Hello everyone!
Random vibration analysis is intended for situations where non-deterministic loading occurs over a variable frequency range,
such as vibrations experienced in a truck driving over a road or loads on an aircraft wing in flight.
The reason we pursue statistical results instead of a time-history dynamics results is because, first, we cannot precisely characterize the loading, it's random,
and second, solving the time-history of a structure under random vibration is computationally expensive and may not always yield useful results in such situations.
For a random vibration analysis, the power spectral density curve, or PSD, is used as the input for the analysis to determine the structural response.
While input PSD curves are usually given based on engineering specifications or criteria that need to be satisfied,
ensuring good quality PSD input is crucial in obtaining reliable random vibration analysis results.
In this video, we will guide you to understand input PSD and check the fidelity of input PSD curves.
Ready? Let's get started!
Looking at a raw random excitation data, we can see that it is extracted from time-history data and contains many frequencies with the amplitude constantly changing.
One feature of a random excitation is that, at a given frequency, the amplitude of the excitation changes,
but for many processes, its average value tends to remain relatively constant.
This aspect can be utilized to generate a power spectrum density to characterize random excitation as a statistical process.
Instead of evaluating the random excitation in time history domain, PSD represents the excitation in frequency domain.
The PSD curve generated from a random excitation looks much less complex compared to the original data.
So how do we understand such a PSD curve?
Looking at the graph, the horizontal axis is frequency with unit Hertz.
The vertical axis is the averaged squared amplitude per Hz, which is (amplitude unit)^2/Hz.
The use of mean-square value is a suitable indicator of the strength of the signal, as the mean value would be closer to zero and have sign,
whereas the mean-square value is always positive and can be used for different frequencies.
Note that the excitation can be acceleration, velocity, or displacement;
therefore, the unit of the vertical axis can be different, depending on what the PSD represents.
Now let’s to move forward to learn how to use input PSD curves in an Ansys Mechanical simulation.
In random vibration analyses, we have the option to excite the base of the structure by acceleration, g acceleration, velocity or displacement.
We simply need to input the input PSD data as tabular data.
Once the data is input, the PSD curve is plotted in the Graph window.
The quality of the input PSD is automatically judged by the software.
Generally speaking, for a good PSD input, the PSD values between consecutive points should not change by more than an order of magnitude.
If the curve is marked as green, the PSD Values are considered reliable and accurate.
If it’s yellow, this is a warning indicator.
Results produced may not be very reliable and accurate.
If the curve is red, this means the results produced are not considered trustworthy.
It is recommended that you modify your input PSD loads prior to the solution process.
In Ansys Mechanical, we can improve the input PSD automatically.
Now let’s use a simple simulation example to show you how to check and improve the fidelity of input PSD curves.
Here, we are looking at a modal analysis of a simple beam-shaped structure.
One end of the beam is fixed.
And 40 modes are found for the structure.
We will perform a random vibration analysis for this beam structure.
PSD G acceleration data is given as the input PSD for this problem as shown here.
Note that the frequencies of the calculated modes should exceed the input PSD frequency range for random vibration analyses.
Here the maximum frequency found is 1540 Hz, and the maximum frequency for the input PSD is 1000 Hz, so we have sufficient modes generated.
Going back to the Workbench schematic, let’s drag a random vibration analysis from the Toolbox on top of the modal analysis,
making sure that the engineering data, geometry, model and solution modules of the modal analysis are shared with the random vibration analysis.
Double-click on the Setup cell to open the random vibration analysis, and we can see the analysis appears in the outline tree.
Right-mouse click on Random Vibration, then click on Insert - we can see the options to add PSD acceleration, PSD velocity, PSD G acceleration and PSD displacement.
For this problem, we are given PSD G acceleration information.
For the boundary condition, we select the Fixed Support applied in the modal analysis.
And the direction of the excitation is in the y direction.
Now, we move to the Tabular Data on the bottom right corner and input the given PSD G data.
We can copy the given data table and paste here.
The PSD curve is instantly plotted, and we notice that most part of the PSD curve shows a yellow color, indicating possible loss of reliability and accuracy.
This is mainly because the current PSD values between consecutive points change by two orders of magnitude.
Before revising the input PSD, let’s first solve the analysis as it is, so that, later we can compare the results.
Once the problem is solved, let’s insert a Directional Deformation in y direction.
On the contour plot, we can see that the 1 sigma results for the maximum deformation in y direction is 74.59 mm, located at the free end of the beam.
This means that 68.3% of the time, the maximum deformation in y direction will be at or below 74.59 mm.
Now, let’s go back to the input PSD to improve the curve.
To do this, we just need to go the details of the PSD G acceleration, click on the little triangle on the side of the Tabular Data, then click on Improve Fit.
Intermediate data points are automatically added to the tabular data and we can see that the entire PSD curve is shown in green now.
This indicates a high-quality input PSD.
Now, solve the random vibration analysis again.
We can see that the 1 sigma value for maximum y deformation is 77.355 mm.
Comparing with the value obtained with the problematic input PSD, which is 74.59 mm, there’s a 3.7% difference in results.
Note that while this simple example showed a slight reduction in accuracy,
the difference in results between a good PSD curve and a problematic one can be more, depending on the model and input PSD.
This completes the walkthrough example. Let's Summarize
input PSD curves are used to characterize random excitation in a statistical manner.
It interprets the random excitation by transforming it to average squared amplitude vs frequency plot.
In Ansys Mechanical, not any input PSD is considered acceptable for use in random vibration analyses.
We should be aware of the indicator of low-quality input PSD, as it will lead to inaccurate results.
One key reason of low-quality input PSD is when the PSD values between adjacent points changes by more than an order of magnitude.
Ansys Mechanical provides an automated feature to add intermediate points to improve the input PSD representation.
I hope you found this video informative.
Thank you for watching and do check out our other courses to discover more useful learning resources