1. Module 6
Spectrum Analysis

2. Module 6 Spectrum Analysis
A. Define a spectrum analysis and its purpose.
B. Understand the underlying concepts and terminology.
C. Learn how to do a response spectrum analysis.
D. Guidelines for spectrum analysis.
E. Random Vibration Analysis
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3. Spectrum Analysis A. Definition & Purpose
What is spectrum analysis?
A technique to compute a structure’s response to transient excitations that contain many frequencies.
Excitations could be from sources such as earthquakes, aircraft noise/ flight history, missile launches.
A spectrum is a representation of a load’s time history in the frequency domain.
This is also referred to as response spectrum.
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4. Spectrum Analysis … Definition & Purpose
El Centro Earthquake ( 1940 )
Acceleration vs. time
Acceleration spectrum (G vs. Hz)
A structure subject to the El Centro earthquake can be analyzed using either a Transient analysis or spectrum analysis.
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5. Spectrum Analysis … Definition & Purpose
Spectrum analysis follows a modal analysis.
Computes the maximum response of the structure to a given spectrum at each natural frequency. This maximum response is computed as scale factor*mode shape.
These maximum responses are then combined to give a total response of the structure.
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6. Spectrum Analysis … Definition & Purpose
An alternative is to perform a transient analysis.
Transient analysis is generally more time consuming, especially when a number of components and load conditions have to be considered.
However, transient analysis is more accurate.
In spectrum analysis the focus is to get the maximum response quickly, and some information is lost (phase).
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7. Spectrum Analysis … Definition & Purpose
Used in the design of:
Nuclear power plants (buildings and components)
Airborne Electronic equipment (aircraft / missile)
Spacecraft components
Aircraft components
Any structure or component that is subjected to seismic or other erratic loads
Building frames and bridges
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8. Spectrum Analysis … Definition & Purpose
ANSYS allows four types of spectrum analysis:
Single-point response spectrum**
A single response spectrum excites all specified points in the model.
Multi-point response spectrum **
Different response spectra excite different points in the model.
Dynamic design analysis method (DDAM)
A specific type of spectrum defined by the U.S. Naval Research Laboratory to evaluate shock resistance of shipboard equipment.
Power Spectral Density (PSD)**
A probabilistic approach used in random vibration analysis.
** Covered in this seminar
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9. Spectrum Analysis B. Terminology & Concepts
Topics covered:
Definition of a spectrum
How a response spectrum is used to calculate a structure’s response to the excitation
Participation factor
Mode coefficient
Mode combination
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10. Spectrum Analysis - Terminology & Concepts Definition of spectrum
What is a spectrum?
A curve representing the maximum response of an idealized system to an excitation. The response may be acceleration, velocity, displacement, or force.
Consider, for example, four single-DOF spring-mass systems mounted on a shaker table. Their frequencies are f1, f2, f3, and f4, with f1 < f2 < f3 < f4. 1 2 3 4
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11. Spectrum Analysis - Terminology & Concepts … Definition of spectrum
If the shaker table is excited at frequency f1 and the displacement response of the four systems is recorded, it will look as shown on the right.
Now add a second excitation of frequency f3 and record the displacement response. Systems 1 and 3 will each reach their peak response.
If now a general excitation containing several frequencies is applied and only the peak responses are recorded, we might get the curve shown. This curve is the spectrum, specifically a response spectrum. u f u f u f
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12. Spectrum Analysis - Terminology & Concepts … Definition of spectrum
Thus a response spectrum is an envelope of the maximum responses of a number of single DOF systems to a given excitation.
Input to a spectrum analysis consists of a response spectrum curve and a direction of excitation.
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13. Spectrum Analysis - Terminology & Concepts Approach
Spectrum analysis follows a modal analysis in which natural frequencies and mode shapes have been computed.
In doing a spectrum analysis you will encounter three new terms:
Participation factor
Mode coefficient
Mode combination
We will define these three terms along with the general outline of how a spectrum analysis is done.
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14. Spectrum Analysis - Terminology & Concepts … Approach - Participation factor
For each mode of the structure, a participation factor gi is calculated in the excitation direction.
The participation factor is a function of the mode shape and the direction of excitation.
This is a measure of how much a mode will contribute to the deflections (and hence stresses) in the direction of excitation.
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15. For example, consider the cantilever beam shown.
