Time-Dependent Loads – TLOAD2 Entry
6.9 Examples of Transient Response Analysis
This section provides several examples showing the input and output. These examples are Model Transient Response Bulk
These examples are described in the sections that follow.
Two-DOF Model
Consider the two-DOF system shown inFigure 6-6. Direct transient response (SOL 109) is run with an initial displacement of 0.1 meter at grid point 2. The analysis is run for a duration of 10 seconds with a Δt of 0.01 second. Damping is neglected in the analysis. Part of the input file is shown below.
Figure 6-6. Two-DOF Model
SOL 109 $ DIRECT TRANSIENT RESPONSE CEND
TITLE = TWO-DOF SYSTEM
SUBTITLE = DIRECT FREQUENCY RESPONSE LABEL = INITIAL DISPL. AT GRID 2
$
Figure 6-7. Input File (Abridged) for the Two-DOF Example
Table 6-8shows the relationship between the Case Control commands and the Bulk Data entries.
This example represents the simplest form of dynamic response input. The only required entries are those that define the time step and the initial conditions. Any unspecified initial conditions are assumed to be zero.
Table 6-8. Relationship Between Case Control Commands and Bulk Data Entries for the Two-DOF Model
Case Control Bulk Data
TSTEP TSTEP
IC TIC
Figure 6-8shows the plots of the resulting displacements for grid points 1 and 2. Note that there are two frequencies of response: a higher frequency of about 5 Hz, and a lower frequency of about 0.25 Hz. The energy (and hence response) appears to be transferred repetitively between grid points 1 and 2 as represented by the lower frequency response. This energy transfer is called beating. Beating occurs when there are closely-spaced modes (in this case, 4.79 Hz and 5.29 Hz) in which energy transfer can readily occur. The response is comprised of two frequencies as given below:
Equation 6-32.
where:
f1 = lower of the closely-spaced mode frequencies f2 = higher of the closely-spaced mode frequencies
In this example, fhigheris 5.04 Hz and floweris 0.25 Hz. The lower frequency is called the beat frequency and is the frequency at which energy transfer occurs.
Figure 6-8. Displacements of Grid Points 1 and 2
Cantilever Beam Model
Consider the cantilever beam shown below. This beam model is the same as in“Examples” in Chapter 5. Modal transient response (SOL 112) is run with loads applied to grid points 6 and 11 as shown inFigure 6-10. The analysis is run for a duration of 2 seconds with a Δt of 0.001 second.
Modal damping of 5% critical damping is used for all modes. Modes up to 3000 Hz are computed using the Lanczos method. Figure 6-11shows part of the input file.
Figure 6-9. Cantilever Beam Model with Applied Loads
Figure 6-10. Applied Loads for the Beam Model
$ FILE bd06bar.dat
$
$ CANTILEVER BEAM MODEL
$ CHAPTER 6, TRANSIENT RESPONSE
$
SOL 112 $ MODAL TRANSIENT RESPONSE TIME 10
CEND
TITLE = CANTILEVER BEAM
SUBTITLE = MODAL TRANSIENT RESPONSE
$ SPC = 21 DLOAD = 22 TSTEP = 27 SDAMPING = 25
$
METHOD = 10
$
$ PHYSICAL OUTPUT REQUEST SET 11 = 6,11
DISPLACEMENT(PLOT) = 11 ACCELERATION(PLOT) = 11
$
$ MODAL SOLUTION SET OUTPUT SET 12 = 1,2
SDISP(PLOT) = 12
$
$ MODAL DAMPING OF 5% IN ALL MODES
$TABDMP1 TID TYPE +TABD
$+TABD F1 G1 F2 G2 ETC.
