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# Impact Energy or Power? Related to impact noise emission, analytically

## Impact Energy or Power? Related to impact noise emission, analytically

(OP)
Hello Gents,
Been a while since I posted here or commented. Good to see this useful set of minds is still very active.

I have a general questions I'd like to discuss and get some thoughts on.

Say I have a mass or inertia and it is being propelled by external forces. Then, it contacts/impacts a stationary mass/system (with it's own stiffness) at a known velocity - resulting in a dynamic impact event. However, there is a remaining force acting on the force before and still there during the impact. Eg. a force holding the mass up against the stationary system (after the impact event also). However, because this force is present during the impact the total energy (or power?) is not the same as if it were not there.
So, I've been posturing the simplest way to derive an analytical relation that can illustrate the contribution to the impact event that varying this force has (while keeping the impact velocity the same).
My end result is a relation that can help understand directionally how to reduce the resulting vibration the impact has on the structure it contacts - which I'm assuming will reduce the resulting noise emitted from it.
I've also made these general hypotheses:
a) keeping the energy the same - varying the time between 2 impact events changes the power input and the mode shapes the impact will excite (fast high power event will excite more and higher frequencies) (Is there any way to easily show this analytically?)
b) damping present upon impact is only internal friction of strained elements - and any energy dissipated due to damping follows coulomb (or any modern variation of it)

Thanks for the help and thoughts!

### RE: Impact Energy or Power? Related to impact noise emission, analytically

I think you are on the wrong track. In the linear case the continuing force is just a DC offset to the vibration, the non-DC component of the vibration will be unchanged.In your hypothesis (a) I don't understand what the 2 impacts are. In (b) I don't even see a hypothesis!

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Impact Energy or Power? Related to impact noise emission, analytically

(OP)
Thanks Greg. I understand the DC offset portion. What I am after is how the non-DC component (or vibration) changes with different impact duration and power.
I know that traditional impluse theory predicts that the impluse response is simple the same as free response for discrete systems - but I have never seen any derivation addressing different impluse/impact durations or power. Or one focused on distributed systems.

Oh and by "2 impacts" I just simply mean comparing 2 different events.

### RE: Impact Energy or Power? Related to impact noise emission, analytically

Oh, right. This where the practical experience of running a modal lab makes the answer so obvious that I misread your question.

When you are doing a hammer test you have to decide what mass of hammer to use, and how hard the tip is. A 2-4lb hammer would be used on a car body, the smallest hammers used for testing plastic parts are like toothpicks. For bridges and the like very large masses are used, or you can use a relaxation excitation, for instance by snapping a pre-tensioned cable. This is nice because the parasitic mass is small. The 'proper' modal hammers come with a variety of tips and some extra weights to screw on. The tip hardness is altered to change the input power spectrum, softer (typically a rubber tip)gives more low frequency energy, harder (nylon or steel) gives a flatter response. The total energy remains the same.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Impact Energy or Power? Related to impact noise emission, analytically

(OP)
Thanks gents.
Now if you had a force acting on the "hammer" during the impact (in the direction of impact), how would this effect the vibration response of the structure? Is there an analytical solution to this?

### RE: Impact Energy or Power? Related to impact noise emission, analytically

In a linear system you'd just get a static deflection superimposed on top of the baseline case. In a non linear system it would depend on the exact non linearity.

It could be calculated fairly esaily. For example if you consider a 2 mass system like this

https://www.researchgate.net/figure/2-DOF-SPRING-M...

m2 is the hammer k2 is the hammer tip and m1/k1 are the system being investigated.

It is obvious in this case that applying a constant leftward force to m2 has no effect on the dynamic response of m1/k1, it just adds a compression to each spring.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Impact Energy or Power? Related to impact noise emission, analytically

(OP)
I can see how that easily works out mathematically.
So, the extra work done by the external force (energy) does not contribute to the vibratory response in any way in a linear system.
If it is nonlinear and has a "hardening" spring - I suspect the energy added cannot be ignored and would add some response in the system. I need to work this out mathematically.

### RE: Impact Energy or Power? Related to impact noise emission, analytically

(OP)
Ok yes, I have proven this with a distributed Beam model subjected to different impact profiles.
So if your noise is emitted from for example 1-5kHz you need to prolong the impact event enough (by lowering the stiffness enough) to not excite these modes and frequencies on the structure.
Now I need to prove that added damping to the impact stiffness does similar also.

### RE: Impact Energy or Power? Related to impact noise emission, analytically

Impact tip hardness controls/limits the F-max of the impact force. The PCB Impulse hammers provide frequency responses for various impact tips.

Walt

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