Spectrum Analysis - Terminology & Concepts … Approach - Participation factor
For example, consider the cantilever beam shown.
If an excitation is applied in Y direction, mode 1 will have the highest PF and mode 2 a lower PF. Mode 3 will have zero PF.
If the excitation is in the X direction, then modes 1 and 2 will have zero PF, whereas mode 3 will have a high PF.
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16. The mode coefficient Ai for each mode is Ai = Sigi *
Spectrum Analysis - Terminology & Concepts … Approach - Mode coefficient
The mode coefficient is the “scale factor” used to multiply the mode shapes to get the maximum response.
The mode coefficient Ai for each mode is Ai = Sigi *
Si is the response spectrum value at frequency wi
gi is the participation factor for mode i
The maximum modal response is then computed as
{U}i max = Ai {f}i
*A different formula is used for acceleration, velocity and force spectra; see the ANSYS Theory Manual.
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17. Spectrum Analysis - Terminology & Concepts … Approach - Mode combination
Once the maximum response at each mode is known for a given response spectrum, these need to be combined in some way to get the total response.
The simplest combination is to add all the maximum modal responses. However, it is highly unlikely that all the maximum modal responses will occur at the same time.
Several standard combination methods are published in the literature. Usually each industry’s regulating authority recommends or enforces a technique most suitable for that industry.
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18. Six different combination methods are available in the ANSYS program:
Spectrum Analysis - Terminology & Concepts … Approach - Mode combination
Six different combination methods are available in the ANSYS program:
Complete Quadratic Combination (CQC) method
Grouping Method (GRP)
Double Sum method (DSUM)
Square Root of the Sum of the Squares (SRSS) method
Naval Research Laboratory (NRL) sum method (DDAM)
Power Spectral Density method
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19. Spectrum Analysis … Terminology & Concepts
We will discuss the procedure for a single-point response spectrum analysis.
In the following discussion, we will use the term “response spectrum” to mean single-point response spectrum.
To learn about multi-point response spectrum and DDAM, please refer to the ANSYS Structural Analysis Guide.
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20. C. Procedure Five main steps: Build the model
Obtain the modal solution
Switch to spectrum analysis type
Define the response spectrum
Solve and review results
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21. Response Spectrum Procedure … Obtain the Modal Solution
Mode extraction:
Only valid methods are Block Lanczos, subspace, or reduced.
Block Lanczos strongly recommended
Extract enough modes to cover the spectrum’s frequency content.
Expand all modes. Only expanded modes can be used for the spectrum solution.
Loads and BC’s: For a base excitation, be sure to constrain the appropriate DOFs.
Files: The .mode file contains the eigenvectors and is needed for the spectrum solution.
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22. Response Spectrum Procedure Switch to Spectrum Analysis Type
Build the model
Obtain the modal solution
Switch to spectrum analysis type
Exit and re-enter Solution
New analysis: Spectrum
Analysis options: Discussed next
Damping: Discussed next
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23. Response Spectrum Procedure … Switch to Spectrum Analysis Type
Analysis options
Type of spectrum: Single point
Number of modes: If 0 or blank, all expanded modes are used for solution.
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24. Response Spectrum Procedure … Switch to Spectrum Analysis Type
Damping
Available forms of damping are:
Beta (stiffness) damping
Constant damping ratio. Can be material dependent but only if specified as a material property* in the modal step.
Frequency dependent damping ratio (modal damping)
Some form of damping must be specified for the CQC mode combination method.
*Material property DAMP in this case is damping ratio, not beta damping.
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25. Response Spectrum Procedure Define the Response Spectrum
Build the model
Obtain the modal solution
Switch to spectrum analysis type
Define the response spectrum
Settings: type of spectrum and excitation direction
Table of spectral value versus frequency
Mode combination method
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26. Response Spectrum Procedure … Define the Response Spectrum
Settings:
Type of spectrum
Seismic or force (not PSD)
Seismic spectra - automatically applied at the base
Force spectrum - manually applied at desired nodes as a force
Excitation direction (global Cartesian)
Specified by a unit vector for seismic spectra: 1,0,0 means X; 0,1,0 means Y; 0,0,1 means Z.
Implied by FX, FY, or FZ labels for force spectrum.
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27. Response Spectrum Procedure … Define the Response Spectrum
Spectral value vs frequency table
First define frequency table. Up to 20 points are allowed.
