Figure 6.2 Simply Supported Beam with Vertical Motion of Both Supports
15. The PRRSOL Command listing window appears. Review the results in the listing window and click on Close to close the PRRSOL Command listing window
6.4.4.20. Exit ANSYS
1. In the ANSYS Toolbar, click on Quit.
2. Choose the save option you want and click on OK.
You are now finished with this sample problem.
6.5. Sample Spectrum Analysis (Command or Batch Method)
You can perform the example spectrum analysis using the ANSYS commands shown below instead of GUI choices.
Items prefaced by an exclamation point (!) are comments.
/PREP7
/TITLE Seismic Response of a Beam Structure ET,1,BEAM3
R,1,273.9726,(1000/3),14 ! A = 273.9726, I = (1000/3), H = 14 MP,EX,1,30E6
MP,DENS,1,73E-5 K,1
K,2,240 L,1,2 ESIZE,,8 LMESH,1
NSEL,S,LOC,X,0 D,ALL,UY
NSEL,S,LOC,X,240 D,ALL,UX,,,,,UY NSEL,ALL
FINISH /SOLU
ANTYPE,MODAL ! Mode-frequency analysis
MODOPT,REDUC,,,,3 ! Householder, print first 3 reduced mode shapes
MXPAND,10,,,YES,0.005 ! Expand 10 mode shapes, calculate element stresses ! set signif=0.005
SOLVE FINISH /SOLU
ANTYPE,SPECTR
SRSS,0.15,DISP ! Square Root of Sum of Squares Mode combination ! with signif=0.15 and displacement solution requested
6.6. Where to Find Other Examples
Several ANSYS publications, particularly the ANSYS Verification Manual, describe additional spectrum analyses.
The ANSYS Verification Manual consists of test case analyses demonstrating the analysis capabilities of the ANSYS program. While these test cases demonstrate solutions to realistic analysis problems, the ANSYS Verification 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 spectrum analysis test cases:
VM19 - Random Vibration Analysis of a Deep Simply-Supported Beam VM68 - PSD Response of a Two DOF Spring-Mass System
VM69 - Seismic Response
VM70 - Seismic Response of a Beam Structure
VM203 - Dynamic Load Effect on Simply-Supported Thick Square Plate
See the ANSYS Commands Reference for a discussion of the ANTYPE, MODOPT, D, EXPASS, MXPAND, SPOPT, SVTYP, SED, FREQ, SV, SRSS, CQC, DSUM, GRP, NRLSUM, and DMPRAT commands.
Section 6.6: Where to Find Other Examples
6.7. How to Do a Random Vibration (PSD) Analysis
The procedure for a PSD analysis consists of six main steps:
1. Build the model.
2. Obtain the modal solution.
3. Expand the modes.
4. Obtain the spectrum solution.
5. Combine the modes.
6. Review the results.
Of these, the first two steps are the same as described for a single-point response spectrum analysis. The procedure for the remaining four steps is explained below. Random vibration analysis is not available in the ANSYS Profes-sional program.
In the GUI method, the dialog box for the modal analysis options [MODOPT] contains an option for mode expan-sion [MXPAND]. Choose YES for mode expanexpan-sion. You then follow the instructions in Section 6.7.1: Expand the Modes. The procedures for obtaining the modal solution and expanding the nodes are combined into a single step.
6.7.1. Expand the Modes
You must expand modes regardless of whether you used the subspace, Block Lanczos, or reduced extraction method. Details about expanding the modes are explained in Section 3.6: Expand the Modes, but keep in mind the following additional points:
• Only expanded modes are used for the mode combination step.
• If you are interested in stresses caused by the spectrum, be sure to request stress calculations here. By default, no stresses are calculated in the expansion pass, which means no stresses are available at the end of the spectrum solution.
• The mode expansion can be performed as a separate step, or can be included in the modal analysis phase.
• At the end of the expansion pass, leave SOLUTION with the FINISH command. If you want to exit ANSYS after running the modal analysis, you must save the database at this point.
As explained in Chapter 3, “Modal Analysis”, you can combine the modal solution and mode expansion steps by including the MXPAND command in the modal analysis step (GUI and batch modes).
6.7.2. Obtain the Spectrum Solution
To obtain the PSD spectrum solution, the database must contain the model data as well as the modal solution data. If you leave ANSYS after running the modal analysis, you must save the database. In addition, the following files from the modal solution must be available: Jobname.MODE, .ESAV, .EMAT, .FULL (only for subspace and Block Lanczos methods), .RST.
1. Enter SOLUTION.
Command(s): /SOLU GUI: Main Menu> Solution
2. Define the analysis type and analysis options:
For spectrum type [SPOPT], choose Power Spectral Density (PSD).
•
• Specify stress calculations ON [SPOPT] if you are interested in stress results. Stresses caused by the spectrum are calculated only if they were also requested during the modal expansion pass.
