ME'scopeVES Application Note #04 - Using Structural Dynamics Modification for Sub-Structuring

App Note #4 www.vibetech.com 25-Feb-14

of 8

ME’scope Application Note #4

Using Structural Dynamics Modification for Sub-Structuring

INTRODUCTION

NOTE: The steps in this Application Note can be dupli-cated using any Package that includes the VES-5000 SDM option.

In this application note, two substructures will be joined together using the SDM (Structural Dynamics Modifica-tion) option in ME’scope. A simple two degree-of-freedom (2-DOF) substructure will be mounted on a flat plate substructure to model the response of the combined substructures.

WHAT IS SUBSTRUCTURING?

In brief, sub-structuring is the process of modeling the at-tachment of two or more structures together using FEA elements. Each of the structures is termed a substructure and it is dynamically described by a set of its modes, called a modal model. The objective is to calculate the new modes of the combined structure, starting with only the modes of each substructure and the attachment FEA elements.

The modes of the substructures may be either EMA modes (obtained experimentally), or FEA modes (obtained from an FEA model).

Each substructure modal model needs to be a complete de-scription of the substructure’s dynamics, including its boundary conditions. If a substructure is modeled in the free-free condition, its modal model must include its rigid-body modes. If a substructure is attached to ground, no rigid-body modes are required.

NOTE: If one substructure is to be mounted onto another and is not attached to ground, the rigid-body modes of the mounted structure must be included in its modal model.

To perform sub-structuring, the following is needed:

1. Properly scaled mode shapes (i.e. a modal model) of each substructure.

2. Properly scaled 3D model of each substructure, with FEA elements added between the substructures where they are to be connected together.

THE SUBSTRUCTURES

The plate-on-springs substructure is an (8 x 10 x ¼ inch) aluminum plate supported vertically by four springs of 100 lb/in stiffness and restrained in-plane by four more springs as shown in Figure 1.

Figure 1. Plate-on-Springs SubStructure.

This constrained structure is represented dynamically by a set of 12 mode shapes. Each mode shape has 63 DOFs, de-scribing Z-axis (vertical) motion at 63 Points in a 7 by 9 grid of Points.

The 2-DOF substructure shown in Figure 2 consists of two point masses connected together with a single spring. The modal model for this 2-DOF spring-mass substructure will be obtained by solving for the modes of its FEA model.

Figure 2. 2-DOF SubStructure.

A lower spring shown in Figure 2 will be used during sub-structuring to “mount” the 2-DOF substructure on the Plate-on-Springs substructure.

App Note #4 www.vibetech.com 2/25/2014

of 8

GETTING STARTED

Open the App Note 04-Using SDM for Sub-Structuring Project from the ME’copeVES\Application Notes folder.

Modes of the Plate-On-Springs

Open STR: Plate on Springs and SHP: Plate on Springs

Right click in the graphics area of the STR: Plate on

Springs window, and execute Draw | Animate Shapes from the menu

Click on each Shape button in the SHP: Plate on Springs window to display its shape

Notice that the first three modes (25.99, 29.93 & 33.27 Hz), are rigid body modes, where the plate simply moves verti-cally on the support springs and does not flex.

Figure 3. First Torsional Mode of the Plate-on-Springs

Notice also that the plate center is located along node lines for all torsional modes. A 2-DOF substructure will be at-tached to the center of the plate.

VERIFYING THE MODAL MODEL

One way to verify the plate modes and also determine which modes are participating in the response at the center of the plate-on-springs is to synthesize Driving Point FRFs from the modal model.

NOTE: A Driving Point FRF is an FRF that has a Rov-ing DOF equal to its Reference DOF.

In order to synthesize FRFs using the mode shapes in SHP: Plate on Springs, they will require modal damping.

Double click on the Damping column heading in the SHP: Plate on Springs window

Enter “1” into the dialog box that opens, and click on OK.

Execute Tools | Synthesize FRFs

In the dialog box that opens, make the selections shown below, and click on OK.

Select Displacement in the next dialog box, and click on OK

Press the New File button in the next dialog box, enter “Driving Point FRFs” into the next dialog box, and click on OK.

Execute Format | Overlaid in the Data Block window that opens.

Figure 4. 63 Overlaid Driving Point FRFs.

Right click, select Horizontal Axis from the command menu, and select Log Frequency in the Show Axis As list in the dialog box that opens.

The overlaid plot of Driving Point FRFs in Figure 4 clear-ly shows peaks for all 12 modes.

