shock spectrum analysis · •post processing of modal analysis (sol 103) •response at each modal...
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MSC.Software Confidential
Shock Spectrum AnalysisMarch 2011
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Shock Spectrum Analysis
• What is Response (Shock) Spectra
• What is the difference between Harmonic and Shock Spectrum
Input
• How to create Shock Spectra from acceleration transient input
• How to analyze structure subjected to shock input
• Various methods to combine modal response
• Comparison between transient and shock spectrum analysis.
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• Poor man’s Transient Analysis
• Approximate method to predict the peak
response of a structure
• Linear Analysis only – nonlinearity required
direct transient analysis
• Widely used in Seismic analysis of structures
(building, nuclear power plants, civil
engineering)
Shock Spectrum Analysis
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What is Response Spectra?
• The peak response of series of SDOF
oscillators (each with different frequency,
same damping) subjected to transient
input
•This can then be repeated for a different
damping
• See next slide for more details
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Transient Input
f1 f2 f3 f4 f5 fi fn
Ma
x. A
cce
lera
tio
n R
esp
on
se
Frequency
ξKi
Mi
Fi = (1/2π) (Ki/Mi) = Constant Dampingξ
Response Spectra, Damping = ξ
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Simple Application
Transient Analysis
Transient Response
Mass of Antenna Structure 2 %
4 %
7 %
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Simple Application
2 %
4 %
7 %
Antenna structure 3%
Interpolated for sub-structure damping
3 %
• Multiple transient analyses
• Multiple representative seismic motion
• Input in different direction
• Envelope all Spectra
• Apply enveloped spectra at base of small
equipment
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• Single Analysis covering multiple transient
events
• Envelope of Response Spectra of
multiple transient events
• Simulation of non-deterministic seismic
events
• Evaluating the frequency content of
transient motion – similar to FFT
• Explosion at base of structure – Shock
Spectrum
Other uses
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Harmonic vs Response Spectra
Frequency
G
2 %
4 %
7 %
Frequency
G
Harmonic Input Shock Spectra Input
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Harmonic Vs Response Spectra
• Harmonic – Sinusoidal Excitation
• Damping independent input
• Steady State Harmonic Response
• Complex Results (Phase angle)
• Response Spectra
• Damping dependent excitation
• Equivalent static response
• No phasing information
• RSS Results – all positive response
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Generation of Response Spectra
• Can be generated in Transient Analysis
• Sol 109 (Direct) or Sol 112 (Modal)
• Old style XYPlot/XYPunch/XYPrint request
• Simple Input Requirement
• Best Pre-processor – Any text editor
• and Post-Processor? XYPunch/xyplot Excel
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Generation of Response Spectra
Input requirement – Case Control Section
• Must request Displacement, Velocity and
Acceleration for all Grids for which Spectra to be
generated
Example: Response Spectra to be generated for grid
123 and 999
Set 45 = 123, 999
Disp(Plot) = 45
Velo(Plot) = 45
Acce(Plot) = 45
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Generation of Response Spectra
Input requirement – Case Control Section
For getting XYPlot, XYpunch of Response Spectra for
grid 123, 999 in direction Z (T3)
Output (Xyout)
Xtitle=Response Spectrum at grid 123 in Z direction
Xyplot,xypunch,xyprint acce, Spectral /123(T3rm)
Xtitle=Response Spectrum at grid 999 in Z direction
Xyplot,xypunch,xyprint acce, Spectral /999(T3rm)
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Generation of Response Spectra
Input requirement – Bulk Data Section
Following PARAM entries are required
Param RSPECTRA – trigger calculation of Response
Spectra in Transient analysis
Param, RSPECTRA, 0 (0 compute, -1 do not compute(default)
Param RSPRINT controls the print output
Param, RSPRINT, 0 (0 print(default), -1 no print)
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$ Specify Grid ID, Damping and Frequencies.
$ Compute Response Spectra at grid 123 and 999
$ for set of damping specified on Set ID 91 of FREQ entry and
$ at all frequencies specified on Set ID 92 of FREQ entry.
dti, spsel, 0
dti, spsel, 1, 91, 92, 999, 123
$
$ set 91 selects damping of oscillator and set 92 selects the
$ frequencies at which spectra will be calculated.
