# Random Vibration and PSD spectrum profiles

• Automotive
• Saumya Kar

#### Saumya Kar

I am starting work on structural durability area for after treatment systems and deal with Random Vibration and PSD profiles quite often. However there are few fundamental questions about PSD profiles that I could not get answer to after a lot of search on internet. So finally decided to write to you. Here are my questions:

1. Why random vibration is represented in Power Spectrum (g^2/Hz) and not amplitude Spectrum (g) ? Both of them represent data in frequency domain and if we assume the random vibration data to be repeatable (which is the case almost always), isn't amplitude spectrum good enough ?

2. What are the steps for calculating PSD from time data ? (Like we do Fourier transform on time data to get amplitude specptrum).

3. When we use PSD profiles as input excitation for shaker test, how is spectrum is converted to time data ? When we test the component for X hours with input PSD profile, is the PSD profile repeated certain number of time in that given duration ? If yes how is that done ? (I am trying to correlate to a sine sweep test where we know the time required to cover frequency range and the cycle is repeated a number of times over total duration).

I am starting work on structural durability area for after treatment systems and deal with Random Vibration and PSD profiles quite often. However there are few fundamental questions about PSD profiles that I could not get answer to after a lot of search on internet. So finally decided to write to you. Here are my questions:

1. Why random vibration is represented in Power Spectrum (g^2/Hz) and not amplitude Spectrum (g) ? Both of them represent data in frequency domain and if we assume the random vibration data to be repeatable (which is the case almost always), isn't amplitude spectrum good enough ?

2. What are the steps for calculating PSD from time data ? (Like we do Fourier transform on time data to get amplitude specptrum).

3. When we use PSD profiles as input excitation for shaker test, how is spectrum is converted to time data ? When we test the component for X hours with input PSD profile, is the PSD profile repeated certain number of time in that given duration ? If yes how is that done ? (I am trying to correlate to a sine sweep test where we know the time required to cover frequency range and the cycle is repeated a number of times over total duration).

Just wanted to make the post active again. If anyone can help with questions, it will be great help :)

Best Regards
Saumya

The random test and sine sweep test are most commonly used to find the natural frequency of a component. They work differently than each other.
The sine sweep test only excites one frequency at a time. Thats useful for finding individual resonances of a component or system.

However, some resonances interfere with each other. Depending on their superposition, this interference might be constructive or destructive. A sine sweep will only excite resonances that share the same frequency. So if your component has a mode at 120hz, but also a mode at 190hz, the shaker will only be able to excite one of them at a time with a sine sweep test.

With a random test, the entire spectrum is excited. So those resonances are going to happen at the same time as each other. You will be able to measure how the modes interfere with each other. There are webinars that you can watch if you do some digging on the internet. I'll see if I can find anything useful.

G2Hz is giving you acceleration spectral density, rather than power spectral density. The PSD that you are used to seeing would be used to represent the input values. The ASD is the output.

Last edited:
• Saumya Kar
The random test and sine sweep test are most commonly used to find the natural frequency of a component. They work differently than each other.
The sine sweep test only excites one frequency at a time. Thats useful for finding individual resonances of a component or system.

However, some resonances interfere with each other. Depending on their superposition, this interference might be constructive or destructive. A sine sweep will only excite resonances that share the same frequency. So if your component has a mode at 120hz, but also a mode at 190hz, the shaker will only be able to excite one of them at a time with a sine sweep test.

With a random test, the entire spectrum is excited. So those resonances are going to happen at the same time as each other. You will be able to measure how the modes interfere with each other. There are webinars that you can watch if you do some digging on the internet. I'll see if I can find anything useful.

G2Hz is giving you acceleration spectral density, rather than power spectral density. The PSD that you are used to seeing would be used to represent the input values. The ASD is the output.
Thank you. This explanation helps.

There is a great article by Tom Irvine on why the units are unusual. I have myself wondered this for some time, working in this field. The units are generally motivated by the practical considerations of signal processing, viz., getting a meaningful measure of amplitude that is free from the effects of a chosen sampling bandwidth.