Random Vibration Procedure and Best
Practices
OptiStruct
David M. Aguilar
Tuesday, September 25, 2018
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Table of Content
• Random Response Background
• Random Response Inputs
• Random Response Setup in OptiStruct
• Post Processing
• Stresses
• Response Spectrums
• Dynamic Responses
• Drawing Conclusions
• Common Mistakes
• Next Steps and Conclusion
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Scope of document
In Scope:
Out of Scope:
- Background of random response analysis
- Creating a PSD input profile from data
- Single direction excitation
- Multi direction excitation
- Analysis setup
- Random response fatigue analysis
- Key outputs and interpreting results
- Test-analysis correlation
- Common Mistakes
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Random Vibration Background
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Random Vibration Overview
In order to evaluate if a design is robust and meets
design margins, engineers use a variety of analytical
tools. Often a product’s duty cycle is not perfectly
characterized but the statistics of a lifetime of excitation
are known.
These excitations can cause fatigue when system level
dynamics are excited. It is very important to understand
how a system responds to these excitations and how
natural frequencies interact with each other.
Power spectral density (PSD) analysis, more commonly
known as random response analysis, is used to
determine stresses and strains in a system that is
subjected to random excitations.
Fender Mounted Vertically on
an Electrodynamic Shaker
(Palve & Roy, 2015)
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Random Response Inputs
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Material Properties
The following material properties are
required for random response analysis.
•
•
•
•
Elastic Modulus
Density
Poisson’s Ratio
Damping
*Note: These material properties are provided as an example.
They are not to be used as a reference nor should they be applied
in analysis without independent verification of their validity.
OptiStruct Material Card in
HyperMesh*
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Input Excitation
• The input excitation for a random response analysis
is a Power Spectral Density (PSD) profile.
• An input profile is generally provided by test
engineers or is part of an engineering test
requirement.
• Since PSD input profiles are based on duty cycle,
physical data must be available in order to create an
input.
Input PSD Profile
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Random Response Setup in OptiStruct
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OptiStruct Random Response Analysis Flow
Unit Load Frequency
Response Analysis
(Mode Based Solution)
Random
Response
Analysis
• Random response analysis is the result of cascading analyses.
• Frequency response analysis can be performed using modal
superposition or a direct solution. This document will use the modal
superposition solution.
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OptiStruct Random Response Card Flow
SPC
Unit Load
Frequency
Response
Analysis
EIGRL
FREQi
TABRND1
Random
Response
Analysis
RANDPS
TABDMP1
Second Subcase
SPCD
RLOAD2
TABLED1
Key
Load Collectors
First Subcase
Subcase
Unit Load Frequency Response Definition
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Excitation
Direction
Unit of
Acceleration
Notes:
• 1g (9810 [mm/s^2]) in Y, between 1 and 1000 [Hz].
• The value of uniform damping, 2.5%, is applied as
critical damping which is twice that value (0.05).
• Modes should be calculated for 1.5x to 2x
excitation range.
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Random Response Definition
8
9
TABRND1
RANDPS
Random
Response
Analysis
PSD input excitation must
be in log-log
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Post Processing
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Steps to Reviewing and Interpreting Results
Stress Contours
Stress
Spectrums
Dynamic
Responses
Basic review of random response results should follow these steps:
1. Review stress contours, find high stress areas, and isolate several elements for further investigation.
2. Using the elements found in step one, generate stress spectrums. It is not feasible to do this for all
elements in the model due to computer storage requirements.
3. The stress spectrums found in step two will highlight frequencies that contribute the most to the
component's stress. Using the results from the frequency response analysis, animate the dynamic
response of influential frequencies and determine ways to modify their behavior.
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Stresses
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Stress in Random Response
Random response results can be viewed per
frequency, Power Spectral Density Function (PSDF), or
as an ensemble of the entire excitation bandwidth,
Root Mean Squared (RMS).
Setting “Random” to PSDF in the stress output card
will result in both the PSDF and RMS results being
output to the results file.
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RMS Stress in Random Response
When looking at RMS stress contours calculated from
a random excitation it is important to remember several
points:
• You are looking at the combination of all response
frequencies across the entire input frequency
range.
• The default display shows the limit of stresses that
can be expected 68% of the excitation time. A
detailed explanation of this can be found on the
next slide.
• Response frequencies do no contribute equally to
the final RMS value. To truly understand what the
stress contours mean, you must determine which
frequencies respond greatest to the input
excitation.
RMS Von Mises Stress [MPa]
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1𝜎 Root Mean Squared Stress
The magnitude of RMS stress can be shown as a one,
two, or three sigma value. These values represent
increasing standard deviations of the response.
Stresses calculated from a random response analysis
have a zero mean. If a one sigma stress is 10 [MPa], then
the three sigma stress is 30 [MPa]. There is a 0.7%
chance that stresses will be greater than 30 [MPa].
If a system has a one sigma stress of 10 [MPa], there is a
32% chance that stress will exceed that value during the
time of excitation. For the same time of excitation, there is
a 68% chance that stresses will be at or below 10 [MPa].
Prob. Of Stress
Within Range
Sigma
1
2
3
68.3%
95.4%
99.3%
Probability of Stresses Occurring
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Selecting Areas of Concern
Areas of concern will typically occur around
welds or geometric stress concentrations.
Once an area has been identified, record the
element number and generate a stress
spectrum. The image to the right shows an
element that occurs in the toe of a weld. While
not the highest stress found in the system, it is
still important to evaluate it further.
