Dynamic Load Set Combination – DLOAD
5.9 Examples of Frequency Response Analysis
This section provides several examples showing the input and output. These examples are:
Model Frequency Response Bulk Data
RLOAD2, DAREA, DPHASE, TABLED1 X-Y plots (log)
Model Frequency Response Bulk Data
Entries Output
bd05bkt EIGRL, FREQ1, TABDMP1, RLOAD1,
LSEQ, TABLED1, PLOAD4 X-Y plot (log) These examples are described in the sections that follow.
Two-DOF Model
Consider the two-DOF system shown inFigure 5-8. Modal frequency response (SOL 111) is run with a 20 N load applied to the primary mass (grid point 2) across a frequency range of 2 to 10 Hz with an excitation frequency increment of 0.05 Hz. Uniform modal damping of 5% critical damping is used. Part of the input file is shown below.
Figure 5-8. Two-DOF Model
SOL 111 $ MODAL FREQUENCY RESPONSE CEND
TITLE = TWO-DOF SYSTEM
SUBTITLE = MODAL FREQUENCY RESPONSE
LABEL = 20 N FORCE APPLIED TO PRIMARY MASS
$
... X-Y plot commands ...
+TAB901 0.0 1.0 10.0 1.0 ENDT
$
$ ALTERNATE LOAD DEFINITION USING DLOAD
$DLOAD SID S S1 RLOAD1
$ MODAL DAMPING OF 5% CRITICAL
$TABDMP1 TID TYPE +TABD1
$+TABD1 F1 G1 F2 G2 ETC.
TABDMP1 777 CRIT +TABD7
+TABD7 0. 0.05 100. 0.05 ENDT
$
$ MODAL EXTRACTION
$EIGRL SID V1 V2 ND MSGLVL
EIGRL 10 -0.1 20. 0
$
... basic model ...
$ ENDDATA
Figure 5-9. Input File (Abridged) for the Two-DOF Example
Table 5-8shows the relationship between the Case Control commands and the Bulk Data entries.
Note that the RLOAD1 entry references the DAREA and TABLED1 entries. The input file also shows an alternate way to specify the dynamic load, by using a DLOAD Bulk Data entry.
Because there is only a single RLOAD1 entry, the DLOAD Bulk Data entry is not required.
Table 5-8. Relationship Between the Case Control Commands and Bulk Data Entries for the Two-DOF Model
The RLOAD1 entry describes a sinusoidal load in the form
Equation 5-28.
where:
A = 20.0 (entered on the DAREA entry)
C = 1.0 for all frequencies entered on the TABLED1 entry D = 0.0 (field 7 of the RLOAD1 entry is blank)
q = 0.0 (field 5 of the RLOAD1 entry is blank) t = 0.0 (field 4 of the RLOAD1 entry is blank)
Output can be printed in either real/imaginary or magnitude/phase format and in either SORT1 or SORT2 format. These formats are illustrated inFigure 5-10,Figure 5-11, and Figure 5-12 showing a portion of their printed output.
