4.6.3.1. Set the Analysis Title
1. Choose menu path Utility Menu> File> Change Title.
2. Type the text "Harmonic Response of Two-Mass-Spring System" and click on OK.
4.6.3.2. Define the Element Types
1. Choose menu path Main Menu> Preprocessor> Element Type> Add/Edit/Delete.
2. Click on Add. The Library of Element Types dialog box appears.
3. Scroll down the list on the left to "Combination" and select it.
4. Click once on "Spring-damper 14" in the list on the right.
5. Click on Apply.
6. Scroll up the list on the left to "Structural Mass" and select it.
7. Click once on "3D mass 21" in the list on the right.
8. Click on OK. The Library of Element Types dialog box closes.
9. Click on Close in the Element Types dialog box.
4.6.3.3. Define the Real Constants
1. Choose menu path Main Menu> Preprocessor> Real Constants.
2. Click on Add. The Element Type for Real Constants dialog box appears.
3. Click once on Type 1 to highlight it.
4. Click on OK. The Real Constants for COMBIN14 dialog box appears.
5. Enter 200 for the spring constant (K) and 0.1 for the damping coefficient (CV1). Click on OK.
6. Repeat steps 2-4 for Type 2, MASS21.
7. Enter .5 for mass in X direction and click on OK.
8. Click on Close to close the Real Constants dialog box.
4.6.3.4. Create the Nodes
1. Choose menu path Main Menu> Preprocessor> Modeling> Create> Nodes> In Active CS.
2. Enter 1 for node number.
3. Enter 0, 0, 0 for the X, Y, and Z coordinates, respectively.
4. Click on Apply.
5. Enter 4 for node number.
6. Enter 1, 0, 0 for the X, Y, and Z coordinates, respectively.
7. Click on OK.
8. Choose menu path Utility Menu> PlotCtrls> Numbering. The Plot Numbering Controls dialog box appears.
9. Click once on "Node numbers" to turn node numbers on.
10. Click on OK.
11. Choose menu path Main Menu> Preprocessor> Modeling> Create> Nodes> Fill between Nds. A picking menu appears.
12. In the ANSYS Graphics window, click once on nodes 1 and 4 (on the left and right sides of the screen). A small box appears around each node.
13. Click on OK on the picking menu. The Create Nodes Between 2 Nodes dialog box appears.
14. Click on OK to accept the default of 2 nodes to fill. Nodes 2 and 3 appear in the graphics window.
4.6.3.5. Create the Spring Elements
1. Choose menu path Main Menu> Preprocessor> Modeling> Create> Elements> Auto Numbered>
Thru Nodes. A picking menu appears.
2. In the graphics window, click once on nodes 1 and 2.
3. Click on Apply. A line appears between the selected nodes.
Section 4.6: Sample Harmonic Response Analysis (GUI Method)
4. Click once on nodes 2 and 3.
5. Click on Apply. A line appears between the selected nodes.
6. Click once on nodes 3 and 4.
7. Click on OK. A line appears between the selected nodes.
4.6.3.6. Create the Mass Elements
1. Choose menu path Main Menu> Preprocessor> Modeling> Create> Elements> Elem Attributes.
2. Enter 2 for element type number.
3. Enter 2 for real constant set number and click on OK.
4. Choose menu path Main Menu> Preprocessor> Modeling> Create> Elements> Auto Numbered>
Thru Nodes. A picking menu appears.
5. In the graphics window, click once on node 2.
6. Click on Apply.
7. Click once on node 3 and click on OK.
4.6.3.7. Specify the Analysis Type, MDOF, and Load Step Specifications
1. Choose menu path Main Menu> Solution> Analysis Type> New Analysis.
2. Click once on "Harmonic" and click on OK.
3. Choose menu path Main Menu> Solution> Analysis Type> Analysis Options.
4. Click once on "Full" to select the solution method.
5. Click once on "Amplitud + phase" to select the DOF printout format and click on OK.
6. Click OK in the Full Harmonic Analysis dialog box.
7. Choose menu path Main Menu> Solution> Load Step Opts> Output Ctrls> Solu Printout.
8. Click on "Last substep" to set the print frequency and click on OK.
9. Choose menu path Main Menu> Solution> Load Step Opts> Time/Frequenc> Freq and Substeps.
10. Enter 0 and 7.5 for the harmonic frequency range.
11. Enter 30 for the number of substeps.
12. Click once on "Stepped" to specify stepped boundary conditions.
13. Click on OK.
4.6.3.8. Define Loads and Boundary Conditions
1. Choose menu path Main Menu> Solution> Define Loads> Apply> Structural> Displacement> On Nodes. A picking menu appears.