Then define corresponding spectral values.
Specify damping ratio only for multiple spectral curves.
For a force spectrum, the spectral values can be scaled by the applied force value.
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28. Response Spectrum Procedure … Define the Response Spectrum
Mode combination method
Determines how the individual modal responses are combined.
Five methods are available:
CQC (Complete Quadratic Combination)
GRP (Grouping)
DSUM (Double Sum)
SRSS (Square Root of Sum of Squares)
NRLSUM (Naval Research Laboratory Sum)
Which method you choose typically depends on company or government standards being followed.
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29. Response Spectrum Procedure … Define the Response Spectrum
Mode combinations (continued)
The significance threshold allows you to include only significant modes in the mode combination. It is the ratio of the mode coefficient of a mode to the maximum mode coefficient. Use a zero value to include all modes.
Type of output allows calculation of different response quantities: displacement, velocity, or acceleration.
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30. Response Spectrum Procedure Solve and Review Results
Build the model
Obtain the modal solution
Switch to spectrum analysis type
Define the response spectrum
Solve and review results
Solve the current load step.
Mode combination calculations are written as POST1 commands to the .mcom file.
Review results: discussed next.
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31. Response Spectrum Procedure … Solve and Review Results
Enter POST1 (general postprocessor).
Perform mode combinations
Commands to do this are written to .mcom file during solution.
Read the file jobname.mcom using Utility Menu > File > Read Input from...
Review deformed shape.
Plot and list stresses and strains.
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32. Response Spectrum Analysis Procedure
Build the model
Obtain the modal solution
Switch to spectrum analysis type
Define the response spectrum
Solve and review results
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33. D. Spectrum Analysis Guidelines
Modal analysis
Make sure you extract and expand enough modes in the modal analysis to cover the frequency range of interest.
For example, if the spectrum extends from 1 to 1000 Hz, a rule of thumb is to extract and expand modes up to 1500 Hz.
Block Lanczos extraction technique recommended
Use Lagrange multiplier (accurate) method if large numbers of constraint equations are present.
If you have material dependent damping ratio, this should be specified in the modal analysis.
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34. … Spectrum Analysis Guidelines
Remember that no results file is written in a spectrum analysis. Instead the instructions for mode combination are written to jobname.mcom.
Most combination methods involve squaring operations causing the component stresses to lose their signs. Hence deriving equivalent or principal stresses from these unsigned components will be non-conservative and incorrect.
If equivalent or principal stresses and strains are of interest then you need to issue the command SUMTYPE,PRIN ( General Postprocessor > Load Case > Stress Option …) before reading in jobname.mcom. This causes direct operation on derived quantities leading to more conservative results.
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35. … Spectrum Analysis Guidelines
During the spectrum analysis the effective mass for each mode as well as the sum of all the effective mass is printed out.
For a lumped mass system the sum of the effective masses should approach the total mass of the structure as the number of modes used in the spectrum analysis is increased.
The total effective mass is an indicator of whether enough modes are included in the spectrum analysis.
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36. E. Workshop - Response Spectrum Analysis
In this workshop, you will determine the response of a workbench table to a response spectrum excitation.
See your Dynamics Workshop supplement for details. (Response Spectrum Workshop - Workbench Table, Page W-40. ).
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37. F. Random Vibration Analysis
Topics covered:
Definition and purpose
Overview of ANSYS capabilities
ANSYS procedure
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38. Random Vibration Analysis Definition and Purpose
What is random vibration analysis?
A spectrum analysis technique based on probability and statistics.
Meant for loads such as acceleration loads in a rocket launch that produce different time histories during every launch .
Reference: Random vibrations in mechanical systems by Crandall & Mark
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39. Random Vibration Analysis … Definition and Purpose
Transient analysis is not an option since the time history is not deterministic.
Instead, using statistics the sample time histories are converted to Power Spectral Density function (PSD), a statistical representation of the load time history.
Image from “Random Vibrations Theory and Practice” by Wirsching, Paez and Ortiz.
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40. Random Vibration Analysis … Definition and Purpose
What is a PSD?
A PSD records the mean square value of the excitation and response as a function of frequency.
The area under a PSD curve is the variance of the response (square of the standard deviation).
The units used in PSD is mean square/Hz (e.g. an acceleration PSD will have units of G2/Hz).
