TomEME,
This is a long reply – but the topic is complicated!
The bottom line is I don’t know a way of taking an SRS input curve and turning it into a PSD input curve. In many industries structures have to be qualified by analysis against both an SRS loading specification, and a PSD curve specification. The analyses are different and carried out completely separately, except from maybe re-using the normal modes in both.
You have neatly described the analysis method to get an SRS response to an SRS input. The input curve is g versus Hz. The process is just to find the natural frequencies of the structure and then look up the corresponding input g level. Knowing the damping level we can get the peak response at each of those frequencies. There is a little bit of black magic to figure out how peaks are combined across frequencies – does all of the structure respond with maximum amplitude at all of its natural frequencies, or do we use a less conservative method. But other than that it is a clear cause and effect.
The PSD input is based on a random simulation of the applied loading, rather than the deterministic SRS loading. The subsequent analysis calculates a random response.
The input is g^2/Hz versus Hz. Unlike the SRS curve you can’t really look at a point on a PSD curve and say what level of acceleration that represents at the particular frequency. The key is to look at the whole curve;
If you take the area under the curve it is g^2/Hz * Hz ==> g^2. The single number represents the square of the input acceleration.
If you take the square root you get back to a g value. This is the famous RMS g – Root Mean Square g. The RMS g is the input or output g level the structure will see during 68.3% of the loading spectrum. It is also equivalent to one standard deviation ‘one sigma’. Most designs are done to three sigma ; which means we multiply g by 3.0 and then the chances of seeing that level of loading or response are 99.73% Chance of exceedence is 0.275%.
The link you referenced is a neat way of getting approximate amplitude for an equivalent deterministic sine response to a PSD input. It is in two parts. The first part uses Miles equation to get an equivalent static g from a PSD response. The second part turns this static g into an oscillating g. The first part using Miles equation makes two big assumptions; the response is dominated by a single strong mode and the PSD input curve is a constant g^2/Hz. This is great for very simple structures that you can equivalence to a few DOF, or to do quick checks on order of magnitude in parts of the structure that may show clear dominant modes. It is not feasible for an overall approach. The structural response and the input PSD are too complicated.
An SRS analysis is very straightforward and most FE solvers have it as a spin off to a normal modes analysis. You don’t need to apply base motion or change the boundary conditions from a normal modes analysis.
A PSD analysis is usually in three phases; calculate the natural frequencies ( normal modes), calculate the frequency response to an input motion or force, apply the PSD input to the frequency response to get the PSD response and finally calculate RMS responses from the PSD response curves.
I checked the COSMOSWORKS website and it seemed that both types of analysis were available.
References for Random analysis I use are:
D.S. Steinberg – Vibration Analysis for Electronic Equipment, Wiley 2000
P. H Wirsching – Random vibrations, Theory and Practice Wiley 1995
Don’t be put off by the title in the first one. It applies to most structures.
I hope this helps,
Regards Tony
Tony Abbey
