Weight drops generates vibrations in the floor they hit. Impulse mdv must be conserved, even if the floor or mass is cushioned with mats. Cushioning leads to less high frequency content in the resulting impulse noise and impact. Does that also lead to a higher content of lower frequency energy in the resulting floor noise and vibrations?
Hi Anders
Contact time, as indicated in your title, matters. That said, I tend to balance energy rather than impulse. See below for some ramblings.
As a rule of thumb, for an effective contact time, dt, the force spectrum is flat up to the frequency 1/dt and contains 90% of its signal energy below 2/dt.
So, yes, you do concentrate energy into a lower frequency range using your mat.
At the same time, bag mass, M, has the velocity, V, and the kinetic energy, M*V2/2, directly before impact. The kinetic energy is handled by the flexible buffer with stiffness K and the potential energy KX2/2. This yields, X = sqrt(M/K)*V.
We see that for a given impulse velocity, V, the higher the mass and the softer the spring, the larger the buffer compression stroke, X. As force is F = K*X, we find also that F = sqrt(K*M)*V and hence, the stiffer the spring and the higher the mass & velocity, the higher the maximum impulse force.
The stroke, velocity and contact time (simplistically) relate as X = V*dt/2 as dt is the time require to reach the stroke X and as 2/dt describes 90% of the total force.
We tend to find that the larger the stroke and the longer the contact time, the lower the contact force and the lower the frequency range that is excited.
The above assumes a perfectly linear spring. Buffer stops tend to be nonlinear which is why Force-Displacement curves tend to be provided for such components.
Now, to further compound matters - we need to take a look at shock response. Long story short, shock theory tells us that we get the highest dynamic response when the contact time, dt = Tj/2, where Tj is the mode j period time. https://qringtech.com/2017/05/23/shock-response-for-equipment-response-to-impulsive-loads/
A soft mat tends to help, though you may be unfortunate and end up shaping the pulse for maximum dynamic response. Loading is quasi-static when the contact duration is much longer than half the dynamic system period time. It is mass controlled when the contact time is much shorter than the dynamic system period time (using impulses work then).
So, as per usual - it depends.... ;)
Hope this helps
Claes
Many thanks!
I read that as a yes. Thinking about it the vibrations are probably low frequency dominant and adding a mat only works on the structural noise part of the spectrum, say from about 100 Hz up. I guess most vibration velocity will be pretty much the same and that the impulse int(Fdt) actually is the same given the same drop energy and thus speed at impact, in spite of a much enlongated and damped impulse force shape. The type may transfer from short to comparative to the slab T/2 Which might lead to a stronger response at that frequency. Then the response elsewhere must go down, as impulse has to be conserved.
The impulses are both in the short and long category in a gym. Most are inbetween T/2 and T/5 in duration in relation to the first floor response. A few are longer. Many of the impulses are double and with two to four bounces due top the dimer nature of the sources and the coefficient of restitution of the mat or weight cushioning.
A (heavy) floating floor should share the impulse then with the main building structure. But may become more noisy than the floor slab if it is lighter. So the more mass the better both for vibrations, structural and airborne noise. But resonance response worsenes things in a frequency region, of course. +/- 1,4 f0.
Is there an easy way to estimate the effective masses of the building structural modes? Maybe the impulse response with a given more or less known force and measured vibration velocity can be one method?
I use both Hertzian and linear flat contact theory for the impact drops, either half sine or a skewed continuous function for the asessments of force (easy to fourier transform), along with the drop energy and known contact time and deflection. I use slow mo video and a motion capture software for extracting these data. «Tracker»
I know that adding a mass to a structure e.g in FEA model of a building floor and comparing mode frequencies before and after addition of that mass can give and estimate for the effective mass of that mode. In a project where the construction cunsultant had a FEA model of a 300 mm concrete floor and building around that with two 1800 kW dieselaggregates on that floor with resonance close to the o/min of the generators gave around 140 t or more, much more than the weight of the floor in the room they occupied. They weighed about 11 t together. And the mode shape covered several rooms on that floor. So the vibrating mass was pretty large. The resonance frequency was also pretty high then, around 24 Hz, close to the 1500 o/min of the W16 engines.
Usually we do not have FEA models.
Hi Anders
Impulse isolation and steady state vibration isolation are very different in that the latter can use multi-stage isolation systems, which do not work for the former.
If falling weights refer to things such as weight lifting, one can probably address the situation. For falling weights such as people running around on the floor, one would have to get a single stage isolation to work as intended. I believe that it can be done but it would probably look very different from conventional systems and its design would require the use of an open mind set.
There are ways to handle the machines you describe. I have designed several such setups for lightweight steel floors as found in offshore structures. Simple design rules can be used but usually come at the cost of space and performance.
In this day and age, we should use FE - it is the better way & there is software out there that can be used. Take a look at the Salome Meca package. https://code-aster.org/V2/spip.php?article303
/C
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