The quantity represented by PSD may be displacement, velocity, acceleration, force, or pressure.
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41. Random Vibration Analysis … Definition and Purpose
Typical applications include
Aircraft electronic packaging
Airframe parts under atmospheric loading
Blast deflectors
Laser guidance systems
Stable optical platform for telescopes
Seismic loading of large structures
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42. Random Vibration Analysis … Definition and Purpose
Input:
The structure’s natural frequencies and mode shapes
The PSD curve (explained next)
Output:
1s displacements and stresses that can be used for fatigue life prediction.
Response PSD curves that show the frequency content of any output quantity ( RPSD ).
Undocumented (FPAS and RISK ) life prediction capability.
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43. Random Vibration Analysis Overview of ANSYS Capabilities
Loading:
Base or nodal excitation
Single-point excitation
e.g. Single PSD excitation applied to all ground nodes
Multi-point (i.e., multi-spectra) excitation
Uncorrelated
Partially correlated
Fully correlated
Partial correlation in terms of spatial coordinates
Partial correlation in terms of a traveling wave
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44. Random Vibration Analysis … Overview of ANSYS Capabilities
Solution:
Relative or absolute 1s output
Option for calculating 1s forces/stresses etc.
Solution for complete structure i.e., results can be contoured.
Output in form of 1s displacements, velocities or accelerations
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45. Random Vibration Analysis … Overview of ANSYS Capabilities
Postprocessing:
1s results can be contoured like any other analysis.
Response PSD can be computed for any result quantity ( e.g. stress or nodal force at a node of an element) or cross response spectra can be computed between any two quantities (RPSD).
This enables the user to look at the frequency content of output.
Covariance between any two quantities can be computed (CVAR).
Undocumented commands RISK and FPAS allow user to compute equivalent stress / predict life.
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46. Random Vibrations Procedure
Six main steps:
Build the model
Obtain the modal solution
Switch to spectrum analysis type
Define and apply the PSD excitation
Solve
Review results
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47. Random Vibrations Build the Model
Same considerations as a modal analysis.
Linear elements and materials only. Nonlinearities are ignored.
Remember density! Also, if material-dependent damping is present, it must be defined in this step.
See also Modeling Considerations in Module 1.
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48. Random Vibrations Obtain the Modal Solution
Build the model
Obtain the modal solution
Same procedure as a normal modal analysis.
A few differences, discussed next.
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49. Random Vibrations … Obtain the Modal Solution
Mode extraction:
Only valid methods are Block Lanczos, subspace, or reduced.
Block Lanczos strongly recommended
Extract enough modes to cover the spectrum’s frequency content.
Expand all modes. Only expanded modes can be used for the spectrum solution.
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50. Random Vibrations … Obtain the Modal Solution
Loads and BC’s:
For a base excitation, be sure to constrain the appropriate DOFs.
For a pressure PSD, apply the pressures on desired surfaces in this step.
Files: The .mode file contains the eigenvectors and is needed for the spectrum solution.
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51. Random Vibrations Switch to Spectrum Analysis Type
Build the model
Obtain the modal solution
Switch to spectrum analysis type
Exit and re-enter Solution
New analysis: Spectrum
Analysis options: Discussed next
Damping: Discussed next
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52. Random Vibrations … Switch to Spectrum Analysis Type
Analysis options
Type of spectrum: PSD
Number of modes: If 0 or blank, all expanded modes are used for solution.
Element calculations: can be ON only if they were ON in the modal step.
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53. Random Vibrations … Switch to Spectrum Analysis Type
Damping
All four forms are available.
Alpha (mass) damping
Beta (stiffness) damping
Constant damping ratio
Frequency dependent damping ratio (modal damping)
If no damping is specified, ANSYS uses a 1% constant damping ratio as default.
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54. Random Vibrations Define and Apply the PSD Excitation
Build the model
Obtain the modal solution
Switch to spectrum analysis type
Define and apply the PSD excitation
Specify PSD settings
Define PSD versus frequency table
Apply excitation at desired nodes
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55. Random Vibrations … Define and Apply the PSD Excitation
PSD settings
Spectrum type (units)
Acceleration (normal units or g2/Hz)
Velocity
Displacement
Force
Pressure
Table number defaults to 1. Used for multiple PSD curves.
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56. Random Vibrations … Define and Apply the PSD Excitation
PSD versus frequency table
Specify table number (usually 1).