Execute Format | Rows Columns, and select 1,1


of 8

Figure 5. Driving Point FRF 32Z:32Z.

Scroll the Trace display to display FRF 32Z:32Z, as shown in Figure 5

Only four resonance peaks (25.99, 476.0, 772.6 & 1731 Hz) appear in FRF 32Z:32Z.

Zoom the display around the highest frequency peak.

Figure 6. Zoomed FRF with Peaks at 1691 &1731 Hz,

The Zoomed display in Figure 6 verifies that both the 1691 Hz & 1732 Hz modes participate in the response at Point 32, the center of plate-on-springs.

Point 32 is a nodal point for the other eight modes (29.93, 33.27, 387.4, 903.1, 1028, 1403, 1692 and 2116 Hz). It is expected that attaching a substructure to this DOF will not affect these modes, but will only affect the modes that have peaks in the Driving Point FRF 32Z:32Z.

Mass & Stiffness Lines

The 32Z:32Z FRF has units of (displacement/force), and clearly shows the participation of the 25.99 Hz rigid-body mode. The sum of the stiffnesses of the four springs sup-porting the plate (4 x 100 lb/in = 400 lb/in) can be estimat-ed from the frequency stiffness line below this rigid body resonance.

Position the Line cursor on the stiffness line, as shown below.

The cursor value is .0025344 in/lb. This flexibility value is equal to the inverse of the stiffness, or 394.5 lb/in, which is close to the stiffness of the four supporting springs.

The mass of the plate (5.78 lb) can be estimated from the mass line which is higher in frequency than the rigid body mode resonance peak. The mass line should be a horizontal line in an (acceleration/force) FRF, which can be obtained by double differentiating the (displacement/force) FRF.

Execute Tools | Differentiate twice in the Data Block window.

Double click on the Units column in the Traces spread-sheet.

In the dialog box that opens, type “g/lb”, and click on OK.

Click on Yes to re-scale the Traces to g/lb units.

Position the Line cursor on the mass line above the rigid body mode, as shown in Figure 7.

Figure 7. Cursor on Mass Line of Rigid Body Mode.

The cursor value is 0.1727 g/lb for the nearly horizontal mass line. The inverse of this value is 5.79 lb/g, which is a close estimate of the mass of the plate in a 1g gravitational field, or the weight of the plate.

By examining properties of synthesized FRFs for the plate, two of its key dynamic properties have been verified. This proves that its modal model is a valid representation of its dynamics, and therefore can be confidently used with SDM for sub-structuring.


of 8

MODES OF THE 2-DOF SUBSTRUCTURE

The modes of the 2-DOF substructure will be calculated from its FEA model, consisting of two FEA Point masses connected together by an FEA linear spring.

Adding Two FEA Masses

Execute Display | Surfaces | Transparent in the STR: 2-DOF SubStructure window.

Right click in the graphics area, and execute Object

List | FEA Masses from the menu

Right click in the graphics area, and execute Add Ob-ject from the menu

Click near the Point in the center of the Top Mass cube (with Point label 100) to add an FEA mass to the Point.

Execute Draw | Substructures | Add Selected Objects to Substructure.

In the dialog box that opens, select Top Mass, and click on Add Objects.

Click near the Point in the center of the Bottom Mass cube (with Point label 101) to add an FEA mass to the Point.


In the dialog box that opens, select Bottom Mass, and click on Add Objects.

Adding an FEA Spring between the Masses

Right click in the graphics area, and execute Object List | FEA Springs from the menu


Click near the Point in the center of the Top Mass (with Point label 100) and then on the Point in the cen-ter of the Bottom Mass (with Point label 101) to add the FEA spring.

Right click in the graphics area, and execute Add Ob-ject again to disable the Add operation.


In the dialog box that opens, select Top Spring, and click on Add Objects

Adding FEA Properties

To create FEA Properties for the two masses and the spring,

Execute FEA | FEA Properties to open the FEA Prop-erties window

Click on the Masses tab

Execute Edit | Add in the FEA Properties window

Enter “0.25” into the Mass (lbm) column.

Click on the Springs tab

Execute Edit | Add in the FEA Properties window

Enter “5000” into the Stiffness (lb/in) column.

Assigning Properties and Constraining Motions

Right click in the graphics area in the STR: 2-DOF Sub-

Structure window, and execute Object List | FEA Masses from the menu

Double click on the FEA Property column heading in the mass properties spreadsheet, select Mass 1 from the list, and click on OK.

Double click on the Direction column heading, and select Z from the list in the dialog box.


