Dynamics: Overdamped vibration have damping ratio greater then 1.0
Dynamics: Overdamped vibration have damping ratio greater then 1.0
(OP)
The system having damping ratio greater then 1.0 (Lets consider 2.0 i.e. 200%) takes greater time to die out against vibration then the system having damping 1.0. Why is it so ?
Ravi K






RE: Dynamics: Overdamped vibration have damping ratio greater then 1.0
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Dynamics: Overdamped vibration have damping ratio greater then 1.0
Ravi K
RE: Dynamics: Overdamped vibration have damping ratio greater then 1.0
In underdamping, it approaches zero position faster and oscillates.
In overdamping, it approaches zero position slowly. When it hits zero, it stays there.
Damping affects speed. Most things are underdamped.
RE: Dynamics: Overdamped vibration have damping ratio greater then 1.0
Here is generic graph:
Edit: Note that there is a labeling error, for underdamped should be "c < 1.0"
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RE: Dynamics: Overdamped vibration have damping ratio greater then 1.0
1) In an undamped system, energy is conserved and, at any point in time, the sum of kinetic and strain/potential energy is constant. You're just switching one out for the other as velocity and strain change over time.
2) What a viscous damper does is withdraw energy from the system to be dissipated as heat etc. Once all of the energy is dissipated by the damper, motion ceases. There's no energy left for motion or strain.
3) Instead of asking the question "why do overdamped systems come to rest slower than critically damped systems", ask the question "why is critical damping the fastest way to bring a system to rest". I believe that to be the case and I think that we can agree that answering the later question effectively answers the former.
4) To bring the system to rest as fast as possible, the damper needs to extract it's energy as fast as possible. There are two way to do this: a) increase the speed of the mass and b) increase the damping ratio. In a viscous damped system, both of these things will increase the rate at which the damper extracts energy from the system. There is, however, a balance between the two that is optimal with respect to bringing the system to rest quickly.
5) One extreme is to have a damping ratio approaching zero. Here you've maximized the velocity of the mass but, because the damper removes so little energy per unit of momentum, it takes forever for the system to come to rest.
6) The other extreme is to have an extremely high damping ratio (10 or 1000). Here, you've maximized the energy dissipated by the damper per unit momentum but, because the damper slows the velocity of the mass to a crawl, there's hardly any momentum to speak of and, again, it takes forever for the system to come to rest.
7) If one does the calculus required to figure out what balance of damping ratio and mass velocity yields the maximum rate of energy dissipation, I believe that the result will be the critical damping ratio combined with the associated displacement curve.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Dynamics: Overdamped vibration have damping ratio greater then 1.0
I think there is another error with the graph in that it shows the underdamped case coming to rest before the critically damped.
RE: Dynamics: Overdamped vibration have damping ratio greater then 1.0
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