Mode Superposition Harmonic Response Analysis

The mode superposition method sums factored mode shapes (obtained from a modal analysis) to calculate the harmonic response. It is the only method allowed in the ANSYS Professional program. The procedure to use the method consists of five main steps:

1. Build the model.

2. Obtain the modal solution.

3. Obtain the mode superposition harmonic solution.

4. Expand the mode superposition solution.

5. Review the results.

Of these, the first step is the same as described for the full method. The remaining steps are described below.

4.10.1. Obtain the Modal Solution

Chapter 3, “Modal Analysis” describes how to obtain a modal solution. Following are some additional hints:

• The mode-extraction method should be Block Lanczos (default), subspace, reduced, PowerDynamics, or QR damped. (The other methods, unsymmetric and damped, do not apply to mode superposition.)

• Be sure to extract all modes that may contribute to the harmonic response.

• If PowerDynamics was used for the modal solution, no nonzero loads or displacements are allowed (that is, only u = 0 is valid as the initial condition). PowerDynamics does not create a load vector; therefore, the LVSCALE command is not valid unless the scale factor is set to zero.

• For the reduced mode-extraction method, include those master degrees of freedom at which harmonic loads will be applied.

• If you use the QR damped mode-extraction method, you must specify any damping (ALPHAD, BETAD, MP,DAMP, or element damping including gyroscopic) that you want to include during preprocessing or in the modal analysis. (ANSYS ignores damping specified during the mode superposition harmonic ana-lysis.) You can set a constant damping ratio (DMPRAT), define constant material damping coefficients (MP,DMPR), or define the damping ratio as a function of mode (MDAMP) in a modal superposition har-monic analysis.

• If you need to apply harmonically varying element loads (pressures, temperatures, accelerations, and so on), specify them in the modal analysis. ANSYS ignores the loads for the modal solution, but calculates a load vector and writes it to the mode shape file (Jobname.MODE). You can then use the load vector for the harmonic solution. The imaginary component of the load vector calculated from element loads will always be zero with only one exception: in a full harmonic response analysis or a mode superposition harmonic response analysis with the Block Lanczos mode-extraction method, you can apply imaginary pressures via SURF153 or SURF154.

• The modes need not be expanded for the mode superposition solution. (If you want to review mode shapes, however, you must expand the mode shapes.)

• Do not change the model data (for example, nodal rotations) between the modal and harmonic analyses.

4.10.2. Obtain the Mode Superposition Harmonic Solution

In this step, the program uses mode shapes extracted by the modal solution to calculate the harmonic response.

The mode shape file (Jobname.MODE) must be available, and the database must contain the same model for which the modal solution was obtained. If the modal solution was performed using the subspace or Block Lanczos

Section 4.10: Mode Superposition Harmonic Response Analysis

method using the default mass formulation (not the lumped mass approximation), the full file (Jobname.FULL) must also be available. The following tasks are involved:

1. Enter SOLUTION.

Command(s): /SOLU GUI: Main Menu> Solution

2. Define the analysis type and analysis options. These are the same as described for the full method, except for the following differences:

• Choose the mode superposition method of solution (HROPT).

• Specify the modes you want to use for the solution (HROPT). This determines the accuracy of the harmonic solution. Generally, the number of modes specified should cover about 50 percent more than the frequency range of the harmonic loads.

• Optionally, cluster the solutions about the structure's natural frequencies (HROUT) for a smoother and more accurate tracing of the response curve.

• Optionally, at each frequency, print a summary table that lists the contributions of each mode to the response (HROUT). Note, OUTPR,NSOL must be specified to print mode contributions at each fre-quency.

3. Apply loads on the model. Harmonic loading is the same as described for the full method, except for the following restrictions:

• Only forces, accelerations, and the load vector created in the modal analysis are valid. Use the LVSCALE command to apply the load vector from the modal solution. Note that ALL loads from the modal analysis are scaled, including forces and accelerations. To avoid load duplication, delete any loads that were applied in the modal analysis.