2. Click on Pick All. The Apply U, ROT on Nodes dialog box appears.
3. In the scroll box for DOFs to be constrained, click once on "UY" to highlight it (make sure no other selec-tions are highlighted).
4. Click on OK.
5. Choose menu path Main Menu> Solution> Define Loads> Apply> Structural> Displacement> On Nodes. A picking menu appears.
6. In the graphics window, click once on nodes 1 and 4.
7. Click on OK. The Apply U, ROT on Nodes dialog box appears.
8. In the scroll box for DOFs to be constrained, click once on "UX" to highlight it and click once on "UY" to deselect it.
9. Click on OK.
10. Choose menu path Main Menu> Solution> Define Loads> Apply> Structural> Force/ Moment> On Nodes. A picking menu appears.
11. In the graphics window, click once on node 2.
12. Click on OK. The Apply F/M on Nodes dialog box appears.
13. In the scroll box for direction of force/moment, click once on "FX."
14. Enter 200 for the real part of force/moment and click on OK.
4.6.3.9. Solve the Model
1. Choose menu path Main Menu> Solution> Solve> Current LS.
2. Review the information in the status window and click on Close.
3. Click on OK on the Solve Current Load Step dialog box to begin the solution.
4. When the solution is finished, a dialog box stating "Solution is done!" appears. Click on Close.
4.6.3.10. Review the Results
For this sample, you will review the time-history results of nodes 2 and 3.
1. Choose menu path Main Menu> TimeHist Postpro> Define Variables. The Defined Time-History Variables dialog box appears.
2. Click on Add. The Add Time-History Variable dialog box appears.
3. Click on OK to accept the default of Nodal DOF result. The Define Nodal Data dialog box appears.
4. Enter 2 for reference number of variable.
5. Enter 2 for node number.
6. Enter 2UX for the user-specified label.
7. In the scroll box on the right, click once on "Translation UX" to highlight it.
8. Click on OK.
9. Click on Add in the Defined Time-History Variables dialog box. The Add Time-History Variable dialog box appears.
10. Click on OK to accept the default of Nodal DOF result. The Define Nodal Data dialog box appears.
11. Enter 3 for reference number of variable.
12. Enter 3 for node number.
13. Enter 3UX for the user-specified label.
14. In the scroll box on the right, click once on "Translation UX" to highlight it.
15. Click on OK.
16. Click on Close.
Section 4.6: Sample Harmonic Response Analysis (GUI Method)
17. Choose menu path Utility Menu> PlotCtrls> Style> Graphs. The Graph Controls dialog box appears.
18. In the scroll box for type of grid, scroll to "X and Y lines" to select it.
19. Click on OK.
20. Choose menu path Main Menu> TimeHist Postpro> Graph Variables. The Graph Time-History Variables dialog box appears. Your graph should look like this:
21. Enter 2 for 1st variable to graph.
22. Enter 3 for 2nd variable to graph.
23. Click on OK. A graph appears in the graphic window.
4.6.3.11. Exit ANSYS
You are now finished with this sample problem.
1. In the ANSYS Toolbar, click on Quit.
2. Choose the save option you want and click on OK.
4.7. Sample Harmonic Response Analysis (Command or Batch Method)
You can perform the example harmonic response analysis of a two-mass-spring system by using the following ANSYS commands instead of the GUI.
/PREP7
/TITLE, Harmonic response of a two-mass-spring system ET,1,COMBIN14,,,2
ET,2,MASS21,,,4
4.8. Where to Find Other Examples
Several ANSYS publications, particularly the ANSYS Verification Manual, describe additional harmonic analyses.
The ANSYS Verification Manual consists of test case analyses demonstrating the analysis capabilities of the ANSYS family of products. While these test cases demonstrate solutions to realistic analysis problems, the ANSYS Verific-ation Manual does not present them as step-by-step examples with lengthy data input instructions and printouts.
However, most ANSYS users who have at least limited finite element experience should be able to fill in the missing details by reviewing each test case's finite element model and input data with accompanying comments.
The ANSYS Verification Manual includes a variety of harmonic analysis test cases:
VM19 - Random Vibration Analysis of a Deep Simply-Supported Beam VM76 - Harmonic Response of a Guitar String
VM86 - Harmonic Response of a Dynamic System VM87 - Equivalent Structural Damping
VM88 - Response of an Eccentric Weight Exciter
VM90 - Harmonic Response of a Two-Mass-Spring System
VM176 - Frequency Response of Electrical Input Admittance for a Piezoelectric Transducer VM177 - Natural Frequency of a Submerged Ring
VM183 - Harmonic Response of a Spring-Mass System
VM203 - Dynamic Load Effect on Simply-Supported Thick Square Plate
Section 4.8: Where to Find Other Examples
4.9. Reduced Harmonic Response Analysis
The reduced method, as its name implies, uses reduced matrices to calculate the harmonic solution. The procedure for a reduced harmonic analysis consists of five main steps:
1. Build the model.
2. Apply the loads and obtain the reduced solution.
3. Review the results of the reduced solution.
4. Expand the solution (expansion pass).
5. Review the results of the expanded solution.
Of these, the first step is the same as for the full method. Details of the other steps are explained below.
