Dynamics: Overdamped vibration have damping ratio greater then 1.0 5

[RK Sriwastav]

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

 

[KootK]

Imagine letting a screen door with a spring and hydraulic piston thingy close under it's own volition. Takes all day if the piston's pushing back too hard. Overdamped.

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.

 

[RK Sriwastav]

I got a dizzy idea but i am still not clear about the cause. Can it be please elaborated ? @kootK

Ravi K

 

[RPMG]

In critical damping, it goes to the zero position and stays there.

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.

 

[SlideRuleEra]

KootK - Great example!

Here is generic graph:
Edit: Note that there is a labeling error, for underdamped should be "c < 1.0"

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[KootK]

Thanks SRE. Seems like my analogy got the job done for most everybody but the OP. I'll try it with words and implied mathematics instead. I'll stick to a viscous damping model until OP says otherwise.

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.

 

[Retrograde]

Edit: Note that there is a labeling error, for underdamped should be "c < 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.

 

[SlideRuleEra]

Retrograde - you are right. Here is a better illustration that also gives an idea of what increasing values of the damping coefficient does to system performance:

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net