1、Chapter 5: Random VibrationANSYS Mechanical DynamicsANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.5-1 July 2009Inventory #002666Random Vibration AnalysisRandom Vibration AnalysisTopics covered: Definition and purpose Overview of Workbench capabilities ProcedureTraining ManualANSYS, In

2、c. Proprietary 2009 ANSYS, Inc. All rights reserved.5-9July 2009Inventory #002666Random Vibration AnalysisA. Definition and PurposeWhat is random vibration analysis?Training Manual A spectrum analysis technique based on probability and statistics. Meant for loads such as acceleration loads in a rock

3、et launch that produce different time histories during every launch . Reference: Random vibrations in mechanical systems by Crandall & MarkRandom Vibration Analysis Definition and PurposeTraining Manual Transient analysis is not an option since the time history is not deterministic (sample is not re

4、peatable). 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.Reference: Random vibrations in mechanical sys

5、tems by Crandall & MarkRandom Vibration AnalysisPower Spectral DensityTraining ManualImage from “Random Vibrations Theory and Practice” by Wirsching, Paez and Ortiz. Sample time histories are converted to Power Spectral Density function (PSD), a statistical representation of the load time history.Ra

6、ndom Vibration AnalysisStatistical RepresentationTraining Manual 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

7、combined effect from each mode and their interactions.3s Gaussian (normal) DistributionRandom Vibration AnalysisPower 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 o

8、f 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.Training ManualRandom Vibration curve by MIL-STD-202Random Vibration AnalysisCommon

9、 Uses Commonly used for Airborne electronics Acoustic loading of Airframe parts Jitter in alignment of optical equipment Relative deformation in large mirrorsTraining ManualRandom VibrationWorkbench Capabilities Input: Natural frequencies and mode shapes from a modal analysis Single or multiple PSD

10、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)Training ManualProcedure: Random VibrationANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.5-10 July 2009Inventory #002666Random VibrationP

11、rocedure Drop a Modal (ANSYS) system into the project schematic.Training ManualANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.5-22July 2009Inventory #002666Random VibrationProcedureTraining Manual Drop a Random Vibration system onto the Solution cell of the Modal system.Random Vibratio

12、nProcedure Create new geometry, or link to existing geometry.Training Manual Edit the Model cell to bring up the Mechanical application.Random VibrationPreprocessing Verify materials, connections, and mesh settings. This was covered in Workbench Mechanical Intro.Training ManualRandom VibrationPrepro

13、cessing Add supports to the model. Displacement constrains must have a magnitude of zero.Training ManualRandom VibrationSolution Settings Choose the number of modes to extract.Training Manual If needed, upper and lower bounds on frequency may be specified to extract the modes within a specified rang

14、e.Random VibrationPostprocessing Review the modal results before proceeding.Training ManualRandom VibrationPreprocessingTraining Manual Insert an Acceleration, Velocity, or Direction PSD base excitation. Set the Boundary Condition, Load (Tabular) Data, and Direction.Random VibrationPostprocessing In

15、sert Directional Deformation, Velocity, or Acceleration. the direction and sigma value may be chosen here note that results are always reviewed with scaling set to 0.0Training ManualRandom VibrationPostprocessingTraining Manual Stress (normal, shear, equivalent) and Strain (normal, shear) results can also be reviewed.Random VibrationPostprocessingTraining Manual Response PSD can be plotted at one DOF (one point in one direction, either absolute o