POINT-ID = 1
C O M P L E X D I S P L A C E M E N T V E C T O R (REAL/IMAGINARY)
FREQUENCY TYPE T1 T2 T3 R1 R2 R3
2.000000E+00 G 0.0 2.813052E-03 0.0 0.0 0.0 0.0
0.0 -2.107985E-04 0.0 0.0 0.0 0.0
2.050000E+00 G 0.0 2.866642E-03 0.0 0.0 0.0 0.0
0.0 -2.229164E-04 0.0 0.0 0.0 0.0
2.100000E+00 G 0.0 2.923141E-03 0.0 0.0 0.0 0.0
0.0 -2.358382E-04 0.0 0.0 0.0 0.0
2.150000E+00 G 0.0 2.982732E-03 0.0 0.0 0.0 0.0
0.0 -2.496362E-04 0.0 0.0 0.0 0.0
2.200000E+00 G 0.0 3.045609E-03 0.0 0.0 0.0 0.0
0.0 -2.643908E-04 0.0 0.0 0.0 0.0
POINT-ID = 2
C O M P L E X D I S P L A C E M E N T V E C T O R (REAL/IMAGINARY)
FREQUENCY TYPE T1 T2 T3 R1 R2 R3
2.000000E+00 G 0.0 2.374954E-03 0.0 0.0 0.0 0.0
0.0 -1.129933E-04 0.0 0.0 0.0 0.0
2.050000E+00 G 0.0 2.397706E-03 0.0 0.0 0.0 0.0
0.0 -1.180853E-04 0.0 0.0 0.0 0.0
2.100000E+00 G 0.0 2.421475E-03 0.0 0.0 0.0 0.0
0.0 -1.234173E-04 0.0 0.0 0.0 0.0
2.150000E+00 G 0.0 2.446311E-03 0.0 0.0 0.0 0.0
0.0 -1.290072E-04 0.0 0.0 0.0 0.0
2.200000E+00 G 0.0 2.472262E-03 0.0 0.0 0.0 0.0
0.0 -1.348744E-04 0.0 0.0 0.0 0.0
Figure 5-10. Real/Imaginary Output in SORT2 Format
POINT-ID = 1
C O M P L E X D I S P L A C E M E N T V E C T O R (MAGNITUDE/PHASE)
FREQUENCY TYPE T1 T2 T3 R1 R2 R3
2.000000E+00 G 0.0 2.820939E-03 0.0 0.0 0.0 0.0
0.0 355.7145 0.0 0.0 0.0 0.0
2.050000E+00 G 0.0 2.875296E-03 0.0 0.0 0.0 0.0
0.0 355.5535 0.0 0.0 0.0 0.0
2.100000E+00 G 0.0 2.932640E-03 0.0 0.0 0.0 0.0
0.0 355.3874 0.0 0.0 0.0 0.0
2.150000E+00 G 0.0 2.993161E-03 0.0 0.0 0.0 0.0
0.0 355.2159 0.0 0.0 0.0 0.0
2.200000E+00 G 0.0 3.057064E-03 0.0 0.0 0.0 0.0
0.0 355.0386 0.0 0.0 0.0 0.0
POINT-ID = 2
C O M P L E X D I S P L A C E M E N T V E C T O R (MAGNITUDE/PHASE)
FREQUENCY TYPE T1 T2 T3 R1 R2 R3
2.000000E+00 G 0.0 2.377640E-03 0.0 0.0 0.0 0.0
0.0 357.2761 0.0 0.0 0.0 0.0
2.050000E+00 G 0.0 2.400612E-03 0.0 0.0 0.0 0.0
0.0 357.1805 0.0 0.0 0.0 0.0
2.100000E+00 G 0.0 2.424619E-03 0.0 0.0 0.0 0.0
0.0 357.0823 0.0 0.0 0.0 0.0
2.150000E+00 G 0.0 2.449710E-03 0.0 0.0 0.0 0.0
0.0 356.9813 0.0 0.0 0.0 0.0
2.200000E+00 G 0.0 2.475939E-03 0.0 0.0 0.0 0.0
0.0 356.8773 0.0 0.0 0.0 0.0
Figure 5-11. Magnitude/Phase Output in SORT2 Format
FREQUENCY = 2.000000E+00
C O M P L E X D I S P L A C E M E N T V E C T O R (REAL/IMAGINARY)
POINT ID. TYPE T1 T2 T3 R1 R2 R3
1 G 0.0 2.813051E-03 0.0 0.0 0.0 0.0
0.0 -2.107985E-04 0.0 0.0 0.0 0.0
2 G 0.0 2.374954E-03 0.0 0.0 0.0 0.0
0.0 -1.129933E-04 0.0 0.0 0.0 0.00
FREQUENCY = 2.050000E+00
C O M P L E X D I S P L A C E M E N T V E C T O R (REAL/IMAGINARY)
POINT ID. TYPE T1 T2 T3 R1 R2 R3
1 G 0.0 2.866640E-03 0.0 0.0 0.0 0.0
0.0 -2.229163E-04 0.0 0.0 0.0 0.0
2 G 0.0 2.397706E-03 0.0 0.0 0.0 0.0
0.0 -1.180853E-04 0.0 0.0 0.0 0.00
FREQUENCY = 2.100000E+00
C O M P L E X D I S P L A C E M E N T V E C T O R (REAL/IMAGINARY)
POINT ID. TYPE T1 T2 T3 R1 R2 R3
1 G 0.0 2.923141E-03 0.0 0.0 0.0 0.0
0.0 -2.358381E-04 0.0 0.0 0.0 0.0
2 G 0.0 2.421475E-03 0.0 0.0 0.0 0.0
0.0 -1.234173E-04 0.0 0.0 0.0 0.00
FREQUENCY = 2.150000E+00
C O M P L E X D I S P L A C E M E N T V E C T O R (REAL/IMAGINARY)
POINT ID. TYPE T1 T2 T3 R1 R2 R3
1 G 0.0 2.982731E-03 0.0 0.0 0.0 0.0
0.0 -2.496362E-04 0.0 0.0 0.0 0.0
2 G 0.0 2.446311E-03 0.0 0.0 0.0 0.0
