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ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-1 July 2009
Inventory #002666
ANSYS Mechanical
Dynamics
Chapter 5:
Random Vibration
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-2 July 2009
Inventory #002666
Random Vibration Analysis
Topics covered:
• Definition and purpose
• Overview of Workbench capabilities
• Procedure
Random Vibration Analysis
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-3 July 2009
Inventory #002666
A. 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
Random Vibration Analysis
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-4 July 2009
Inventory #002666
• Transient analysis is not an option since the time history is not
deterministic (sample is not repeatable).
• Instead, using statistics the sample time histories are converted to
Power Spectral Density function (PSD), a statistical representation of
the load time history.
… Definition and Purpose
Image from “Random Vibrations Theory and Practice” by Wirsching, Paez and Ortiz.
Random Vibration Analysis
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-5 July 2009
Inventory #002666
Power Spectral Density
• Sample time histories are converted to Power Spectral Density
function (PSD), a statistical representation of the load time history.
Reference: Random vibrations in
mechanical systems by Crandall
& Mark
Image from “Random Vibrations Theory and
Practice” by Wirsching, Paez and Ortiz.
Random Vibration Analysis
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-6 July 2009
Inventory #002666
Statistical Representation
• A Random Vibration analysis computes the probability distribution of
different results, such as displacement or stress, due to some
random excitation
• The analysis follows a modal analysis
• An internal combination is done to compute the combined effect from
each mode and their interactions.
3sGaussian
(normal)
Distribution
Random Vibration Analysis
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-7 July 2009
Inventory #002666
Power Spectral Density
• The Power Spectral Density is the
mean square value of the excitation
for a unit frequency band.
– The area under a PSD curve is
the variance of the response
(square of the standard
deviation).
– The units used in PSD are 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.
Random Vibration curve by MIL-STD-202
Random Vibration Analysis
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-8 July 2009
Inventory #002666
Common Uses
• Commonly used for
– Airborne electronics
– Acoustic loading of Airframe parts
– Jitter in alignment of optical
equipment
– Relative deformation in large
mirrors
Random Vibration Analysis
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-9 July 2009
Inventory #002666
Workbench Capabilities
• Input:
– Natural frequencies and mode shapes from a modal analysis
– Single or multiple PSD excitations applied to ground nodes
• Output:
– 1s results can be contoured like any other analysis.
– Response PSD at one DOF (one point in one direction)
Random Vibration
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-10 July 2009
Inventory #002666
Procedure:
Random Vibration
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-11 July 2009
Inventory #002666
Procedure
• Drop a Modal (ANSYS) system into the project schematic.
Random Vibration
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-12 July 2009
Inventory #002666
Procedure
• Drop a Random Vibration system onto the Solution cell of the Modal
system.
Random Vibration
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-13 July 2009
Inventory #002666
Procedure
• Create new geometry, or link to
existing geometry.
• Edit the Model cell to bring up the
Mechanical application.
Random Vibration
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-14 July 2009
Inventory #002666
Preprocessing
• Verify materials, connections, and mesh settings.
– This was covered in Workbench Mechanical Intro.
Random Vibration
Training Manual
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© 2009 ANSYS, Inc. All rights reserved.5-15 July 2009
Inventory #002666
Preprocessing
• Add supports to the model.
– Displacement constrains must have a magnitude of zero.
Random Vibration
Training Manual
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© 2009 ANSYS, Inc. All rights reserved.5-16 July 2009
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Solution Settings
• Choose the number of modes to
extract.
• If needed, upper and lower bounds
on frequency may be specified to
extract the modes within a specified
range.
Random Vibration
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-17 July 2009
Inventory #002666
Postprocessing
• Review the modal results before
proceeding.
Random Vibration
Training Manual
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© 2009 ANSYS, Inc. All rights reserved.5-18 July 2009
Inventory #002666
• Insert an Acceleration, Velocity, or Direction PSD base excitation.
• Set the Boundary Condition, Load (Tabular) Data, and Direction.
Preprocessing
Random Vibration
Training Manual
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© 2009 ANSYS, Inc. All rights reserved.5-19 July 2009
Inventory #002666
Postprocessing
• Insert Directional Deformation, Velocity, or Acceleration.
– the direction and sigma value may be chosen here
– note that results are always reviewed with scaling set to 0.0
Random Vibration
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-20 July 2009
Inventory #002666
Postprocessing
• Stress (normal, shear, equivalent) and Strain (normal, shear) results
can also be reviewed.
Random Vibration
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-21 July 2009
Inventory #002666
Postprocessing
• Response PSD can be plotted at one DOF (one point in one direction,
either absolute or relative to base excitation).
Random Vibration
Training Manual
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.5-22 July 2009
Inventory #002666
Workshop – Random Vibration
• In workshop 5A, you will determine the displacements and stresses
in a girder assembly due to an acceleration PSD.
WS5A: Random Vibration (PSD) Analysis of a Girder Assembly