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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

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    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

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    2009 ANSYS, Inc. All rights reserved.5-4 July 2009

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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

  • 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

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    2009 ANSYS, Inc. All rights reserved.5-6 July 2009

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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

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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

  • 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

  • Training Manual

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    2009 ANSYS, Inc. All rights reserved.5-9 July 2009

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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

  • ANSYS, Inc. Proprietary

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    Procedure:

    Random Vibration

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    Procedure

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

    Random Vibration

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    Procedure

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

    system.

    Random Vibration

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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

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    Preprocessing

    Verify materials, connections, and mesh settings.

    This was covered in Workbench Mechanical Intro.

    Random Vibration

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    Preprocessing

    Add supports to the model.

    Displacement constrains must have a magnitude of zero.

    Random Vibration

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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

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    2009 ANSYS, Inc. All rights reserved.5-17 July 2009

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    Postprocessing

    Review the modal results before

    proceeding.

    Random Vibration

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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

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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

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    Postprocessing

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

    can also be reviewed.

    Random Vibration

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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

  • Training Manual

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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

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