# 83rd Shock and Vibration Symposium, Shock Tutorial Session

A number of my colleagues have told me that they will be unable to participate in the Symposium due to travel cost, schedule conflicts, etc.

So here are the slides for my presentation:   SAVE_conference_2012_Irvine

The presentation includes Matlab exercises.  The scripts are given in:  Matlab_exercises.zip

I express appreciation to the NASA Engineering & Safety Center for sponsoring this presentation.

– Tom Irvine

## 9 thoughts on “83rd Shock and Vibration Symposium, Shock Tutorial Session”

1. Hello Tom,

Thank-you very much for your presentation.

It’s a good document, which is too very simple to read (and to understand SRS theory).

Best regards,

COLIN Bruno

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2. Hi,
I was wondering whether the SRS wouldn’t be limited to the case of small/light structures shocked by only bigger/heavier structure. Indeed, the SDOF model supposes that the excitation is caused by an input acceleration (instead of a force).
cheers,
Lionel

• The SRS assumes that the test item has no mass-loading effect on the base input. So your statement is ideally correct.

In reality, we have cases where a component may be mounted on a relatively lightweight, compliant structure. An example, would be an avionics box mounted on a honeycomb-sandwich bulkhead. But the component is typically tested on fixture with a higher mechanical impedance than that of its field installation mounting surface.

This issue tends to come up more in vibration than in shock, but it still may be a concern for shock. So there are people writing papers on force limiting, spectrum notching, mechanical impedance, etc.

– Tom Irvine

3. Thanks a lot M. Irvine for this answer.
Moving on to another point of your presentation, the wavelet synthesis. It’s not perfectly clear for me why you have to minimize displacement, velocity and acceleration of the base input.
What is the reason for this?
Lionel.

• Shaker table systems have limitations for the following: displacement, velocity, acceleration, force. Shakers and their amplifiers also have overheating concerns.

In many cases, the base drive signal for the SRS specification is on the edge of the shaker’s capabilities. Fortunately, an SRS specification can be satisfied by a variety of base inputs.

So we want to use the least possible base acceleration that will still allow satisfaction of the SRS specification. This will hopefully allow margin with respect to the previously mentioned limitations.

Tom

4. Point taken, it’s clearer now.

Last question regarding your presentation. In the continuous plate illustration, you show two kind of transfer function : Response Accel / Base Accel and Relative Displacement / Base Accel.

The physical meaning of the first one is quite clear : It’s a transmissibility, i. e. we compare the acceleration between two different points of the structure.

The second one is more ambiguous. If I’m not mistaken, the relative displacement is proportional to the stress. So does it mean that this transfer function (FRF) is actually a sort of “impedance”?

Lionel

• Relative displacement is simply the displacement at a point on the structure minus the base displacement.

Bending stress in a beam or plate is proportional to the second spatial derivative of relative displacement.

Tom

5. You’re absolutely right.

But I’m perpetually confused about the field to consider…
The loading field (stress, force, pressure …) is a priori direcly related to damage, failure and fatigue. Nevertheless, SRS seems rather favor the cinematic field (acceleration).
The relation between the both fields varies according to the type of waves (longitudinal or bending waves, but also evanescent or propagative waves).

If the acceleration is high, then can we affirm that the stress is also high ?

Lionel

• Stress increases with acceleration but there can be a diminishing returns effect depending on a number of factors.

The frequency of the excitation and the natural frequency of the structure must also be considered. Damping is also a factor.

The California Department of Transportation (CALTRANS) requires that bridges withstand an “equivalent static load” of 2 G.

In contrast, an avionics component on a launch vehicle may be required to withstand hundreds or even thousands of Gs due to a pyrotechnic stage separation event.

The difference is that a bridge may be excited by wind or seismic energy where most of the energy is < 10 Hz. But pyrotechnic shock energy has a spectrum of energy up to 10 KHz and beyond.

Some have argued that velocity response is the metric which best correlates with stress. See:

https://vibrationdata.wordpress.com/2012/03/18/the-great-amplitude-format-debate/

I tend to favor calculating stress from strain, because it requires fewer assumptions than calculating stress from acceleration or velocity.

– Tom