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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
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Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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Page 1: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

ANSYS, Inc. Proprietary

© 2009 ANSYS, Inc. All rights reserved.5-1 July 2009

Inventory #002666

ANSYS Mechanical

Dynamics

Chapter 5:

Random Vibration

Page 2: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

Training Manual

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© 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

Page 3: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

Training Manual

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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

Page 4: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

Training Manual

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• 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

Page 5: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

Training Manual

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© 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

Page 6: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

Training Manual

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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

Page 7: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

Training Manual

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© 2009 ANSYS, Inc. All rights reserved.5-7 July 2009

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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

Page 8: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

Training Manual

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© 2009 ANSYS, Inc. All rights reserved.5-8 July 2009

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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

Page 9: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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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

Page 10: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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Procedure:

Random Vibration

Page 11: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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Procedure

• Drop a Modal (ANSYS) system into the project schematic.

Random Vibration

Page 12: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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Procedure

• Drop a Random Vibration system onto the Solution cell of the Modal

system.

Random Vibration

Page 13: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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Procedure

• Create new geometry, or link to

existing geometry.

• Edit the Model cell to bring up the

Mechanical application.

Random Vibration

Page 14: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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Preprocessing

• Verify materials, connections, and mesh settings.

– This was covered in Workbench Mechanical Intro.

Random Vibration

Page 15: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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Preprocessing

• Add supports to the model.

– Displacement constrains must have a magnitude of zero.

Random Vibration

Page 16: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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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

Page 17: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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Postprocessing

• Review the modal results before

proceeding.

Random Vibration

Page 18: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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• Insert an Acceleration, Velocity, or Direction PSD base excitation.

• Set the Boundary Condition, Load (Tabular) Data, and Direction.

Preprocessing

Random Vibration

Page 19: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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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

Page 20: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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Postprocessing

• Stress (normal, shear, equivalent) and Strain (normal, shear) results

can also be reviewed.

Random Vibration

Page 21: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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Postprocessing

• Response PSD can be plotted at one DOF (one point in one direction,

either absolute or relative to base excitation).

Random Vibration

Page 22: Chapter 5: Random Vibration ANSYS Mechanical …Chapter 5: Random Vibration. Training Manual ANSYS, Inc. Proprietary ... Image from “Random Vibrations Theory and Practice” by Wirsching,

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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