How does a floor mat dissipate noise/vibration?

[nomisme]

First of all, can the floor mat be assumed to be a spring?
The spring takes in loading gradually instead of taking an impact force.
But how does elongating the time duration of a force reduce the noise?

Does it have something to do with the frequency of the vibration?
In the case of impact force, I assume it is high frequency.
In the case of spring force, I assume it is low frequency.
But they eventually have the same amplitude of force.
What the former case has a higher noise?

 

[sophiecentaur]

First of all, can the floor mat be assumed to be a spring?

Most floor mats are not designed to give totally elastic collisions; they dissipate a lot of the energy of a collision and also any other sounds / vibrations.
A steel spring is pretty lossless so it returns most of the energy used to deform it. You can make a spring with the same stiffness as a floor mat but the shape would be hard to model. Two perfectly rigid plates with a number of springs sandwiched between them, perhaps. But you would need some friction material (damping) in there too, to absorb some of the energy as the plates move. There is also the mass to be considered. Perhaps if you wrote more about the purpose of this question. Are you trying to characterise a soundproofing system or to model it for real?
The questions you have asked show that you are thinking in the right direction. A sound reduction system can be looked upon as a damped oscillator, it will have a natural frequency of oscillation and a loss mechanism in it that will give a very wide frequency response. The secret is to match the absorber to the source of the vibration (could be the air or the floors of a building) and to dissipate as much of the energy as possible. It's quite a complicated business and people can make a fortune selling not very good systems, based on having a 'feel for it'. Getting the best results is not easy and it's actually quite hard to measure the effect, in a practical situation.
There is a vast amount published about suppressing sound and vibrations - this link is a good example. Perhaps a Google search on 'damped vibrations' could yield something that suits you.

 

[nomisme]

Most floor mats are not designed to give totally elastic collisions; they dissipate a lot of the energy of a collision and also any other sounds / vibrations.
A steel spring is pretty lossless so it returns most of the energy used to deform it. You can make a spring with the same stiffness as a floor mat but the shape would be hard to model. Two perfectly rigid plates with a number of springs sandwiched between them, perhaps. But you would need some friction material (damping) in there too, to absorb some of the energy as the plates move. There is also the mass to be considered. Perhaps if you wrote more about the purpose of this question. Are you trying to characterise a soundproofing system or to model it for real?
The questions you have asked show that you are thinking in the right direction. A sound reduction system can be looked upon as a damped oscillator, it will have a natural frequency of oscillation and a loss mechanism in it that will give a very wide frequency response. The secret is to match the absorber to the source of the vibration (could be the air or the floors of a building) and to dissipate as much of the energy as possible. It's quite a complicated business and people can make a fortune selling not very good systems, based on having a 'feel for it'. Getting the best results is not easy and it's actually quite hard to measure the effect, in a practical situation.
There is a vast amount published about suppressing sound and vibrations - this link is a good example. Perhaps a Google search on 'damped vibrations' could yield something that suits you.

The thing I don't understand is:
if you hit a soft pad with your fist, the other side of the soft pad which is a weigh balance will have the same force measurement as you hit directly on the weigh balance.
But hitting soft pad will result in a lower sound. So the dissipation of energy cannot be reflected in terms of force?

 

[jbriggs444]

But hitting soft pad will result in a lower sound. So the dissipation of energy cannot be reflected in terms of force?

Not in terms of force alone. Force and displacement graphed over time would be quite relevant.

 

[nomisme]

Not in terms of force alone. Force and displacement graphed over time would be quite relevant.

I see. Please confirm me.
Can I say the above two cases have the same work done energy but due to the time duration differences, one has a lower intensity soundwave travel?

Does the soft pad case has slower propagating soundwaves with lower amplitude which adds up to become the same force as the case without the pad?

But one author suggested the soft pad dissipates energy, which gives the soft pad case a lower force reading?

 

[jbriggs444]

Can I say the above two cases have the same work done energy but due to the time duration differences, one has a lower intensity soundwave travel?

If you are talking about energy dissipation then displacement is relevant.
If you are talking about momentum dissipation then time is relevant.
Which do you want to discuss?

