dampin constant

[hellen8]

With a selfexcited system (nonlinear equation of Duffing/van der Pol type) what does the constant which multiplies the damping term mean in physical, real terms? Thanks

 

[MikeyP]

It depends on the form of the Duffing equation you are looking at. If the damping term is of the form

constant*dx/dt

then this is simple linear damping. In that case the physical interpretation is the same as a linear oscillator, i.e. a measure of the rate at which energy is lost from the system. In lumped mechanical system this would be a viscous loss; in an electrical system it would be thermal dissipation by a resistor.

M

--
Dr Michael F Platten

 

[hellen8]

Thank you. I'm afraid I misled. What I am looking for is a physical meaning for the constant multiplying the nonlinear damping term in the van der Pol equation. I am using a comined van der Pol and Duffing and did not make myself clear. I do understand the meaning of the damping constant with linear damping.

 

[hellen8]

I guess I am rather disappointed by the lack of response to this question which plagues me considerably. Is it lack of interest or that no one knows? I'd be happy with any guesses or a simple statement that no one knows much less the "final"answer.

 

[heitor]

Can you write down the equation?

 

[heitor]

Maybe it's the equation in the following site:

http://www.iro.umontreal.ca/~eckdoug/vibe/Relaxation/VanDerPol.html

You will find there the meaning of the constant alpha, is this the one you are looking for?

 

[hellen8]

The equation:

y"+a(y^2-1)y'+by=0
Where y is displacement, y" is acceleration, y' is velocity and a and b are constants. b,of course, is the stiffness constant and a is what I want to know what it is. Any help, even wild guesses appreciated.

 

[hellen8]

Thank you, Heitor. I have seen that site and the definition of alpha as flow of voltage(or something like that; I don't have the site in front of me). I still would like to know, however, what that means in a mechanical system.I may be able to understand mediation of voltage flow but simply cannot get that into mechanical terms (thick in the head as we say; tick as the Irish would say!). Please stay with me on this.

 

[MikeyP]

The van der Pol equation is just that - an equation. The terms in the equation have no "physical meaning" unless you assign meaning to them yourself by telling us what it is you are using the van der Pol equation to model.

The classical use of the van der Pol equation is to model the behaviour of thermionic valve oscillator. In that instance, the term a(y^2-1) represents a non-linear resistance. the resistance being small and negative for low values of y and large and positive for high values of y. The constant "a" represents how non-linear the circuit is.

How do I know this? I typed "van der pol equation" as a search term into Google and clicked on the 2nd hit.

Your last post seems to suggest you are modelling a mechanincal system (as you mention displacement, velocity and acceleration). Mechanical systems with negative damping at low displacements but positive damping at high displacements are not common. An example off the top of my head would be aerodynamic flutter, where in some instances the instability is self-limiting (a "limit cycle oscillation&quot rather than catastrophic.

M

--
Dr Michael F Platten

 

[hellen8]

Thank you very much, Dr. Platten, that puts me where I need to be. Thank you all.

 

[GregLocock]

Another mechanical example is brake squeal on disc brakes.

Cheers

Greg Locock