$
freq, 91, 0.02, 0.04, 0.07
freq2, 92, 1.0, 40.0, 200
freq4, 92, 1.0, 40.0, 0.2, 5
$
Generation of Response Spectra
Input requirement – Bulk Data Section
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Structure subjected to Response Spectra
• Post processing of modal analysis (Sol 103)
• Response at each modal frequency is calculated
• The modal response is dependent on
• Participation factor in direction of excitation
• Spectrum input value at modal damping
• Stress/Forces based on mode shape
• Each modal response is combined using
• Absolute Summation
• RSS Summation
• NRL Specification
• Param,Option,ABS/RSS/NRL to select method
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Structure subjected to Response Spectra
• Absolute Method (Param,Option,Abs)
• Most conservative of all method.
• Add absolute modal response of each mode
• Not recommended for short duration pulse
• More suitable for long term event (e.g. earthquake)
• SRSS Method (Param,Option,Srss)
• Most widely used method.
• Square root of sum of square of modal response of each mode
• Suitable for well separated modes
• Use PARAM,CLOSE – ABS for closely spaced modes
• Sum response within “CLOSE” using ABS and then SRSS with rest
of the modes.
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• NRL Method (Param,Option,NRL)
• Developed by Naval Research Laboratories
• Peak response dominated by one mode
• Add absolute value of highest magnitude producing
mode to SRSS of rest of the modes
• Use PARAM,CLOSE – ABS for closely space modes
• Sum response within “CLOSE” using ABS and then
SRSS with rest of the modes.
Structure subjected to Response Spectra
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Structure subjected to Response Spectra
• Modeling and Analysis Consideration
• Unrestrained Structure in direction of spectrum
input
• Only Large Mass Option Available
• Use Param, Post, -1 for post processing in Patran
• SUPORT entry at spectrum input location required
• Modes must be MASS normalized (default)
• Limit number of modes using Param, HFREQ to
avoid extrapolation of input spectra
• Spectrum excitation may be in multiple directions
and acting simultaneously
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$
$ 201 202 203 204 205 206 207 208 209 210 211
$ Y *----*----*----*----*----*----*----*----*----*----*
$ ^ /| | | | | | | | | | |
$ | 99 * | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
$ | \| | | | | | | | | | |
$ +--->X *----*----*----*----*----*----*----*----*----*----*
$ 101 102 103 104 105 106 107 108 109 110 111
$
Structure subjected to Response Spectra
Best way to demonstrate is to consider the following
Example
Structure Subjected to Spectra simultaneously acting in
• X+Z direction (ABS option) and
• X+Y+Z direction (SRSS option)
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Structure subjected to Response Spectra
Input Specification
Input in X-Direction Acceleration Input in Y-Direction Acceleration
2% Damping 5% Damping 7% Damping 1% Damping 4% Damping 8% Damping
Freq G Freq G Freq G Freq G Freq G Freq G10 2 12 1.5 5 1 10 1 12 0.8 5 0.4
100 8 90 4 110 3 20 1 15 0.8 25 0.4
900 8 1200 4 850 3 100 6 90 5 110 3
1100 1 1300 0.7 1200 0.5 900 6 1200 5 850 3
2000 1 2500 0.7 3000 0.5 2000 1.5 2500 0.9 3000 0.5
Input in Z-Direction Acceleration
1% Damping 3% Damping 7% Damping
Freq G Freq G Freq G10 1.5 12 1 5 0.6
20 1.5 15 1 25 0.6
100 7 90 5 110 3.5
900 7 1200 5 850 3.5
2000 1.8 2500 1.4 3000 0.7
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Structure subjected to Response Spectra
SOL 103 $ Modal Frequency Response
CEND
Stress = all
Acceleration = all
Spc = 77
METHOD = 66
SDAMP = 88
$ Param to trigger Response Spectrum Analysis after mode
calculation.