TABDMP1 25 CRIT +TABD
+TABD 0. 0.05 1000. 0.05 ENDT
$
$ DYNAMIC LOADING
$DLOAD SID S S1 L1 S2 L2
DLOAD 22 1.0 1.0 231 1.0 232
$TLOAD2 SID DAREA DELAY TYPE T1 T2 F P +TL1
$+TL1 C B
Figure 6-11. Input File (Abridged) for the Beam Example
Table 6-9shows the relationship between the Case Control commands and the Bulk Data entries. The DLOAD Bulk Data entry references two TLOAD2 entries, each of which references separate DAREA entries. A TLOAD2 entry also references a DELAY entry to apply the time delay to the load at grid point 6.
Table 6-9. Relationship Between Case Control Commands and Bulk Data Entries for the Bar Model
Case Control Bulk Data
METHOD EIGRL
TSTEP TSTEP
SDAMPING TABDMP1
Table 6-9. Relationship Between Case Control Commands and Bulk Data Entries for the Bar Model
Case Control Bulk Data
DLOAD
Plotted output is shown in the following figures. Figure 6-12shows the applied loads at grid points 6 and 11. Figure 6-13shows the plots of the displacements for grid points 6 and 11. Figure 6-14shows the accelerations for grid points 6 and 11. Figure 6-15shows the bending moment at end A in plane 1 for element 6. Figure 6-16shows the modal displacements for modes 1 and 2.
Figure 6-12. Applied Loads at Grid Points 6 and 11
Figure 6-13. Displacements at Grid Points 6 and 11
Figure 6-14. Accelerations at Grid Points 6 and 11
Figure 6-15. Bending Moment A1 for Element 6
Figure 6-16. Modal Displacements for Modes 1 and 2
Bracket Model
Consider the bracket model shown in Figure 6-17. A pressure load of 3 psi is applied to the elements in the top face in the z-direction with the time history shown inFigure 6-18. The modal transient analysis is run for 4 seconds with a time step size of 0.005 second. Modal damping of 2% critical damping is used for all modes. Modes up to 3000 Hz are computed with the Lanczos method. The model is constrained near the base.
Figure 6-17. Bracket Model
Figure 6-18. Time Variation for Applied Load
Figure 6-19shows the abridged input file. The LSEQ entry is used to apply the pressure loads (PLOAD4 entries). Note that the LSEQ and TLOAD1 entries reference a common DAREA ID (999) and that there is no explicit DAREA entry. Table 6-10shows the relationship between the Case Control commands and the Bulk Data entries.
$ FILE bd06bkt.dat
$
$ BRACKET MODEL
$ CHAPTER 6, TRANSIENT RESPONSE
$
SOL 112 $ MODAL TRANSIENT RESPONSE TIME 100
CEND
TITLE = BRACKET MODEL
SUBTITLE = MODAL TRANSIENT RESPONSE ANALYSIS
$
SPC = 1
$
METHOD = 777
$
DLOAD = 2 LOADSET = 3 SDAMPING = 4 TSTEP = 5
$
$ OUTPUT REQUEST SET 123 = 999
DISPLACEMENT(PLOT)=123
$
$ NORMAL MODES TO 3000 HZ
$EIGRL SID V1 V2
$ MODAL DAMPING OF 2% CRITICAL
$TABDMP1 TID TYPE +TABD1
$+TABD1 F1 G1 F2 G2 ETC.
TABDMP1 4 CRIT +TABD1
+TABD1 0.0 0.02 3000.0 0.02 ENDT
$
$ LOAD DEFINITION
$
$TLOAD1 SID DAREA DELAY TYPE TID
TLOAD1 2 999 22
$ PRESSURE LOAD OF 3 PSI PER ELEMENT
$PLOAD4 SID EID P1
Figure 6-19. Input File (Abridged) for the Bracket Model
Table 6-10. Relationship Between Case Control Commands and Bulk Data Entries for the Bracket Model
Figure 6-20shows a plot of the z-displacement of grid point 999, which is the concentrated mass at the center of the cutout.
Figure 6-20. Displacement Time History for Grid Point 999