dampin constant
dampin constant
(OP)
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
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RE: dampin constant
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
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Dr Michael F Platten
RE: dampin constant
RE: dampin constant
RE: dampin constant
RE: dampin constant
http://www.iro.umontreal.ca/~eckdoug/vibe/Relaxation/Va...
You will find there the meaning of the constant alpha, is this the one you are looking for?
RE: dampin constant
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.
RE: dampin constant
RE: dampin constant
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") rather than catastrophic.
M
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Dr Michael F Platten
RE: dampin constant
RE: dampin constant
Cheers
Greg Locock