# Homework Help: Relating pavement roughness in frequency to displacement

1. Aug 9, 2015

### KToal

Hi all,

I'm attempting to optimise a suspension system's spring and damping rate via vibrational analysis.
Working in the frequency domain, I have calculated the input-output relationship as a ratio (i.e. ground to body, x/q2 in the attachment) and the mean square acceleration response based on an input modelled using an exponential power spectral density.

From here I want to calculate the corresponding stroke of the suspension components and the separation between the road and the suspension system as a measure of road adhesion. My intention is to optimise the k and c values based on these three measures.

So what I'm asking is how do I relate the frequencies I've used in my MSAR calculation to the change in vertical height of the road or vice versa? Or am I going about this in the wrong way?

Attached is the half car model I'm using and the key equations along with my rough spreadsheet used for calculations.

#### Attached Files:

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• ###### RMSAR.xlsx
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2. Aug 10, 2015

### Nidum

3. Aug 10, 2015

### KToal

Thanks for the reply. Perhaps I need to be a bit more specific.

What I'm after is a way of finding q2 or x for a given frequency. So would it be valid to divide the Mean Square Acceleration Response by -omega^2 to get the displacement? I.e. x(f).

I have delved into a considerable amount of the literature but I can't find an adequate answer.