Chapter 5: Random Vibration. ANSYS Mechanical. Dynamics. 5-1 July ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.

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1 Chapter 5: Random Vibration ANSYS Mechanical Dynamics 5-1 July 2009

2 Analysis Random Vibration Analysis Topics covered: Definition and purpose Overview of Workbench capabilities Procedure 5-2 July 2009

3 Analysis 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 5-3 July 2009

4 Analysis Definition and Purpose 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. Image from Random Vibrations Theory and Practice by Wirsching, Paez and Ortiz. 5-4 July 2009

5 Analysis 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. 5-5 July 2009

6 Analysis 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. Gaussian (normal) Distribution 3s 5-6 July 2009

7 Analysis 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 G 2 /Hz). The quantity represented by PSD may be displacement, velocity, acceleration, force, or pressure. Random Vibration curve by MIL-STD July 2009

8 Analysis Common Uses Commonly used for Airborne electronics Acoustic loading of Airframe parts Jitter in alignment of optical equipment Relative deformation in large mirrors 5-8 July 2009

9 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) 5-9 July 2009

10 Procedure: Random Vibration 5-10 July 2009

11 Procedure Drop a Modal (ANSYS) system into the project schematic July 2009

12 Procedure Drop a Random Vibration system onto the Solution cell of the Modal system July 2009

13 Procedure Create new geometry, or link to existing geometry. Edit the Model cell to bring up the Mechanical application July 2009

14 Preprocessing Verify materials, connections, and mesh settings. This was covered in Workbench Mechanical Intro July 2009

15 Preprocessing Add supports to the model. Displacement constrains must have a magnitude of zero July 2009

16 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 July 2009

17 Postprocessing Review the modal results before proceeding July 2009

18 Preprocessing Insert an Acceleration, Velocity, or Direction PSD base excitation. Set the Boundary Condition, Load (Tabular) Data, and Direction July 2009

19 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 July 2009

20 Postprocessing Stress (normal, shear, equivalent) and Strain (normal, shear) results can also be reviewed July 2009

21 Postprocessing Response PSD can be plotted at one DOF (one point in one direction, either absolute or relative to base excitation) July 2009

22 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 5-22 July 2009