Shock Spectrum Analysis · •Post processing of modal analysis (Sol 103) •Response at each modal frequency is calculated •The modal response is dependent on •Participation

MSC.Software Confidential

Shock Spectrum AnalysisMarch 2011


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.


• 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


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


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


Simple Application

Transient Analysis

Transient Response

Mass of Antenna Structure 2 %

4 %

7 %


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


• 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


Harmonic vs Response Spectra

Frequency

G

2 %

4 %

7 %

Frequency

G

Harmonic Input Shock Spectra Input


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


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



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



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)



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)


$ 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

$


Input requirement – Bulk Data Section


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



• 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.


• 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.




• 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


$

$ 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

$


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)



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



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


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

$


$ 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


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


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.


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



-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



1.00E+02

1.00E+03

1.00E+00 1.00E+01

Response Spectra 2 % Damping -1940 El Centro North-South


Transient Analysis Response Spectra Analysis

Maximum Acceleration


Transient Analysis Response Spectra Analysis

Maximum Stress


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?


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


Thank You Very Much !

Documents

Shock Spectrum Analysis · •Post processing of modal analysis (Sol 103) •Response at each modal frequency is calculated •The modal response is dependent on •Participation