Then enter frequency and PSD value pairs.
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57. Random Vibrations … Define and Apply the PSD Excitation
PSD versus frequency table (continued)
Graph the PSD table to verify the input.
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58. Random Vibrations … Define and Apply the PSD Excitation
Procedure depends on the type of PSD.
Acceleration, velocity, or displacement PSD:
These are base excitations and can be applied only at previously constrained nodes.
Apply as a constraint in UX, UY, or UZ (excitation direction) with a value of 1.0.
Pick nodes...
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59. Random Vibrations … Define and Apply the PSD Excitation
Apply the PSD (cont'd.)
Force PSD
Nodal excitation
Apply as a force in FX, FY, or FZ (excitation direction) with a value of 1.0 (or desired scale factor).
Pressure PSD
Requires pressure to be applied in the modal step.
Use the load vector (calculated during modal solution) to apply the pressure PSD excitation.
Set value to 1.0 or desired scale factor.
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60. Random Vibrations Solve
Build the model
Obtain the modal solution
Switch to spectrum analysis type
Define and apply the PSD excitation
Solve
Activate PSD mode combination method
Specify items to be calculated*
Calculate participation factors*
Initiate PSD solution*
*Discussed next
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61. Random Vibrations … Solve
Items to be calculated:
Default is to calculate the displacement solution (including stresses and strains) relative to base excitation.
Velocity and acceleration solutions are also available, relative to base or absolute.
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62. Random Vibrations … Solve
Calculate participation factors:
Must be done for each PSD table defined.
Specify base or nodal excitation.
Initiate PSD solution:
Results are written to the .rst file.
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63. Random Vibrations Review Results
Build the model
Obtain the modal solution
Switch to spectrum analysis type
Define and apply the PSD excitation
Solve
Review results
Plot and list 1s quantities (POST1)
Generate a response PSD (POST26)
Calculate covariance between two quantities (POST26)
Life prediction
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64. Random Vibrations- Review Results Review 1-Sigma Stresses
Random vibration results are 1s quantities: 1s displacements, 1s stresses, etc.
All quantities assume a Gaussian (normal) distribution with zero mean.
For example, a maximum displacement of Umax = 0.15 indicates a 68% probability (1s) that Umax will be 0.15 or less. It also indicates:
a 95% probability (2s) that Umax will be 0.15x2 = 0.3 or less.
a 98% probability (3s) that Umax will be 0.15x3 = 0.45 or less.
Gaussian (normal) Distribution 1s 2s 3s
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65. Random Vibrations- Review Results … Review 1-Sigma Stresses
To review 1s displacements & stresses:
Enter POST1 (General Postproc).
Read results from load step 3, which is where 1s results are stored on the results file.
Note: 1s velocities and 1s accelerations, if requested, are stored in load steps 4 and 5, respectively always.
Then plot and list the desired quantities.
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66. Random Vibrations- Review Results Review 1-Sigma Stresses
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67. Random Vibrations- Review Results Review 1-Sigma Stresses
1s results are typically used for:
Fatigue calculations
In PSD analyses, the average frequency of excitation (number of cycles/second) is given by 1s velocity / 1s displacement.
Using normal distribution the stress level is at 1s 68% of the time, at 2s 27% of the time (95-68), and at 3s 3% of the time (98-95).
Knowing the above two quantities, fatigue life can be predicted using usual S-N diagram procedures.
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68. Random Vibrations- Review Results Response PSD
Gives engineers an idea of how a response quantity (stress, for example) varies with frequency.
Results file contains 1s values, which is the square root of the area under the PSD curve.
POST26, the time-history postprocessor, is used to calculate response PSD.
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69. Random Vibrations- Review Results … Response PSD
To calculate response PSD
1. Enter POST26 and first store the frequency vector.
You can use 1 to 10 additional data points on either side of a natural frequency for a smoother frequency curve. Default is 5.
Variable 1 is automatically assigned to the frequency vector.
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70. Random Vibrations- Review Results … Response PSD
2. Identify results quantities for which response PSD is to be calculated.
TimeHist Postpro > Define Variables...
Can be any nodal or element result item.
Choose category, then pick node...
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71. Random Vibrations- Review Results … Response PSD
3. Calculate and plot the response PSD.
TimeHist Postpro > Calc Resp PSD...
