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Re: Not quite true…

Posted by David Aiken (A) on October 8, 2005 at 15:33:18

In Reply to: Re: Not quite true… posted by Dave Kingsland on October 8, 2005 at 05:16:06:

We really are getting beyond my physics at this point, but I don't think the whole picture is as simple as you're painting it.

Accepting what you say about propagation speeds and the frequencies/wavelengths concerned, I still think the assertion that the "whole shelf moves as a unit" is a simplification. The whole shelf is definitely moving as a unit if, by that, we mean that the movement at any point in it is related to the movement at any other point. Given that the movement involves flexing, not all of the shelf is moving in the same direction at the same time, or even at the same speed. We don't have a rigid structure simply shifting back and forth uniformly at all points so whatever motion it imparts to a component resting upon it and coupled to it by 3 or 4 cones is also going to be a bit more complex. There's also the point that the shelf is effectively anchored at it's own points of support and its motion at those points is going to be different to it's motion elsewhere where it isn't anchored.

The shelf is moving as a unit and all aspects of the shelf's motion are definitely related to each other, but we don't have movement in unison at all points in the shelf.

Given that the mass of the component is acting vertically on the cone and we have a minimal area contact, the tendency is going to be for the cone to remain aligned vertically as the shelf flexes. There will be a tendency for a given cone to slide as the shelf flexes under it, but not all points of the shelf are going to be flexing in the same direction at the same time. And since we have at least 3 cones located at different points on the shelf, and the cones are constrained at both ends due to contact with the component as well as the shelf, and the shelf motion is one of flexing, there is going to be movement of the cones in relation to at least one of the 2 surfaces they are in contact with, and possibly both. If all 3 shelf contact points are flexing in the same direction, the tendency will definitely be for the cones and component to slide in that direction but it's unlikely that all three shelf contact points are flexing in the same direction simultaneously so the tendency will be for each cone to slide in a different direction but their freedom to do so is limited by their contact with the component. The end result of that is that the ability of the cones to move in conjunction with the shelf is constrained to some degree.

Which is what we would expect since we can't achieve perfect coupling. Without perfect coupling the shelf/cones/component simply aren't going to move in unison.

And we also have to consider that the shelf isn't the only thing moving. The component has its own vibratory state and the cones are coupling that state to the shelf just as they are coupling the shelf's state to the component. Once again it's unlikely that the vibratory state of the shelf and the component are going to match perfectly so at some times they will be working against each other and at other times in concert with each other. The cone's tendency to move in conjunction to the shelf will be modified by its other tendency to move in conjunction with the component, and vice versa.

Upshot of all that: we have imperfect coupling and the combination of factors affecting what is going on is messy. It simply isn't as simple as CD wants or as you suggest and I still believe there are definitely frequency dependent aspects to what happens. My wave/pier support analogy may not be correct, but that doesn't mean that my belief that there is frequency dependent behaviour is wrong - it would simply mean that if there is frequency dependent behaviour, the explanation is different. Even if there is nothing frequency dependent going on, things aren't going to be as simple as you suggest once you factor in shelf flexing, at least 3 cones, contact at both ends of the cone, and the different rates/directions of vibration in the component and the shelf.

There are simply more forces and factors involved than the coefficient of friction between cone tip and shelf, surface area of contact and any deformation aspects, and the vertical force arising from the mass of the component supported by the cone. We also have to consider, at the very least, those same factors at the cone/component interface, angular displacement in both shelf and component due to vibratory flexing, the change in the coefficients of friction with angular displacement, possible flexing in the cone itself, and the influence of at least 3 cones with movement constraints top and bottom. Your account of the forces operating at the cone tip is most definitely incomplete and overly simplified.

I've said it before and I'll say it again now: I'd really like to see a good account of what actually is happening in a real life situation with cones. I've seen some explanations that are patently wrong, and some that are right as far as they go but simply incomplete, which is where I'm placing your posts. And among the things that account should deal with are the observations of many including myself that different cone materials and shapes have an impact on the results that we hear. It's those differences, plus the difference that more than a few of us hear when we reverse the cone orientation, that have me convinced that something frequency dependent is going on. I could be wrong and those differences may well be the result of something else, but I'd really like to get an understanding of what is contributing to those differences. Nothing in this thread has helped me there.

David Aiken

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