0.0 -1.290072E-04 0.0 0.0 0.0 0.00
FREQUENCY = 2.200000E+00
C O M P L E X D I S P L A C E M E N T V E C T O R (REAL/IMAGINARY)
POINT ID. TYPE T1 T2 T3 R1 R2 R3
1 G 0.0 3.045608E-03 0.0 0.0 0.0 0.0
0.0 -2.643907E-04 0.0 0.0 0.0 0.0
2 G 0.0 2.472263E-03 0.0 0.0 0.0 0.0
0.0 -1.348744E-04 0.0 0.0 0.0 0.0
Figure 5-12. Real/Imaginary Output in SORT1 Format
Figure 5-13shows the plots of the resulting displacement magnitudes for grid points 1 and 2.
Note that the response for grid point 1 is nearly an order of magnitude larger than that of grid point 2. This large difference in response magnitudes is characteristic of dynamic absorbers (also called tuned mass dampers), in which an auxiliary structure (i.e., the small mass and stiffness) is attached to the primary structure in order to decrease the dynamic response of the primary structure. If this same model is rerun without the auxiliary structure, the response of the primary structure (grid point 2) at 5.03 Hz is twice what it was with the auxiliary structure attached, as shown inFigure 5-14.
Figure 5-13. Displacement Response Magnitudes With the Auxiliary Structure
Figure 5-14. Displacement Response Magnitude Without the Auxiliary Structure
Cantilever Beam Model
Consider the cantilever beam shown inFigure 5-15. This model is a planar model of the
cantilever beam introduced in“Real Eigenvalue Analysis”with unrestrained DOFs in the T2 and R3 directions. Two loads are applied: one at grid point 6 and the other at grid point 11. The loads have the frequency variation shown inFigure 5-16. The loads in the figure are indicated with a heavy line in order to emphasize their values. The load at grid point 6 has a 45-degree phase lead, and the load at grid point 11 is scaled to be twice that of the load at grid point 6.
Modal frequency response is run across a frequency range of 0 to 20 Hz. Modal damping is used with 2% critical damping between 0 and 10 Hz and 5% critical damping above 10 Hz. Modes to 500 Hz are computed using the Lanczos method.
Figure 5-15. Cantilever Beam Model with Applied Loads
Figure 5-16. Applied Loads
The abridged input file is shown below. The output quantities, as defined in the Case Control Section, are the applied loads (OLOAD) for grid points 6 and 11, physical displacements (DISPLACEMENT) for grid points 6 and 11, solution set displacements (SDISPLACEMENT) for modes 1 and 2, and element forces (ELFORCE) for element 6. These output quantities are plotted rather than printed.
$ FILE bd05bar.dat
$
$ CANTILEVER BEAM MODEL
$ CHAPTER 5, FREQUENCY RESPONSE
$
SOL 111 $ MODAL FREQUENCY RESPONSE
+TABD1 0.0 0.02 10.0 0.02 10.01 0.05 25.0 0.05 +TABD2 +TABD2 ENDT
$
$ DYNAMIC LOADING
$DLOAD SID S S1 L1 S2 L2
DLOAD 22 1.0 1.0 231 1.0 232
$RLOAD2 SID DAREA DELAY DPHASE TB TP
RLOAD2 231 241 261 25
Figure 5-17. Input File (Abridged) for the Beam Example
Table 5-9shows the relationship between the Case Control commands and the Bulk Data entries.
Note that the DLOAD Bulk Data entry references two RLOAD2 entries, each of which references a separate DAREA entry and a common TABLED1 entry. The RLOAD2 entry for grid point 6 also references a DPHASE entry that defines the 45-degree phase lead.