TimeHist Postpro > Graph Variables…
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72. Random Vibrations- Review Results Covariance
Covariance represents the correlation between two quantities.
Can be calculated between any two response quantities; for example, stress at two different points in the model.
POST26, the time-history postprocessor, is used to calculate covariance.
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73. Random Vibrations- Review Results … Covariance
To calculate covariance:
1. Reset or exit and re-enter POST26.
2. Identify the two response quantities for which covariance is to be calculated.
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74. Random Vibrations- Review Results … Covariance
3. Calculate and retrieve the covariance.
TimeHist Postpro > Calc Covariance...
Use *GET to retrieve the covariance: *GET,COVAR,VARI,#,EXTREM,CVAR -or- Utility Menu > Parameters > Get Scalar Data...
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75. Random Vibrations- Review Results RISK & equivalent stress
In PSD analysis only component stresses are valid (the mode combinations work only on component stresses).
Since the component stresses are 1s statistical quantities, equivalent stress and principal stresses cannot be computed in the usual way.
The RISK command can calculate equivalent stress by Monte Carlo simulation. RISK can also be used for life prediction.
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76. Random Vibrations- Review Results … RISK & equivalent stress
Sample uses of RISK command
CASE 1
INPUT: Location of interest and Design strength (or mean and standard deviation of strength)
OUTPUT: Safety margin, Probability of failure, PDF, CDF
CASE 2
INPUT: Location of interest and Acceptable probability of failure
OUTPUT: Required design strength, PDF, CDF
PDF - probability density function
CDF- Cumulative probability density function
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77. Random Vibrations- Review Results … RISK & equivalent stress
RISK analysis sample output
RISK COMMAND WAS ISSUED FOR NODE OF ELEMENT 28
SIX ESOL COMMANDS WITH VARIABLE NUMBERS 3 THRU 8 ARE CREATED
THE COVARIANCE MATRIX OF CARTESIAN STRESS RESPONSES IS COMPUTED BELOW:
SX SY SZ SXY SXZ SYZ
0.1665E E E E E E+00
0.2156E E E E E E+00
0.0000E E E E E E+00
E E E E E+00
A DETERMINISTIC DESIGN STRENGTH = WAS SPECIFIED
STATISTICS BASED ON THE SAFETY MARGIN OF VON MISES STRESS WILL BE COMPUTED
MEAN OF THE SAFETY MARGIN =
STANDARD DEVIATION =
COEFFICIENT OF SKEWNESS =
COEFFICIENT OF KURTOSIS =
COMPUTED SAFETY INDEX =
COMPUTED PROBABILITY OF FAILURE = E-02
COEFFICIENT OF VARIATION FOR COMPUTED PROBABILITY OF FAILURE = E-01
BASED ON 95% CONFIDENCE THE PROBABILITY OF FAILURE IS LESS THAN = E-02
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78. Random Vibrations- Review Results First Passage Failure
When will it fail?
What is the probability of failure? a
X(t) t t
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79. Random Vibrations- Review Results First Passage Failure
The FPAS command can be used to estimate first passage failure
FPAS Works with displacement and component stresses
Sample uses of FPAS command:
CASE 1
INPUT: location , max. allowable value, desired probability of failure
OUTPUT: Statistical average frequency, life in seconds
CASE 2
INPUT: Location, maximum allowable value, time to failure
OUTPUT: Statistical average frequency, probability of failure
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80. Random Vibrations- Review Results First Passage Failure
Typical output for First Passage Failure
fpas,ttfa,4,3,1,6.0,0.001
COMPUTED STATISTICAL AVERAGE FREQUENCY IS
THE EXPECTED NUMBER OF POSITIVE CROSSING OF THRESHOLD VALUE
PER UNIT TIME IS E-06
BASED ON FAILURE PROBABILITY OF E-02 THE TIME TO FAILURE IS
TIME TO FAILURE IS E+04
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81. Random Vibrations Procedure
Build the model
Obtain the modal solution
Switch to spectrum analysis type
Define and apply the PSD excitation
Solve
Review results
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82. G. Workshop – Random Vibration (PSD)
In this workshop, you will determine the displacements and stresses in a model airplane wing due to an acceleration PSD.
See your Dynamics Workshop supplement for details (Random Vibration Workshop - Model Airplane Wing , Page W-43 ).
January 30, 2001
Inventory #001447
6-82