as shown in Figure 9–12.

Figure 9–12

2. Mesh the model using the All with Properties option.

3. Note the number of Tri, Quad and Tetra elements in the AutoGEM Summary dialog box. The model appears as shown in Figure 9–13.

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The shell elements (Tri and Quad) are shown in green and 3D solid elements (Tetra) are shown in blue.

Figure 9–13

4. Close the AutoGEM dialog box and save the mesh.

Task 7: Create measure.

This measure is useful for locating the center of mass of an assembly model.

1. Click Insert > Simulation Measure to define a centre of mass measure to locate the model’s centre of mass relative to WCS in

the X-direction. Select . The Measure Definition dialog box appears.

2. Name the measure [mass_centre].

3. Select the Center of Mass in the Quantity pull-down menu. Note the analysis types for which you can set this measure, as shown in Figure 9–14.

Figure 9–14

Summary

In the previous tasks, you created the simulation entities required to analyze your model.In the following tasks, you specify the analysis type and the convergence method and run the analysis.

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Analysis Tasks

Task 8: Set up the analysis.

In this task, you specify the analysis type. First, the hook is analyzed using the Quick Check convergence option, which checks for errors. You then analyze the hook using the Multi-Pass Adaptive convergence option.

1. Click File > New Modal in the Analysis and Design Studies dialog box. The Modal Analysis Definition dialog box appears as shown in Figure 9–15.

The objective of a modal study is to ensure that the system does not have a resonant frequency near the operating frequency.

Figure 9–15

2. Enter [modal_hook] in the Name field.

Select the Constrained and With rigid mode search options when you are not sure if your model is fully constrained.

3. Enter a description of the analysis in the Description field (optional).

4. Accept the defaults in the Constraints section.

5. Enter [25] in the Number of Modes field.

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6. Select the Convergence tab and select Quick Check in the Method pull-down menu.

7. Select the Output tab, as shown in Figure 9–16.

Figure 9–16

8. Select all of the options in the Calculate section.

9. Accept the default option in the Plotting Grid field.

10. Select to accept the selections and close the Modal Analysis Definition dialog box.

11. Check the validity of the model and run the analysis.

The solution converges on frequency.

12. Set up the Multi-Pass Adaptive analysis. Enter [9] in the Polynomial Order field and accept the defaults in the Percent Convergence field in the Limits section and Converge on section.

13. Run the analysis. If time permits compare your results to those provided in the canned_results directory.

14. Extract the following information from the modal_hook.rpt:

• Stress errors for modes 1 to 4, as shown in Figure 9–17.

These values are a Pro/MECHANICA benchmark of the result. You should not accept more than 5 to 10% of the maximum stress value.

Figure 9–17

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Note that the high percentage stress error is due to re-entrant corners, which are caused by the intersection of shell elements and 3D solid elements around the hook area. The solution converges and stress errors are within the limits (10%), except mode 3. Therefore, the results are valid.

• Frequencies for modes 1 to 4, as shown on Figure 9–18

Resonant frequencies occur for the hook model under set conditions.

Figure 9–18

Note convergence percentage for the four modes. The solution converges on frequency (you set the convergence in step 12. of this task). Convergence was obtained on pass six.

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Results Tasks

Task 9: Display the results.

In this task, you create, animate, and show four von Mises stress fringe plots for the first four modes of vibration. You are interested in the first four modes.

1. Select the icon from the Analyses and Design Studies dialog box. The Untitled Result Window appears.

2. Select the icon. The Result Window Definition dialog box appears.

3. Select the icon and open the modal_hook study. The Result Window Definition dialog box appears as shown in Figure 9–19.

Figure 9–19

4. Enter [mode1_window] in the Name field and [mode_1] in the Title field.

5. Select Stress in the first Quantity pull-down menu and select von Mises in the Component pull-down menu.

6. Select the Display Options tab and enter the information shown in Figure 9–20.

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Figure 9–20

7. Show the "mode_1" fringe plot. Step through the animation to the frame shown in Figure 9–21.

Figure 9–21

Frame number

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In this mode (mode1), examine the areas of high stress and the vibrational mode of the hook.

8. Create, animate, and show a von Mises stress for mode 2. Enter [mode2_window] in the Name field and [mode_2] in the Title field.

9. Select the second checkbox in the Include column, as shown in Figure 9–22, and clear the first checkbox.

Figure 9–22


Figure 9–23

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In this mode (mode 2), examine the areas of high stress and the vibrational mode of the hook.


12. Select the third checkbox in the Include column and clear the second checkbox.


Figure 9–24

In this mode (mode3), examine the areas of high stress and the vibrational mode of the hook.


15. Select the fourth checkbox in the Include column and clear the third checkbox.

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Figure 9–25

It is recommended that the natural frequency of the system occur below 1/3 or above 3 times the operating frequency.

In this mode (mode 4), examine the areas of high stress and the vibrational mode of the hook.

17. Save the model and close the window.

Task 10: Set up and run a new analysis (optional).

1. Delete the mesh.

2. Delete the mid-surface shells.

3. Mesh the model with 3D solid elements only.

4. Set up and run a new Multi-Pass Adaptive analysis. Enter a different name for the analysis. Enter [9] in the Polynomial Order field, and accept the defaults in the Percent Convergence field in the Limits section and Converge on section.

5. Compare the results.

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Documents

Modal Analysis