Table 5-9. Relationship Between Case Control Commands and Bulk Data Entries for the Beam Model
Case Control Bulk Data
METHOD EIGRL
FREQUENCY FREQ1
SDAMPING TABDMP1
Table 5-9. Relationship Between Case Control Commands and Bulk Data Entries for the Beam Model
Case Control Bulk Data
DLOAD
The RLOAD2 entry describes a sinusoidal load in the form
Equation 5-29.
where:
A = 1.0 for grid point 6 and 2.0 for grid point 11 (entered on the DAREA entry) B = function defined on the TABLED1 entry
f = 0.0 (field 7 of the RLOAD2 entry is blank)
q = phase lead of 45 degrees for grid point 6 (entered on the DPHASE entry) t = 0.0 (field 4 of the RLOAD2 entry is blank)
Logarithmic plots of the output are shown in the following figures. Figure 5-18shows the magnitude of the displacements for grid points 6 and 11. Figure 5-19shows the magnitude of the modal displacements for modes 1 and 2. Figure 5-20shows the magnitude of the bending moment at end A in plane 1 for element 6. Logarithmic plots are especially useful for displaying frequency response results since there can be several orders of magnitude between the maximum and minimum response values.
Figure 5-18. Displacement Magnitude (Log)
Figure 5-19. Modal Displacement Magnitude (Log)
Figure 5-20. Bending Moment Magnitude at End A, Plane 1 (Log)
Bracket Model
Consider the bracket model shown inFigure 5-21. An oscillating pressure load of 3 psi is applied to the elements on the top face in the z-direction. The model is constrained at its base. Modal frequency response is run from 0 to 100 Hz with a frequency step size of 0.2 Hz. Eigenvalues to 1000 Hz are computed using the Lanczos method. Modal damping is applied as 2% critical damping for all modes.
Figure 5-21. Bracket Model
Figure 5-22shows the abridged input file. The LSEQ entry is used to apply the pressure loads (PLOAD4 entries). Note that the LSEQ and RLOAD1 entries reference a common DAREA ID (999) and that there is no explicit DAREA entry. Table 5-10shows the relationship between the Case Control commands and the Bulk Data entries.
$ FILE bd05bkt.dat
$
$ BRACKET MODEL
$ CHAPTER 5, FREQUENCY RESPONSE
$
SOL 111 $ MODAL FREQUENCY RESPONSE TIME 100
CEND
TITLE = BRACKET MODEL
SUBTITLE = MODAL FREQUENCY RESPONSE ANALYSIS
$
$ NORMAL MODES TO 1000 HZ
$EIGRL SID V1 V2
EIGRL 777 -0.1 1000.
$
$ EXCITATION FREQUENCY DEFINITION 0 TO 100 HZ
$FREQ1 SID F1 DF NDF
FREQ1 5 0.0 0.2 500
$
$ MODAL DAMPING OF 2% CRITICAL FOR ALL MODES
$TABDMP1 TID TYPE +TABD1
$+TABD1 F1 G1 F2 G2 ETC.
TABDMP1 4 CRIT +TABD1
+TABD1 0.0 0.02 1000.0 0.02 ENDT
$
$ LOAD DEFINITION
$
$RLOAD1 SID DAREA DELAY DPHASE TC TD
RLOAD1 2 999 22
+TABL1 0.0 1.0 1000.0 1.0 ENDT
$
$ PRESURE LOAD OF 3 PSI PER ELEMENT
$PLOAD4 SID EID P1
PLOAD4 1 171 -3.
PLOAD4 1 172 -3.
PLOAD4 1 160 -3.
etc.
$
... basic model ...
$ ENDDATA
Figure 5-22. Abridged Input File for the Bracket Model
Table 5-10. Relationship Between Case Control Commands and Bulk Data Entries for the Bracket Model
Case Control Bulk Data
METHOD EIGRL
FREQUENCY FREQ1
SDAMPING TABDMP1
LOADSET
DLOAD
Figure 5-23shows a logarithmic plot of the z-displacement magnitude of grid point 999, which is the concentrated mass at the center of the cutout.
Figure 5-23. Displacement Magnitude (Log)