• If mode shapes from a reduced modal solution are being used, forces may be applied only at master DOF.

4. Specify load step options. These are the same as described for the reduced method except that you can also specify modal damping (MDAMP). In addition, if the QR damped method is specified, constant material damping coefficients (MP,DMPR) can be defined.

The NSUBST command specifies the number of solutions on each side of a natural frequency if the clustering option (HROUT) is chosen. The default is to calculate four solutions, but you can specify any number of solutions from 2 through 20. (Any value over this range defaults to 10 and any value below this range defaults to 4.)

5. If you used either the Block Lanczos (default) or the subspace option for the modal analysis (MOD-OPT,LANB or SUBSP), you may use a nodal component with the OUTRES,NSOL command to limit the displacement data written to the reduced displacement file Jobname.RFRQ. The expansion pass will only produce valid results for those nodes and for those elements in which all of the nodes of the elements have been written to the .RFRQ file. To use this option, first suppress all writing by invoking

OUTRES,NSOL,NONE, then specify the item(s) of interest by invoking OUTRES,NSOL,ALL,component.

Repeat the OUTRES command for any additional nodal components that you want to write to the .RFRQ file.

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 3 to 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.

9. Leave SOLUTION.

Command(s): FINISH

GUI: Close the Solution menu.

The mode superposition harmonic solution is written to the reduced displacement file, Jobname.RFRQ, regardless of whether the subspace, Block Lanczos, reduced, PowerDynamics, or QR damped method was used for the modal solution. You will therefore need to expand the solution if you are interested in stress results.

4.10.3. Expand the Mode Superposition Solution

The procedure for the expansion pass is the same as described for the reduced method. Jobname.TRI from the modal analysis is needed only if the reduced eigenvalue extraction method was used. The output from the ex-pansion pass includes the structural results file, Jobname.RST, containing expanded results. See Section 4.9.3:

Expand the Solution (Expansion Pass).

4.10.4. Review the Results

Results consist of harmonically varying displacements, stresses, and reaction forces at each forcing frequency for which the solution was calculated. You can review these results using POST26 or POST1, as explained for the reduced method.

4.10.5. Sample Input

A sample input listing for a mode superposition harmonic response analysis is shown below:

! Build the Model

! Obtain the Modal Solution

/SOLU ! Enter SOLUTION

! Obtain the Mode Superposition Harmonic Solution /SOLU ! Enter SOLUTION

Section 4.10: Mode Superposition Harmonic Response Analysis

DMPRAT,... ! Damping ratio

MDAMP,... ! Modal damping ratios

NSUBST,... ! Number of harmonic solutions KBC,... ! Ramped or stepped loads SAVE

SOLVE ! Initiate solution FINISH

! Review the Results of the Mode Superposition Solution /POST26

FILE,,RFRQ ! Postprocessing file is Jobname.RFRQ NSOL,... ! Store nodal result as a variable PLCPLX,... ! Define how to plot complex variables PLVAR,... ! Plot variables

FINISH

! Expand the Solution (for Stress Results) /SOLU! Re-enter SOLUTION

EXPASS,ON ! Expansion pass

EXPSOL,... ! Expand a single solution

HREXP,... ! Phase angle for expanded solution SOLVE

FINISH

! Review the Results of the Expanded Solution /POST1

SET,... ! Read results for desired frequency PLDISP,... ! Deformed shape

PLNSOL,... ! Contour plot of nodal results

---FINISH

See the ANSYS Commands Reference for a discussion of the ANTYPE, MODOPT, M, TOTAL, HROPT, HROUT, LVSCALE, F, HARFRQ, DMPRAT, MDAMP, NSUBST, KBC, FILE, NSOL, PLCPLX, PLVAR, EXPASS, EXPSOL, HREXP, SET, and PLNSOL commands.