3. Specify load step options. The following options are available for a random vibration analysis:
• Spectrum Data – Type of PSD
Command(s): PSDUNIT
GUI: Main Menu> Solution> Load Step Opts> Spectrum> PSD> Settings
The PSD type can be displacement, velocity, force, pressure, or acceleration. Whether it is a base excitation or a nodal excitation is specified in Steps 4 and 5. If a pressure PSD is to be applied, the pressures should be applied in the modal analysis itself.
– PSD-versus-frequency table
Define a piecewise-linear (in log-log scale) PSD versus frequency table. Since a curve-fitting polynomial is used for the closed-form integration of the curve, you should graph the input, which is overlaid with the fitted curve, to ensure a good fit. If the fit is not good, you should add one or more intermediate points to the table until you obtain a good fit.
Command(s): PSDFRQ, PSDVAL, PSDGRAPH
GUI: Main Menu> Solution> Load Step Opts> Spectrum> PSD> PSD vs Freq Main Menu> Solution> Load Step Opts> Spectrum> PSD> Graph PSD Tables PSDFRQ and PSDVAL are used to define the PSD-versus-frequency table. Step 6 describes how to apply additional PSD excitations (if any).
You can issue STAT to list PSD tables and issue PSDGRAPH to graph them.
• Damping (Dynamics Options)
The following forms of damping are available: ALPHAD, BETAD, and MDAMP result in a frequency-dependent damping ratio, whereas DMPRAT specifies a constant damping ratio to be used at all frequencies. If you specify more than one form of damping, ANSYS calculates an effective damping ratio at each frequency.
Note — If no damping is specified in a PSD analysis, a default DMPRAT of 1 percent is used.
– Alpha (Mass) Damping
Command(s): ALPHAD
GUI: Main Menu> Solution> Load Step Opts> Time/Frequenc> Damping – Beta (Stiffness) Damping
Command(s): BETAD
GUI: Main Menu> Solution> Load Step Opts> Time/Frequenc> Damping – Constant Damping Ratio
Command(s): DMPRAT
GUI: Main Menu> Solution> Load Step Opts> Time/Frequenc> Damping – Frequency-Dependent Damping Ratio
Command(s): MDAMP
GUI: Main Menu> Solution> Load Step Opts> Time/Frequenc> Damping
Section 6.7: How to Do a Random Vibration (PSD) Analysis
The remaining steps are specific to a random vibration analysis:
4. Apply the PSD excitation at the desired nodes.
Use a value of 1.0 to indicate points where the PSD excitation applies. A value of 0.0 (or blank) can be used to remove a specification. The excitation direction is implied by the UX, UY, UZ labels on the D command (for base excitation), and by FX, FY, FZ on the F command (for nodal excitation). For nodal excitation, values other than 1.0 can be used to scale the participation factors. For pressure PSD, bring in the load vector from the modal analysis (LVSCALE). You can use the scale factor.
Note — You can apply base excitations only at nodes that were constrained in the modal analysis.
Command(s): D (or DK, DL, or DA) for base excitation F (or FK) for nodal excitation LVSCALE for pressure PSD
GUI: Main Menu> Solution> Define Loads> Apply> Structural> Spectrum> Base PSD Excit>
On Nodes
5. Begin participation factor calculations for the above PSD excitation.
Use the TBLNO field to indicate which PSD table to use, and Excit to specify whether the calculations are for a base or nodal excitation.
Command(s): PFACT
GUI: Main Menu> Solution> Load Step Opts> Spectrum> PSD> Calculate PF
6. If you need to apply multiple PSD excitations on the same model, repeat steps 3, 4, and 5 for each addi-tional PSD table. Then define, as necessary, the degree of correlation between the excitations, using any of the following commands:
Command(s): COVAL for cospectral values QDVAL for quadspectral values PSDSPL for a spatial relationship PSDWAV for a wave propagation relationship PSDGRAPH to graph the data overlaid with the fitted curve
GUI: Main Menu> Solution> Load Step Opts> Spectrum> PSD> Correlation Main Menu> Solution> Load Step Opts> Spectrum> PSD> Graph Tables
When you use the PSDSPL or PSDWAV command, you must use SPATIAL or WAVE, respectively, for Parcor on the PFACT command. PSDSPL and PSDWAV relationships might be quite CPU intensive for multi-point base excitations. Nodal excitation and base excitation input must be consistent when using PSDWAV and PSDSPL (for example, FY cannot be applied to one node and FZ be applied to another).
The PSDSPL and PSDWAV commands are not available for a pressure PSD analysis.
7. Specify the output controls.
The only valid output control command for this analysis is PSDRES, which specifies the amount and form of output written to the results file. Up to three sets of solution quantities can be calculated: dis-placement solution, velocity solution, or acceleration solution. Each of these can be relative to the base or absolute.
Command(s): PSDRES
GUI: Main Menu> Solution> Load Step Opts> Spectrum> PSD> Calc Controls
Table 6.3: “Solution Items Available in a PSD Analysis” shows a summary of the possible solution sets. To limit the amount of data written to the results file, use OUTRES at the mode expansion step. Using OUTPR,NSOL,ALL provides a summary table of the significant modal covariance terms.