Details on how to create a stress spectrum can
be found in the next section of this document.
1𝜎 RMS Von Mises Stress [MPa]
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Response Spectrums
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Response Spectrums
Important outputs that give significant insight to the
response of a particular element are its response
spectrums. Response spectrums will show frequencies
at which the element strongly responds to the input. In
order to get these graphs, unsupported cards must be
created before the solution is calculated.
- Navigate to the Analysis Panel and select Control
Cards
- On the first page select Case_Unsupported_Cards
- Enter XYPLOT or XYPEAK.
- E.g. XYPLOT,STRESS,PSDF/ elem#1(Stress
component), elem#2(Stress component), … ,
elem#n(stress component).
Sxx1 Stress Spectrum
Details on how to use these cards can be found in the
help documentation under XYPEAK/XYPLOT
Since stress spectrums are generated for a specific
stress tensor, it is important to review each component
to determine which are the most excited.
Input Deck Example
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XYPLOT Card Explained
Stress
PSDF
302780
(3)
(10)
(5)
(12)
Outputs Stress
The square of stress
Element Number
Normal X at Z1
Normal X at Z2
Normal Y at Z1
Normal Y at Z2
Response Spectrums
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Problem
Frequencies
1𝜎 RMS Von Mises Stress [MPa]
Sxx1 Stress Spectrum
The spectrum shows that the two frequencies that respond the strongest to the input and
contribute the most to the stress are 29 [Hz] and 96 [Hz]. The motion of the component
at these frequencies should be reviewed in order to make design change suggestions.
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Dynamic Responses
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Dynamic Response
After the stress spectrums have been reviewed and a
few interesting frequencies have been identified, it is
time to study the dynamic response of the system at
those frequencies.
In the example plot to the right, 29 [Hz] and 96 [Hz] need
to be reviewed further. While these frequency values
occur very close to the natural frequencies of the
system, reviewing the mode shapes will not give a full
picture of the response.
Sxx1 Stress Spectrum
By definition, mode shapes are unforced responses,
while the results of a PSD are forced. Looking at
frequency response results at problem frequencies will
give a complete picture of the system’s problematic
dynamic responses.
Natural Frequencies of the system
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Component Motion at 96 [Hz]
To review the dynamic response of a system at a
problem frequency, simply select the frequency
response subcase and frequency.
In the example to the right, stresses were
observed in the PSD Z analysis so the FRF Z
results are reviewed. When animated, the vertical
excitation is clearly observed along with the
dynamic response of the system. Knowledge of
how the system vibrates near areas of high stress
can be used to change the design.
Forced Dynamic Response of the system at 96 [Hz]
Subcase and load selection in HyperView
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Drawing Conclusions
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Drawing Conclusions
The ultimate goal of running a PSD analysis is generating fatigue damage values. In situations where
that has not been done, there are several ways to evaluate results. It should be noted that these
methods are purely rules of thumb and ways to quickly evaluate results. They should not be used as
the final determination of a design’s robustness.
•
•
𝑈𝑇𝑆
Ultimate tensile strength by half: If the 3𝜎 RMS VM stress is below
then the component should
2
not fail due to fatigue. This should not be applied to welds.
Stress below fatigue limit: If the 1𝜎 RMS VM stress of a component is below the fatigue limit of the
material, the system should not fail due to fatigue.
Fatigue is the result of stresses repeatedly occurring in a material. Therefore, these rules of thumb are
based off the likely hood of the stresses occurring. Since one sigma stresses are more likely to occur,
they must be below the lower stress threshold, the fatigue limit of the material. Three sigma stresses
are less likely to occur, so they must be below the higher limit, half the ultimate tensile strength of the
material.
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Common Mistakes
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Common Mistakes
-
Setting the unit acceleration to 1 rather than setting it
to a unit of acceleration in the SPCD card.
-
-
-
Acceleration load set to the
gravitational constant.
Linearly interpolating the input PSD profile rather than
logarithmically.
-
-
Most input PSD profiles are in [G^2/Hz] which means that
the unit load applied in the SPCD card needs to be equal
to the gravitational constant of your unit system. If you are
working in [MPa] your unit load needs to be equal to 9810
[mm/s^2].
If your PSD input profile is in [(m/s^2)^2/Hz], the SPCD
value would be 1 since the gravitational unit is accounted
for in the input profile.
For PSD analysis you must use logarithmic interpolation,
which can be set in the TABRND1 card.
Too coarsely calculating the frequency response.
-
PSD responses are calculated by multiplying the result of
the FR and the input PSD. Therefore an analyst should
use a frequency step of ~1 [Hz] in the FREQi card. This
value should be adjusted by considering the input PSD
and the number and spacing of the component’s modes.
Setting logarithmic interpolation
for the input PSD profile.
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Next Steps and Conclusions
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Next Steps
After a basic review of random response results, an analyst may wish to dive deeper into post
processing. The next logical step is to calculate fatigue damage values of high stress
locations. The information garnered from fatigue calculations will give the analyst a better
understanding of if a location is in danger of failing and by what degree.
Detailed information on how to calculate fatigue due to random excitation is outside of the
scope of this document.
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Conclusions
Random vibration analysis is a tool that can
provide powerful predictions on the
robustness of a system’s design. There are
many pitfalls during setup and post processing
but following a well defined procedure will
ensure the generation of meaningful results.
PSD Stress Results