4.9.1. Apply Loads and Obtain the Reduced Solution
By reduced solution, we mean the degree of freedom solution calculated at the master DOF. The tasks required to obtain the reduced solution are as follows:
1. Enter the ANSYS solution processor.
Command(s): /SOLU GUI: Main Menu> Solution
2. Define the analysis type and options. Options for the reduced solution are the same as described for the full method except for the following differences:
• Choose the reduced solution method.
• You can include prestress effects (PSTRES). This requires element files from a previous static (or transient) analysis that also included prestress effects. See Section 4.11.1: Prestressed Harmonic Re-sponse Analysis for details.
3. Define master degrees of freedom. Master DOF are essential or dynamic degrees of freedom that char-acterize the dynamic behavior of the structure. For a reduced harmonic response dynamic analysis, master DOF are also required at locations where you want to apply forces or nonzero displacements.
See Section 3.14: Matrix Reduction for guidelines to choose master DOF.
4. Apply loads on the model. Harmonic loading is the same as described for the full method, except for the following restrictions:
• Only displacements and forces are valid. Element loads such as pressures, temperatures, and accel-erations are not allowed.
• Forces and nonzero displacements must be applied only at master DOF.
5. Specify load step options. These are the same as described for the full method except that the OUTRES and ERESX commands are not available, and the constant material damping coefficient (MP,DMPR) is not applicable for the reduced method. The OUTPR command controls the printout of the nodal solution at the master DOF (OUTPR,NSOL,ALL (or NONE)).
6. Save a copy of the database.
Command(s): SAVE
GUI: Utility Menu> File> Save as 7. Start solution calculations.
Command(s): SOLVE
GUI: Main Menu> Solution> Solve> Current LS
8. Repeat steps 4 through 7 for any additional loads and frequency ranges (that is, for additional load steps).
If you plan to do time-history postprocessing (POST26), the frequency ranges should not overlap from one load step to the next. Another method for multiple load steps, which allows you to store the load steps on files and then solve them at once using a macro, is described in the ANSYS Basic Analysis Guide.
9. Leave SOLUTION.
Command(s): FINISH
GUI: Close the Solution menu.
4.9.2. Review the Results of the Reduced Solution
Results from the reduced harmonic solution are written to the reduced harmonic displacement file, Job-name.RFRQ. They consist of displacements at the master DOF, which vary harmonically at each forcing frequency for which the solution was calculated. As with the full method, these displacements will be complex in nature if damping was defined or if out-of-phase loads were applied. You can review the master DOF displacements as a function of frequency using POST26. (POST1 cannot be used, because the complete solution at all DOF is not available.)
The procedure to use POST26 is the same as described for the full method, except for the following differences:
• Before defining the POST26 variables, use the FILE command to specify that data are to be read from Jobname.RFRQ. For example, if HARMONIC is the jobname, the FILE command would be: FILE,HARMON-IC,RFRQ. (By default, POST26 looks for a results file, which is not written by a reduced harmonic solution.)
• Only nodal degree of freedom data (at master DOF) are available for processing, so you can use only the NSOL command to define variables.
4.9.3. Expand the Solution (Expansion Pass)
The expansion pass starts with the reduced solution and calculates the complete displacement, stress, and force solution at all degrees of freedom. These calculations are done only at frequencies and phase angles that you specify. Therefore, before you begin the expansion pass, you should review the results of the reduced solution (using POST26) and identify the critical frequencies and phase angles.
An expansion pass is not always required. For instance, if you are interested mainly in displacements at specific points on the structure, then the reduced solution could satisfy your requirements. However, if you want to de-termine displacements at non-master DOF, or if you are interested in the stress solution, then you must perform an expansion pass.
4.9.3.1. Points to Remember
• The .RFRQ, .TRI, .EMAT, and .ESAV files from the reduced solution must be available.
• The database must contain the same model for which the reduced solution was calculated.
4.9.3.2. Expanding the Modes
1. Reenter the ANSYS solution processor.
Command(s): /SOLU GUI: Main Menu> Solution
Section 4.9: Reduced Harmonic Response Analysis
Note — You must explicitly leave SOLUTION (using the FINISH command) and reenter (/SOLU) before performing the expansion pass.
2. Activate the expansion pass and its options. ANSYS offers these options for the expansion pass: