Modeling Non-Viscous Damping with DE

[Quadruple Bypass]

im trying to model a mass hitting a block of honeycomb aluminum with a DE.

is the whole mx"+bx'+kx=F(t) eqn. void because b isn't viscous? Is there a way to get around that?

 

[Gokul43201]

Why is the damping not viscous? What exactly do you mean by that?

 

[Quadruple Bypass]

the honeycomb will be used as the damper. i was told by a professor that i couldn't use that equation

 

[Gokul43201]

I've seen elastic constants and damping ratios specified for honeycomb dampers. I don't see why this is different. Maybe someone else will have a better idea.

 

[Quadruple Bypass]

I've seen elastic constants and damping ratios specified for honeycomb dampers. I don't see why this is different. Maybe someone else will have a better idea.

where did you find it? I've looked everywhere online but haven't had any luck =/

 

[timmay]

There are two main approaches to damping - viscous damping and hysteretic damping.

You may find that as a simple approximation a viscous damping model may still be useful. But it's often argued that a hysteretic damping model will more accurately represent what really happens in solid structures, especially metals. Hysteretic damping basically assumes a damping force proportional to displacement but in phase with velocity. You should be able to find out more in vibrations or dynamics textbooks.

 

[minger]

Hysteretic damping basically assumes a damping force proportional to displacement but in phase with velocity

You may find more results looking for "viscoelastic" damping. I just had a project on the same stuff.

 

[Gokul43201]

where did you find it? I've looked everywhere online but haven't had any luck =/

I can't recall where, sorry. This was a small part of a term paper I wrote many years ago. But I think the honeycombs I was looking at were cardboard honeycombs, which behave more like traditional viscous dampers than perhaps aluminum honeycombs do.

So, to make sure I understand, hysteretic damping involves straining the metallic structure beyond the linear regime, but not so far that it goes deep into the plastic regime?

 

[FredGarvin]

You're not real specific with what end result you are looking for. If you are working towards stresses developed, like Minger mentioned, you may look at viscoelasticity although it tends to be more of a study in creep and such. It may not be what you need in the end. Anyways, the is the main viscoelastic model I studied was the Maxwell model:

http://en.wikipedia.org/wiki/Maxwell_material

Other models include:
Voight-Kelvin:
http://en.wikipedia.org/wiki/Kelvin-Voigt_material

 

[timmay]

Polymer systems are generally modeled by viscous damping, which adds a consideration of a velocity-dependent damping force. In the simplest case, a single degree of freedom system comprising a mass with a spring and dashpot in parallel (i.e. Kelvin-Voigt) the equation of motion for the system in free vibration is:

$$m\ddot{x} + c\dot{x} + kx = 0$$

where m is the system mass, c the viscous damping coefficient and k the spring stiffness.

It's been found that damping in metallic systems is better explained by hysteretic damping, which considers a displacement-dependent force in phase with system's velocity. Here:

$$m\ddot{x} + k(1+i\eta)x = 0$$

where $$\eta$$ is the hysteretic damping coefficient divided by the spring constant, or the ratio of hysteresis loss during a cycle.

An even better approach is to assume that damping is a mixture between the two models. This is known as a fractional damping model. All these relationships assume that damping is linear, and as a result is generally limited to small strains although there are corrections for non-linear behaviour too.

If your honeycomb were polymeric, then a viscous damping approach would be pretty good. But as it's aluminium, as mentioned you're probably better looking at the hysteretic model. A pretty simple method of doing that would be to take a solid phase sample of the honeycomb aluminium and test it in tension or compression through a series of cycles, and measure the hysteresis loss per cycle (i.e. the difference between loading and unloading curves).

With a little bit of consideration, you can plug it back into your equation of motion and see what happens.

 

[Quadruple Bypass]

Alright, thanks guys. I am going to take a look at it again tonight and hopefully I will understand it :P