Double click on the FEA Property column heading in the spring properties spreadsheet, select Spring 1 from the list, and click on OK.

Double click on the Point 1 Direction column heading, and select Z from the list in the dialog box.


Solving for the 2-DOF Substructure Modes

The 2-DOF FEA model now consists of 2 FEA Masses con-nected together with an FEA Spring. To solve for the two modes of this model,

Execute FEA | Calculate FEA Modes

The following dialog box will open.

Click on Yes, set up the next dialog box as shown below, and click on OK


of 8

Enter “2-DOF Substructure Modes” into the dialog box that opens, and click on OK.

The Shape Table shown below will open with two modes in it. Notice that the first mode at 0.0 Hz is a rigid body mode, with equal mode shape components. The second mode at 625.45 Hz is a flexible body mode, with equal and opposite mode shape components.

Figure 8. 2-DOF Substructure Modes.

MERGING THE TWO MODELS

Sub-structuring requires that the substructure models be merged together in the same Structure window, and also that the mode shapes of the two substructures be merged together in the same Shape Table window.

Merging the Substructure Models

The two substructures will be copied into a new Structure window.

Execute Edit | Copy Objects to File in the STR: Plate-On-Springs window.

Click on New File in the dialog box that opens, and enter “Merged Substructures” into the next dialog box.

Execute Edit | Paste Objects from File in the STR: Merged Substructures window.

Select STR: 2-DOF Substructure in the dialog that opens, and click on Paste.

The two substructures will be displayed together in the Merged Substructures window, as shown in Figure 9.

Figure 9. 2-DOF & Plate-on-Springs Substructures.

Merging the Two Shape Tables

To merge together the mode shapes of the two substructures,

Execute Edit | Copy Shapes to File in the SHP: Plate-On-Springs window.

Click on New File in the dialog box that opens, and enter “Merged Mode Shapes” into the next dialog box.

Execute Edit | Paste Shapes from File in the SHP: Merged Mode Shapes window.

Select SHP: 2-DOF Substructure Modes from the list in the dialog box that opens, and click on OK.

Block Diagonal Format

The two modes of the 2-DOF substructure have now been merged with the modes of the plate-on-springs substructure. Because the DOFs of the 2-DOF substructure are different than the DOFs of the plate-on-springs substructure, the shapes have been merged together in a “block diagonal” format. In block diagonal format (shown in Figure 10), all shapes share the same DOFs, and the shape components of each shape are zero for DOFs where that shape was not originally defined.

Notice also in Figure 10 that the M#s were also copied from the two Shape Tables, and that the list of M#s no longer con-tains unique M#s. To give all of the shape components unique M#s,

Execute Tools | Renumber M#s in SHP: Merged Mode Shapes to renumber the shape M#s.

Execute Tools | Create Animation Equations in SHP: Merged Mode Shapes to create new animation equations


of 8

Figure 10. Substructure Modes in Block Diagonal Format.

ADDING THE ATTACHMENT FEA SPRING

An FEA Spring Object will be used to mount the 2-DOF substructure on the plate-on-springs substructure, by adding an FEA Spring between the Bottom Mass and the center of the plate.

Right click in the graphics area, and execute Object List | FEA Springs from the menu in the STR: Plate-on-Springs window


Click on the Point in the center of the Bottom Mass cube (with Point label 101) and then on the Point at the bottom of the Bottom Spring substructure to add the FEA spring as shown below.

Right click in the graphics area, and execute Add Object again to disable the Add operation.

Double click on the FEA Property column heading in the spring properties spreadsheet, select Spring 1 from the list, and click on OK.



INTERPOLATION OF UN-MEASURED POINTS

The corner Points of the Mass substructures, and all of the interior Points on the two Spring substructures are un-measured Points.

NOTE: An un-measured Point is also called an Interpolated Point because it requires an Interpolated animation equation in order to be animated.

Interpolating the Mass Cube Points

Select the Top Mass and Bottom Mass substructures.

Execute Draw | Animation Equations | Create Interpo-lated.

Click through the dialog boxes that open.

Interpolating the Spring Points


Hold down the Ctrl key and click near the bottom Point of FEA Spring 2 and the center Point (Point 32) of the plate-on-springs to select them, as shown in Figure 11.

Execute Draw | Animation Equations | Create Interpo-lated

Click through several dialog boxes until the following box opens indicating that one Interpolated equation has been created for the un-measured spring end Point.


of 8

Figure 11. Spring Point and Center Point Selected.

