*Here is letter that I recently send to some of my colleagues…*

We have been discussing establishing a database of shock data both for characterizing source shock levels and attenuation through material distance and joints. We have also discussed sharing attenuation curves if the actual data is proprietary.

Measured data from flight or ground tests is as precious as gold, and I fully support sharing data.

We have also discussed complex software modeling tools.

But sometimes, simple models can give us important insights which can then be used to guide our data compilation and interpretation.

I am enclosing some simple papers and Matlab scripts which I wrote some years ago on modeling shock propagation through uniform material. The bottom line is that propagated shock levels are highly dependent on structural damping. It has been said by Isam Yunis and Paul Blelloch in another context that damping is the largest uncertainty factor in structural dynamics. I would claim that the material fatigue exponent is even less certain, but I otherwise agree with their sentiment.

So building a structual damping database should be a parallel effort, or at least the attenuation curves from measured data should have a damping reference.

Yes, I know that structures are continuous systems with potentially many modes in the frequency domain of interest and that damping varies by mode, can be nonlinear, etc. So the task is challenging.

As an aside…. propagating shock waveforms may be longitudinal, bending, or complex cylindrical modes.

Longitundinal waves are governed by a second-order differential equation and are nondispersive. i.e. the wavespeed is the same for all frequencies.

Bending waves are governed by a fourth-order equation and are dispersive. The wavespeed varies with frequency.

Cylinders have ring modes, as well as a high-density of structural modes near the ring frequency. Note that wave propagation in a cylinder is governed by the Donnell-Mushtari-Vlasov eighth-order partial differential equation (or by an equivalent pair of coupled lower-order equations.) This equation covers both bending and membrane effects. Some cylinder modes are “acoustically fast” and others “acoustically slow.”

So I need to model propagation in cylindrical shells, as I have done for the simple beam and rod examples in the enclosed papers.

Pyrotechnic Shock Distance Attenuation via Wave Propagation Analysis

Pyrotechnic Shock Joint Attenuation via Wave Propagation Analysis

Pyrotechnic Shock Distance & Joint Attenuation Slides

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More Slides

ESA Pyrotechnic Shock Distance & Joint Attenuation via Wave Propagation Analysis

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Finite Element Approaches:

Attenuation of Bending Shock Waves in a Beam

Beam Bending Matlab Script

Attenuation of Longitudinal Shock Waves in a Rod

Rod Longitudinal Matlab Script

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See also: shock propagation

– Tom Irvine