Param, SCRSPEC, 0
Param,wtmass,.002588
Param, Post, -1
SUBCASE 1
subtitle = Excitation in X + Z Direction : Option : ABS
Param, Option, ABS
DLOAD = 701
SUBCASE 2
subtitle = Combined X+Y+Z Direction : Option : SRSS
Param, Option, SRSS
Param, Close, 0.1
DLOAD = 702
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BEGIN BULK
Conm2,199,99,,1.e8
Suport,99,123
Spc1,77,456,99
Eigrl,66,-.1,5000.
Tabdmp1,88,crit
+, 0.0, 0.03, 100.0, 0.05, 1500.0, 0.05, 2000., 0.02
+, 5000.0, 0.02, Endt
$ Note on DLOAD cards : The DLOAD card in response spectrum analysis
$ will select DTI entry with name SPECSEL. The DLOAD card must
$ contain 'r' pairs of Si, Li entries where 'r' is the number of DOF
$ listed on SUPORT card. In addition, the Li, Si pairs (i=1,2..,6)
$ correspond to the components motion entered on the SUPORT card when
$ these components, i.e. any integers 1 thru 6, are entered in
$ ascending order.
$ Subcase 1 – Input in X + Z direction
Dload, 701, 386.4, 1.0, 71, 0.0, 72, 1.0, 73
$ Subcase 2 – Input in X + Y + Z direction
Dload, 702, 386.4, 1.0, 71, 1.0, 72, 1.0, 73
$
$ The ID 71 select DTI,SPECSEL,71 that defines spectra in X direction
$
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$ Input Spectrum in direction X
$
DTI, SPECSEL, 71, , A, 101, 0.02, 102, 0.05
+, 103, 0.07
$ Table 101 – spectrum in X direction, 2% damping
Tabled1, 101
+, 10.0, 2.0, 20.0, 2.0, 100.0, 8.0, 900.0, 8.0
+, 1100.0, 1.0, 2000.0, 1.0, Endt
$ Table 102 – spectrum in X direction, 5% damping
Tabled1, 102
+, 12.0, 1.5, 15.0, 1.5, 90.0, 4.0, 1200.0, 4.0
+, 1300.0, 0.7, 2500., 0.7, Endt
$ Table 103 – spectrum in X direction, 7% damping
Tabled1, 103
+, 5.0, 1.0, 25.0, 1.0, 110.0, 3.0, 850.0, 3.0
+, 1200.0, 0.5, 3000.0, 0.5, Endt
$
$ Use DTI, SPECSEL, 72 and 73 to define input
$ spectra in Y and Z direction.
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Shock Spectrum Vs Transient
Chimney subjected to 1940 El Centro Earthquake
• Step 1: Transient Response Sol 112
• Input earthquake time history
• Create Response Spectra of base motion
• Plot Maximum Response
• Step 2: Response Spectrum Analysis Sol 103
• Input Response Spectra created in step 1
• Plot Maximum Response
• Step 3: Compare the maximum response
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Shock Spectrum Vs Transient
-1.50E+02
-1.00E+02
-5.00E+01
0.00E+00
5.00E+01
1.00E+02
1.50E+02
0.0 2.0 4.0 6.0 8.0 10.0 12.0
1940 El Centro North-South Acceleration
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Shock Spectrum Vs Transient
1.00E+02
1.00E+03
1.00E+00 1.00E+01
Response Spectra 2 % Damping -1940 El Centro North-South
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Transient Analysis Response Spectra Analysis
Maximum Acceleration
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Transient Analysis Response Spectra Analysis
Maximum Stress
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Word of Caution
• Response Spectrum Analysis – Suitable for Base Input
• Not to be used for other than input at base
• Pyro Shock – Very Short Duration Impulse
• Pyro Shock – at base or at middle of structure
• For Linear System only
• What to do for nonlinear and shock at middle of structure?
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Pyro Shock
• Very short duration pulse
• Response Spectra – very high value at high frequencies
• High frequency content
• Create artificial short pulse input and create response spectra
• Envelope the artificial spectra over design spectra
• Perform transient analysis using artificial created short pulse
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
0.0000 0.0002 0.0004
Acce - Pulse Response Spectra
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Thank You Very Much !