The un-measured end Point at the bottom of Spring 2 now has the same animation equation as Point 32 on the plate, but it is an Interpolated equation. This equation will be converted from an Interpolated to a Measured equation so that the rest of the Points on the Spring substructure can be Interpolated from its two Measured end Points.

Execute Draw | Animation Equations | Interpolated to Measured

To create Interpolated equations for all of the Spring sub-structures,

Select all of the Spring substructures in the STR: Merged Substructures window

Execute Draw | Animation Equations | Create Inter-polated

Make sure that the following dialog box has a “2” in it, and click on OK

SUB-STRUCTURING WITH SDM

SDM will use the following to calculate new modes for the combined substructures;

Shapes in the SHP: Merged Mode Shapes window

The FEA Spring 2 object that connects the two sub-structures together in the STR: Merged Substructures window

Checking the Animation Equations

SDM uses the animation equations on the structure model for its computations. Therefore, the structure should be animated using the shapes of the un-modified structure before using SDM to calculate new modes.

Right click in the graphics area in the STR: Merged Sub-structures window, and execute Animate Shapes

When a plate mode is selected, the plate should be deflected. When a 2_DOF mode is selected the masses and spring should be deflected.

Figure 12. Animation of the 625.45 Hz mode.

When you are satisfied that both the plate modes and the 2-DOF modes are animating correctly,

Execute SDM | Calculate New Modes

Select SHP: Merged Mode Shapes in the dialog box that opens, and click on OK

If the following dialog box opens, click on No, make the two FEA Masses and the FEA Spring 1 invisible, and execute SDM | Calculate New Modes again.

When the SDM calculation has completed, a dialog box will open for saving the new mode shapes.


of 8

Enter “New Mode Shapes” into the dialog box, and click on OK.

The new mode shapes can now be displayed in animation of the model in STR: Merged Substructures.

Right click in the graphics area in the STR: Merged Substructures window, and execute Animate Shapes

Note that the first mode (24.92 Hz) is a rigid-body transla-tion and that the springs of the 2-DOF substructure do not deform. The attached 2-DOF is acting like a rigid mass (of 0.5 lb) attached to the center of the plate. The deformation of the plate is of the same as that of its original 25.99 Hz mode shape before the 2-DOF substructure was attached to it. The frequency of the new mode can be calculated by the simple SDOF relationship of a mass on a spring:

93.245.078.5

78.599.25

Final

PlatePlateFinal Mass

Massff Hz

COMPARING SHAPES

Right click in the graphics area in the STR: Merged Substructures window, and execute Compare Shapes

Right click in the graphics area, execute Structure Op-tions, and check Display MAC on the Animation tab

Right click in the graphics area, and execute Compare Shapes | Synchronize Shapes

The first modes of the modified and unmodified structure should be displayed as shown below. The MAC value indi-cates that these mode shapes are 95% alike.

Modes 2 & 3 remain unchanged because DOF 32Z was a node point for these shapes in the plate-on-springs sub-structure. Modes 5 and 9 through 14 also remain un-changed because all of these modes have a node point at DOF 32Z.

Modes 4 and 6 reflect interaction between the 2-DOF sub-structure and the 476.0 Hz mode of the plate substructure. With mode 4 (276.8 Hz), the masses move in-phase with one another and tend to suppress or absorb motion from the plate. In mode 6 (481.2 Hz), the upper mass moves out-of-

phase with the plate center and the lower mass is nearly sta-tionary.

Modes 7 & 8 show interaction between the 2-DOF substruc-ture and the 772.6 Hz mode of the plate substructure. In mode 7 (704.2 Hz), the masses move out-of-phase with one anoth-er, and the lower mass moves in-phase with the plate center. The motion of the plate is small, again indicating that the 2-DOF substructure is absorbing energy from the plate. In mode 8 (797.3 Hz), the plate is quite active. The lower mass moves out-of-phase with both the plate and the upper mass.

SUMMARY

Two substructures were dynamically coupled together using SDM. In this application note you:

1. Added FEA Masses and FEA Springs to 3D model of a 2-DOF structure.

2. Solved for the modes of 2-DOF FEA model.

3. Merged the modes of this model with the modes of a se-cond plate-on-springs structure.

4. Connected the two substructures together with an FEA Spring.

5. Solved for the new modes of the coupled substructures using SDM.

ME'scopeVES Application Note #04 - Using Structural Dynamics Modification for Sub-Structuring

Documents

Transcript of ME'scopeVES Application Note #04 - Using Structural Dynamics Modification for Sub-Structuring