 

[sophiecentaur]

So the dissipation of energy cannot be reflected in terms of force

Force and Energy are, as you imply, not the same. Mechanical Work (Energy) done on an object is equal to a Force times the distance moved along the line of the force. To dissipate a certain amount of energy you can use a small force over a large distance or a large force over a short distance. However, your model situation of punching a pad is not as simple to describe as that. It is much more complicated, in fact. If you punch a wall, your fist stops moving very quickly and it moves a very short distance. So you can't do much actual work on a thin pad in between. If you use a thick, soft pad, your fist will travel further and you can actually deliver more energy because the muscles are operating over a longer distance. So the two situations are not directly comparable. A comparable example would be using a pendulum with a heavy ball on it and letting it fall against a pad on the wall from a constant height. In both cases, the same amount of energy would be dissipated but the force on the wall would be much less with the soft pad because it is resisting the falling ball for a greater distance. The sound of the impact will contain higher frequencies for a shorter impact but, unless the system is actually designed to make a noise (hollow soundboard rather than a solid wall), not much of the energy absorbed will turn up as sound, it will heat up the pad (minuscule) and possibly distort it permanently (perhaps the majority of the ball's energy).

 

[russ_watters]

I think a floor mat should be pretty easy to analyze: since your foot doesn't bounce back off the mat, it is essentially completely inelastic, absorbing essentially all of the energy and momentum imparted on it.

 

[sophiecentaur]

I think a floor mat should be pretty easy to analyze: since your foot doesn't bounce back off the mat, it is essentially completely inelastic, absorbing essentially all of the energy and momentum imparted on it.

A sideways collision is easier to analyse because there is no normal force at the end of the collision. I am not sure what the OP actually wants out of this, though. Is it just to do with the 'sound' waveform that is produced?

 

[nomisme]

Force and Energy are, as you imply, not the same. Mechanical Work (Energy) done on an object is equal to a Force times the distance moved along the line of the force. To dissipate a certain amount of energy you can use a small force over a large distance or a large force over a short distance. However, your model situation of punching a pad is not as simple to describe as that. It is much more complicated, in fact. If you punch a wall, your fist stops moving very quickly and it moves a very short distance. So you can't do much actual work on a thin pad in between. If you use a thick, soft pad, your fist will travel further and you can actually deliver more energy because the muscles are operating over a longer distance. So the two situations are not directly comparable. A comparable example would be using a pendulum with a heavy ball on it and letting it fall against a pad on the wall from a constant height. In both cases, the same amount of energy would be dissipated but the force on the wall would be much less with the soft pad because it is resisting the falling ball for a greater distance. The sound of the impact will contain higher frequencies for a shorter impact but, unless the system is actually designed to make a noise (hollow soundboard rather than a solid wall), not much of the energy absorbed will turn up as sound, it will heat up the pad (minuscule) and possibly distort it permanently (perhaps the majority of the ball's energy).

um... does it mean that if I jump on a weigh balance indirectly with a mat, I will have a smaller reading on the balance than jumping directly on top of it?

Maybe i should put it this way... if a pendulum hit a compression spring attached to the balance, since it absorb all the energy, the balance will have a zero reading? But it my mind, with or without the spring, they will have the same normal force on the balance, right?

if there is a constant force on the compression spring and a case where the force is directly landed on the balance, they have the same reading? then it comes to the part that the energy absorption of the spring is missing.

 

[sophiecentaur]

um... does it mean that if I jump on a weigh balance indirectly with a mat, I will have a smaller reading on the balance than jumping directly on top of it?

Maybe i should put it this way... if a pendulum hit a compression spring attached to the balance, since it absorb all the energy, the balance will have a zero reading? But it my mind, with or without the spring, they will have the same normal force on the balance, right?

if there is a constant force on the compression spring and a case where the force is directly landed on the balance, they have the same reading? then it comes to the part that the energy absorption of the spring is missing.

Whatever you stick on the wall, the final balance reading will be Zero (if, of course, the string ends up vertical). If you stop something on a floor mat, the final reading will be the weight of the ball. I am discussing what happens whilst things are changing. A vast lump of marshmallow will start retarding the ball at, say 20cm from the wall. The 'average' Force will be KE/Thickness (Energy / retardation distance). Compare this with a thin layer of chewing gum (thick enough so that there is no bounce). The distance will be, say 5mm so the average force will be 40X the force from the marshmallow.
That is totally in line with everyone's experience, surely and it's why we use crash mats.

"same normal force on the balance, right?" Wrong, of course and it's not what you have felt with your own body. The distance and time that the force acts will govern the peak value of that force (all other things being equal).

 

[A.T.]

f I jump on a weigh balance indirectly with a mat, I will have a smaller reading on the balance than jumping directly on top of it?

You can reduce the peak force that way, by distributing the momentum transfer over longer time.